├── .gitignore ├── Algebra.md ├── Analysis.md ├── CS.md ├── Calculus.md ├── GeomTopo.md ├── IndiaRussia.md ├── LICENSE ├── LinearAlgebra.md ├── LogicDiscrete.md ├── OnlineCourses.md ├── Picks.md ├── ProbStats.md ├── README.md ├── SchoolElem.md ├── SchoolLevel.md ├── Sciences.md └── Sequence.md /.gitignore: -------------------------------------------------------------------------------- 1 | *~ 2 | .* 3 | -------------------------------------------------------------------------------- /Algebra.md: -------------------------------------------------------------------------------- 1 | 2 | ## Linear Algebra 3 | 4 | See the [Linear Algebra section](LinearAlgebra.md). 5 | 6 | ## Algebra (aka Abstract Algebra, Modern Algebra) 7 | 8 | ### First books 9 | 10 | - Pinter, *A Course in Abstract Algebra* ([2e Dover](https://smile.amazon.com/dp/0486474178/)) 11 | 12 | Pinter gives you a smooth start in algebra from the very beginning. Each chapter gives a short exposition (typically 4-8 pages) followed by lots of problems. Often the problems fill more pages than the text. In each chapter, problems begin with simple applications of definitions to concrete examples, progress to relatively simple proofs that follow from the definitions and theorems in the text to more difficult problems and, in an extended series of exercises, a proof of Sylow's Theorem. 13 | 14 | - Herstein, *Abstract Algebra* ([3e hardcover OOP](https://smile.amazon.com/dp/0133745627/), [3e paperback](https://smile.amazon.com/dp/0471368792/)) or *Topics in Algebra* ([2e paperback](https://smile.amazon.com/dp/0471010901/), [2e intl](http://www.abebooks.com/products/isbn/9788126510184?cm_sp=bdp-_-9788126510184-_-isbn10)) 15 | 16 | Herstein has lots of great problems. *Topics* is considered somewhat more challenging than *AA*. 17 | 18 | - Gallian, *Contemporary Abstract Algebra* ([8e paperback](https://smile.amazon.com/dp/8131520749/), [7e](https://smile.amazon.com/dp/0547165099/), [6e](https://smile.amazon.com/dp/0618514716/)) 19 | 20 | - Shoup. *A Computational Introduction to Number Theory and Algebra* ([**FREE ONLINE**](http://shoup.net/ntb/); [2e at Amazon](https://smile.amazon.com/dp/0521516447)) 21 | 22 | - Connell, *Elements of Abstract and Linear Algebra* ([**FREE ONLINE**](http://www.math.miami.edu/~ec/book/)) 23 | 24 | I haven't looked at this one at all yet, but it's free: 25 | 26 | ### Major textbooks 27 | 28 | - Artin, *Algebra* ([2e [expensive!]](https://smile.amazon.com/dp/0132413779/), [2e intl](https://smile.amazon.com/dp/9332549834/), [2e intl @AbeBooks](http://www.abebooks.com/servlet/SearchResults?an=Michael%20Artin&bi=0&bx=off&ds=30&n=100121501&recentlyadded=all&sortby=17&tn=Algebra)) 29 | - Jacobson, *Basic Algebra I* ([2e Dover](https://smile.amazon.com/dp/0486471896/)) 30 | - Jacobson, *Basic Algebra II* ([2e Dover](https://smile.amazon.com/dp/048647187X/)) 31 | - Dummit and Foote, *Algebra* ([3e intl](https://smile.amazon.com/dp/8126532289/), [3e [expensive!]](https://smile.amazon.com/dp/B007CJ4C1U), [2e](https://smile.amazon.com/dp/0471368571)) 32 | - Mac Lane and Birkhoff, *Algebra 3e* ([3e](https://smile.amazon.com/dp/0821816462/)) 33 | - Lang, *Algebra* ([3e](https://smile.amazon.com/dp/038795385X/)) 34 | - Hungerford, *Algebra* ([Springer hardcover](https://smile.amazon.com/dp/0387905189/)) 35 | 36 | ### Other books 37 | 38 | * Beachy. *Abstract Algebra: Study Guide* ([1e](https://smile.amazon.com/dp/1493574116)) - Contains problems with solutions. 39 | 40 | ### Free resources 41 | 42 | * J. S. Milne, course notes: 43 | * Ash. *Abstract Algebra: The Basic Graduate Year* (with solutions) 44 | * Ash. *A Course in Algebraic Number Theory* (with solutions) 45 | 46 | ### Group theory 47 | 48 | * Carter. *Visual Group Theory* ([1e](https://smile.amazon.com/dp/088385757X)) 49 | * Rose. *A Course on Group Theory* ([Dover](https://smile.amazon.com/dp/0486681947)) - Covers the basics. 50 | * Rotman. *An Introduction to the Theory of Groups* ([4e](https://smile.amazon.com/dp/0387942858)) 51 | * Scott. *Group Theory* ([Dover](https://smile.amazon.com/dp/0486653773)) - Theorem-proof. 52 | * Robinson. *A Course in the Theory of Groups* ([2e](https://smile.amazon.com/dp/0387944613)) - A solid second course in group theory. 53 | * Humphreys. *A Course in Group Theory* ([1e](https://smile.amazon.com/dp/0198534590)) 54 | * Dixon. *Problems in Group Theory* ([Dover](https://smile.amazon.com/dp/0486459160)) 55 | * Isaacs. *Character Theory of Finite Groups* ([Dover](https://smile.amazon.com/dp/0486680142)) 56 | * Kurzweil, Stellmacher. *The Theory of Finite Groups: An Introduction* (2004) 57 | * Wilson. *The Finite Simple Groups* ([1e](https://smile.amazon.com/dp/1848009879)) 58 | * Lyndon, Schupp. *Combinatorial Group Theory* ([Dover](https://smile.amazon.com/dp/3540411585)) 59 | 60 | ### Lie theory (Lie groups/algebras, representation theory, linear algebraic groups) 61 | 62 | * Tapp. *Matrix Groups for Undergraduates* ([2e](https://smile.amazon.com/dp/1470427222), [1e](https://smile.amazon.com/dp/0821837850)) 63 | * Fulton and Harris. *Representation Theory: A First Course* ([1e](https://smile.amazon.com/dp/0387974954)) 64 | * Humphreys. *Introduction to Lie Algebras and Representation Theory* ([1e](https://smile.amazon.com/dp/0387900535)) 65 | * Serre. *Linear Representations of Finite Groups* ([1e](https://smile.amazon.com/dp/0387901906)) 66 | * Procesi. *Lie Groups: An Approach through Invariants and Representations* ([1e](https://smile.amazon.com/dp/0387260404)) 67 | * Warner. *Foundations of Differentiable Manifolds and Lie Groups* ([1e](https://smile.amazon.com/dp/0387908943)) 68 | * Stillwell. *Naive Lie Theory* ([1e](https://smile.amazon.com/dp/0387782141)) 69 | * Knapp. *Lie Groups: Beyond an Introduction* ([2e](https://smile.amazon.com/dp/0817642595)) 70 | * Goodman and Wallach. *Symmetry, Representations, and Invariants* ([1e](https://smile.amazon.com/dp/038779851X)) 71 | * Pollatsek. *Lie Groups: A Problem Oriented Introduction via Matrix Groups* ([1e](https://smile.amazon.com/dp/0883857596)) 72 | * Jacobson. *Lie Algebras* ([Dover](https://smile.amazon.com/dp/0486638324)) 73 | * Borel. *Linear Algebraic Groups* ([2e](https://smile.amazon.com/dp/0387973702)) 74 | * Humphreys. *Linear Algebraic Groups* ([1e](https://smile.amazon.com/dp/0387901086)) 75 | * Hall. *Lie Groups, Lie Algebras, and Representations: An Elementary Introduction* ([2e](https://smile.amazon.com/dp/3319134663)) 76 | * Chevalley. *Theory of Lie Groups* ([PUP 1946](https://smile.amazon.com/dp/0691049904)) 77 | * James and Liebeck. *Representations and Characters of Groups* ([2e](https://smile.amazon.com/dp/052100392X)) 78 | 79 | ### Commutative algebra 80 | 81 | - Eisenbud, *Commutative Algebra: with a View Toward Algebraic Geometry* ([Springer paperback](https://smile.amazon.com/dp/0387942696/)) 82 | - Atiyah and MacDonald, *Introduction To Commutative Algebra* ([Paperback](https://smile.amazon.com/dp/0201407515/)) 83 | - Matsumura, tr. Reid. *Commutative Ring Theory* ([1e](https://smile.amazon.com/dp/0521367646/)) 84 | - Miller and Sturmfels. *Combinatorial Commutative Algebra* ([1e](https://smile.amazon.com/dp/0387237070)) 85 | - Ene and Herzog. *Grobner Bases in Commutative Algebra* ([1e](https://smile.amazon.com/dp/0821872877)) 86 | - Zariski and Samuel. *Commutative Algebra* ([Vol I](https://smile.amazon.com/dp/0387900896), [Vol II](https://smile.amazon.com/dp/038790171X)) 87 | 88 | ### Noncommutative algebra 89 | 90 | - Lam. *A First Course in Noncommutative Rings* ([2e](https://smile.amazon.com/dp/0387953256)) 91 | - Lam. *Lectures on Modules and Rings* ([1e](https://smile.amazon.com/dp/0387984283)) 92 | - Lam. *Exercises in Modules and Rings* ([1e](https://smile.amazon.com/dp/0387988505)) 93 | - Farb and Dennis. *Noncommutative Algebra* ([1e](https://smile.amazon.com/dp/038794057X)) 94 | 95 | ## Number theory 96 | 97 | ### Introductions 98 | 99 | - Ireland and Rosen. *A Classical Introduction to Modern Number Theory* ([2e](https://smile.amazon.com/dp/038797329X)) 100 | 101 | Perhaps the most popular introduction to number theory. 102 | 103 | - Hardy and Wright. *An Introduction to the Theory of Numbers* ([6e/2008 updated by Heath-Brown and Silverman](https://smile.amazon.com/dp/0199219869), [5e/1980](https://smile.amazon.com/dp/0198531710), [4e/1960 at Archive.org](https://archive.org/details/AnIntroductionToTheTheoryOfNumbers-4thEd-G.h.HardyE.m.Wright)) 104 | 105 | A classic introduction to number theory. One of the most popular books. The 6th edition has been updated with recent developments. 106 | 107 | - Davenport. *The Higher Arithmetic: An Introduction to the Theory of Numbers* ([CUP 8e/2008](https://smile.amazon.com/dp/0521722365), [Dover 7e/1983 at AbeBooks](http://www.abebooks.com/products/isbn/9780486244525)) 108 | 109 | Another classic introduction to number theory. It's quite short. 110 | 111 | - Dudley. *Elementary Number Theory* ([Dover 2e](https://smile.amazon.com/dp/048646931X)) 112 | 113 | - Jones and Jones. *Elementary Number Theory* ([1e corr](https://smile.amazon.com/dp/3540761977)) 114 | 115 | - Andrews. *Number Theory* ([Dover 1e](https://smile.amazon.com/dp/0486682528)) 116 | 117 | A combinatorial approach to elementary number theory. Includes the theory of partitions. 118 | 119 | - Stillwell. *Elements of Number Theory* 120 | 121 | - Crawford. *Introduction to Number Theory* ([At AOPS](https://www.artofproblemsolving.com/store/item/intro-number-theory), [At Amazon](https://smile.amazon.com/dp/1934124125)) 122 | 123 | - Pommersheim, Marks, Flapan. *Number Theory: A Lively Introduction with Proofs, Applications, and Stories* ([1e](https://smile.amazon.com/dp/0470424133)) 124 | 125 | - Samuel, tr. Silberger. *Algebraic Theory of Numbers* ([Dover](https://smile.amazon.com/dp/0486466663)) 126 | 127 | Another short, classic introduction to number theory. A bit old-fashioned. It emphases algebraic structures, as the title suggests. 128 | 129 | ### Beyond 130 | 131 | - Apostol. *Introduction to Analytic Number Theory* ([1e/1976 corr 1998](https://smile.amazon.com/dp/0387901639)) 132 | - Koblitz. *A Course in Number Theory and Cryptography* ([2e](https://smile.amazon.com/dp/0387942939)) 133 | - Koblitz. *p-adic Numbers, p-adic Analysis, and Zeta-Functions* ([2e](https://smile.amazon.com/dp/0387960171)) 134 | - Koblitz. *Introduction to Elliptic Curves and Modular Forms* ([2e](https://smile.amazon.com/dp/0387979662)) 135 | - Edwards. *Riemann's Zeta Function* ([Dover](https://smile.amazon.com/dp/0486417409)) 136 | - Andrews. *The Theory of Partitions* ([1e](https://smile.amazon.com/dp/052163766X)) 137 | - Andrews and Eriksson. *Integer Partitions* ([2e](https://smile.amazon.com/dp/0521600901)) 138 | 139 | #### Ramanujan 140 | 141 | Online copies of Ramanujan's work can be found here: 142 | 143 | - Berndt. *Number Theory in the Spirit of Ramanujan* ([1e](https://smile.amazon.com/gp/product/0821841785)) - An introduction to Ramanujan's work for someone already acquainted with number theory. 144 | - Ramanujan, ed. Hardy, Aiyar, Wilson. *Collected Papers of Srinivasa Ramanujan* ([1e](https://smile.amazon.com/gp/product/1107536510)) 145 | - Hardy. *Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work* ([AMS Chelsea](https://smile.amazon.com/gp/product/0821820230)) 146 | - Andrews and Berndt. *Ramanujan's Lost Notebook* ([Part I](https://smile.amazon.com/dp/038725529X), etc.) 147 | -------------------------------------------------------------------------------- /Analysis.md: -------------------------------------------------------------------------------- 1 | 2 | ## Analysis 3 | 4 | ### Real Analysis 5 | 6 | #### Proofs books 7 | 8 | These aren't actually analysis books, but in the math curriculum that's often where they get used, since intro to real analysis is often the place where math students start to write (and really have to understand) proofs. 9 | 10 | - Velleman, *How to Prove It* ([2e](https://smile.amazon.com/dp/0521675995/), [1e](https://smile.amazon.com/dp/0521446635/)) 11 | 12 | A series of blog posts discussing solutions to Velleman's exercises: 13 | 14 | - Solow, *How to Read and Do Proofs: An Introduction to Mathematical Thought Processes* ([6e](https://smile.amazon.com/dp/1118164024/), [5e](https://smile.amazon.com/dp/0470392169/), [4e](https://smile.amazon.com/dp/0471680583/)) 15 | 16 | #### Introductory analysis 17 | 18 | These books ease you into real analysis. They are designed to address a difficulty in the evolving US math curriculum, namely that because rigorous calculus textbooks (like Spivak and Apostol, or those books titled "Advanced Calculus") are no longer commonly used in lower-level courses, students arrive in real analysis courses without knowing how to read and write proofs or understanding the theoretical foundation of calculus. These books help you with understanding how to do proofs, and they feed you the information in a way that's easier to digest. They don't cover all the material you need, and thus they aren't sufficient on their own to master the subject, but they can make the other books (which I call "standard" below) more manageable. 19 | 20 | All of these books stop short of Lebesgue integration, so they can't be considered complete introductions to real analysis. 21 | 22 | - Alcock, *How to Think About Analysis* ([1e](https://smile.amazon.com/dp/0198723539/)) 23 | 24 | This book begins with a discussion of how to read a math book. This might seem like a trivial thing to discuss, but it is a real problem for many people because math books are presented in a way that requires a lot of engagement on the part of the reader. Many students are not prepared when they encounter a book that is full of proofs and not much else. Alcock covers topics like how to relate theorems to definitions, and even how to study. The remainder of the book introduces major topics in analysis: sequences, series, continuity, differentiability, integrability, the real numbers. This book is written in such an elementary manner that it has a bit of a "for dummies" feel to it (though it's never condescening or childish), but if you can swallow your pride, there's a lot of good information here. 25 | 26 | - Schramm, *Introduction to Real Analysis* ([Dover](https://smile.amazon.com/dp/0486469131)) 27 | 28 | Schramm begins with a section on how to write proofs. What's really notable about the rest of the book is that he discusses how a number of major theorems about the real numbers are essentially equivalent, and he shows you how to establish this equivalence. He wraps up by constructing the real number system via Dedekind cuts, which is a sensible transition to a book like Rudin that begins with Dedekind cuts. Every section is followed by a fair number of problems: they aren't particularly difficult for the most part, but they do a good job of seeing that you understand the material. 29 | 30 | - Ross, *Elementary Analysis: The Theory of Calculus* ([2e](https://smile.amazon.com/dp/1461462703/), [1e](https://smile.amazon.com/dp/038790459X)) 31 | 32 | Ross eases you into real analysis by putting extra emphasis on the fundamental topics. The book uses a decent number of illustrations when discussing basic topology. 33 | 34 | - Abbot, *Understanding Analysis* ([1e paperback](https://smile.amazon.com/dp/1441928669)) 35 | 36 | Abbot's book is more a traditional real analysis book that the previous ones in this section. It doesn't include chapters teaching you how to do mathemetics, it just gives good, clear explanations of the material. 37 | 38 | - Rosenlicht. *Introduction to Analysis* ([1e](https://smile.amazon.com/dp/0486650383/)) 39 | 40 | A classic book (1968), well-regarded for its clarity. 41 | 42 | #### Standard undergraduate analysis 43 | 44 | These books present the standard undergraduate course in real analysis. They include the Lebesgue integral, but stop short of measure theory. 45 | 46 | - Rudin, *Principles of Mathematical Analysis* ([3e intl](https://smile.amazon.com/dp/0070856133/), [3e intl PIE](https://smile.amazon.com/Principles-Mathematical-Analysis-Rudin/dp/1259064786/)) 47 | 48 | AKA "Baby Rudin". The definitive book on real analysis. For some, it's the yardstick by which all other real analysis textbooks are measured, and found wanting. (For others, it's a work of elitist arrogance designed to make you feel inferior to the author.) Rudin expects you to keep up with him, and makes no apologies if you don't. The book is carefully constructed, though, so that at each step you have the definitions and theorems needed to proceed. This approach requires a lot of work from you as reader, but it does pay off. His exercises are demanding, but they force you to engage the material on another level and really understand it. 49 | 50 | If you don't have experience reading serious math books, one of the "hand-holding" books mentioned above is strongly suggested. Those authors no doubt had this book in mind as one of the texts that they intended to prepare you for. 51 | 52 | Most students (especially those not taking a university course) will use some other textbook along with Rudin. Pretty much any of the other books mentioned here makes a suitable counterpoint to Rudin's style and fills in many of the details that he glosses over. 53 | 54 | In struggling with Rudin, I found various supplements and partial solutions manuals online. Of these, most were not very helpful; often, I had actually worked out the same proof that the they showed, but I didn't understand how it served to prove the premise and the solution came with no explanation. (That's still some help; though: if I have some reassurance that I've seen the statement that's necessary for the proof, then I know I'm on the right track.) 55 | 56 | The one resource that I did find most helpful is George Bergman's "Supplements", which has commentary on Rudin's text as well as the exercises [https://math.berkeley.edu/~gbergman/ug.hndts/m104_Rudin_exs.pdf]. Bergman also wrote up his own errata listing things he had asked Rudin to change: [https://math.berkeley.edu/~gbergman/ug.hndts/m104_Rudin_notes.pdf]. 57 | 58 | UW-Madison hosts a solution manual by Roger Cooke, [http://minds.wisconsin.edu/handle/1793/67009]; this wasn't always thorough enough, but it was of some help. 59 | 60 | - Apostol, *Mathematical Analysis* ([2e](https://smile.amazon.com/dp/0201002884)) 61 | 62 | Another classic text (1974), with more extensive explanations than Rudin. 63 | 64 | This page has some solutions for exercises: 65 | 66 | - Pugh, *Real Mathematical Analysis* ([2e](https://smile.amazon.com/dp/3319177702), [1e](https://smile.amazon.com/dp/0387952977)) 67 | 68 | Pugh's book is probably the main competitor to Baby Rudin among more recent books. Notable for its clear explanations and its many exercises. It contains many illustrations, but I find most of them to be poorly chosen, as if the author recognizes that illustrations are good to have but doesn't grasp how to use them to illustrate concepts. This isn't much of a con, just puzzling. 69 | 70 | - Stromberg, *An Introduction to Classical Real Analysis* ([AMS 2015 reissue](https://smile.amazon.com/dp/1470425440), [Wadsworth 1981 original](https://smile.amazon.com/dp/0534980120)) 71 | 72 | Well-liked for its topic selection and exercises. Exercise difficulty scales more smoothly than Rudin's. The AMS edition is very nice, and probably almost as cheap new as a used copy of the Wadsworth will be. 73 | 74 | - Tao, *Analysis* (I and II) 75 | 76 | Tao's approach is a rigorous construction of analysis beginning with the foundations of the number system. Proofs are largely left as exercises, and it lacks much intuitive discussion, so I don't think it's appropriate for self-study except in combination with some other book. It's published by Hundustan Book Agency and sold in the USA via AMS ([AMS store page](http://bookstore.ams.org/hin-66)). It can be ordered from India via these links: 77 | 78 | - I: 79 | - II: 80 | 81 | - Shilov, *Elementary Real and Complex Analysis* ([Dover](https://smile.amazon.com/dp/0486689220)) 82 | 83 | This translation of a Russian book is an exception to what I said at the beginning of this section: it doesn't cover the Lebesgue integral. Instead, it includes a chapter on analytic functions, which (in the US system) is more typically covered in a course on complex analysis. Shilov covers the Lebesgue integral in his graduate-level sequel: Shilov and Gurevich, *Integral, Measure and Derivative*. 84 | 85 | - Bressoud's "Radial Approch" books 86 | - Bressoud, *A Radical Approach to Real Analysis* ([2e](https://smile.amazon.com/dp/0883857472/)) 87 | - Bressoud, *A Radical Approach to Lebesgue's Theory of Integration* ([1e](https://smile.amazon.com/dp/0521711835/)) 88 | 89 | I discuss both of these books by Bressoud together. Bressoud's concept is to teach analysis by tracing the history of the mathematical concepts, and the telling the story of the problems and controversies that played out over the course of the 19th Century that gave shape to modern analysis. He states that his main purpose is to teach you the math, though, not to teach you the history of mathematics. 90 | 91 | Bressoud summarizes *A Radical Approach to Real Analysis* thus: "The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early nineteenth century. It follows Cauchy's attempts to establish a firm foundation for calculus, and considers his failures as well as his successes. It culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof." 92 | 93 | The second book is summarized thus: "The story begins with Riemann's definition of the integral, a definition created so that he could understand how broadly one could define a function and yet have it be integrable. The reader then follows the efforts of many mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work in the late nineteenth and early twentieth centuries of Jordan, Borel, and Lebesgue, who finally broke with Riemann's definition. Ushering in a new way of understanding integration, they opened the door to fresh and productive approaches to many of the previously intractable problems of analysis." 94 | 95 | - Johnsonbaugh and Pfaffenberger, *Foundations of Mathematical Analysis* ([1e](https://smile.amazon.com/dp/0486477665)) 96 | 97 | - Ash. *Real Variables, with basic metric space topology* ([**FREE ONLINE**](http://www.math.uiuc.edu/~r-ash/RV.html), [Dover](https://smile.amazon.com/dp/0486472205)) 98 | 99 | An introduction to real analysis. Includes solutions to problems! 100 | 101 | - Trench. *Introduction to Real Analysis* ([**FREE ONLINE**](http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF)) 102 | 103 | - Carothers, *Real Analysis* ([1e](https://smile.amazon.com/dp/0521497566/)) 104 | 105 | - Erdman. *Companion to Real Analysis* ([**FREE ONLINE**](http://web.pdx.edu/~erdman/CRA/CRAlicensepage.html)) 106 | 107 | Free course notes covering a wide range of topics. 108 | 109 | ### Graduate analysis 110 | 111 | These books are generally considered graduate level, and cover measure theory. (Measure theory is generally the big thing that's left out of undergraduate analysis courses.) 112 | 113 | - Royden ([3e](https://smile.amazon.com/dp/0024041513/)) 114 | 115 | Royden is one of the most popular classic real analyis texts. One thing to be aware of is that a fourth edition was published with Patrick Fitzpatrick as co-author, but it hasn't been well-received: many felt that the third edition was in no need of revision, and the fourth introduced new errors. Since it was popular, many copies of the 3rd edition (of 1988) are still available on the used market at a reasonable price. I've also seen used copies of the 2nd edition floating around at secondhand stores. 116 | 117 | - Rudin, *Real and Complex Analysis* ([3e intl](https://smile.amazon.com/dp/0070619875/), [3e intl @AbeBooks](http://www.abebooks.com/products/isbn/9780070619876/19190730510)) 118 | 119 | A traditional heavyweight, also known as "Big Rudin", "Adult Rudin" or "Daddy Rudin". Extremely expensive, but you can buy the Indian edition. 120 | 121 | - Kolmogorov and Fomin, *Elements of the Theory of Functions and Functional Analysis* ([Martino](https://www.amazon.com/dp/1614273049/), [Dover](https://www.amazon.com/dp/0486406830/)) 122 | 123 | Kolmogorov was one of the great mathematicians of the 20th Century. Translated from Russian. This seems to be 124 | the preferred translation. (It's roughly the same book as Silverman's translation, which is titled *Introductory Real Analysis*.) 125 | 126 | - Folland, *Real Analysis: Modern Techniques and Their Applications* ([2e](https://smile.amazon.com/dp/0471317160/)) 127 | 128 | "Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis." 129 | 130 | It's said to be an excellent book, and it's popular. Too bad it's so expensive. There's an older edition but even that one isn't cheap. 131 | 132 | - Bartle. *The Elements of Integration and Lebesgue Measure* ([1e](https://smile.amazon.com/Elements-Integration-Lebesgue-Measure/dp/0471042226/), [1e intl @AbeBooks](http://www.abebooks.com/products/isbn/9780471042228/19427046996)) 133 | 134 | Well-regarded text on the more advanced topics of real analysis. 135 | 136 | - Taylor, *General Theory of Functions and Integration* ([Dover](https://smile.amazon.com/dp/0486649881)) 137 | 138 | Another classic text (1965). It is notably clear in its explanations. This one doesn't seem to be very popular, but personally I like it. 139 | 140 | - Bass, *Real Analysis for Graduate Students* ([**FREE ONLINE**](http://bass.math.uconn.edu/real.html), [2e self-published paperback](https://smile.amazon.com/dp/1481869140/)) 141 | 142 | Designed as an overview of all the real analysis that a grad student should need to pass a prelim in real analysis. Not intended to teach it to you the first time. 143 | 144 | - Stein and Shakarchi, *Real Analysis: Measure Theory, Integration, and Hilbert Spaces* ([1e](https://smile.amazon.com/Real-Analysis-Integration-Princeton-Lectures/dp/0691113866/)) 145 | 146 | One of four books form a series (*Princeton Lectures in Analysis*) at the level of advanced 147 | undergraduate or beginning graduate analysis. 148 | They are widely praised for their quality, but they are also a bit pricey for what you get (and used 149 | copies aren't much cheaper). 150 | 151 | - Shilov and Gurevich, *Integral, Measure and Derivative* ([Dover](https://smile.amazon.com/dp/0486635198)) 152 | 153 | Shilov's graduate analysis textbook on Lebesgue integration and measure theory. 154 | 155 | - Lieb and Loss, *Analysis* ([2e](https://smile.amazon.com/dp/0821827839)) 156 | 157 | Largely focuses on applications. Includes the Fourier transform, Sobolev spaces and the calculus of variations. A more advanced book that seems to assume a prior introduction to measure theory. 158 | 159 | - Folland, *A Guide to Advanced Real Analysis* ([1e](https://smile.amazon.com/dp/0883853434)) 160 | 161 | "This book is an outline of the core material in the standard graduate-level real analysis course. .... Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted." (Usually when someone refers to the Folland book, though, it's his other one at this level.) 162 | 163 | ### Problem books 164 | 165 | - Larson. *Problem-Solving Through Problems* ([1e PB](https://smile.amazon.com/dp/0387961712)) 166 | 167 | - Aksoy and Khamsi. *A Problem Book in Real Analysis* ([1e](https://www.amazon.com/dp/1441912959)) 168 | 169 | Covers basic topics in real analysis. Includes solutions! 170 | 171 | - Erdman. *A ProblemText in Advanced Calculus* ([**FREE ONLINE**](http://web.pdx.edu/~erdman/PTAC/PTAClicensepage.html)) 172 | 173 | - Moise. *Introductory Problem Courses in Analysis and Topology* ([1e PB](https://smile.amazon.com/dp/0387907017)) 174 | 175 | - Shakarchi. *Problems and Solutions for Undergraduate Analysis* ([1e](https://smile.amazon.com/dp/0387982353)) 176 | - Shakarchi. *Problems and Solutions for Complex Analysis* ([1e](https://smile.amazon.com/dp/0387988319)) 177 | 178 | All the exercises from Serge Lang's *Undergraduate Analysis* and *Complex Analysis* respectively, with solutions. These are apparently intended for use with Lang's textbooks, but since the problems are included I guess you could use them on their own as well. (Significant because they cost as much as the textbooks themselves.) 179 | 180 | - Volkovyskii, Lunts, Aramanovich. *A Collection of Problems on Complex Analysis* 181 | 182 | - Gelbaum. *Problems in Real and Complex Analysis* ([1e HC](https://smile.amazon.com/dp/038797766X)) 183 | 184 | - Kirillov and Gvishiani. *Theorems and Problems in Functional Analysis* ([1e](https://smile.amazon.com/dp/038790638X)) 185 | 186 | - Yeh. *Problems and Proofs in Real Analysis: Theory of Measure and Integration* ([1e](https://smile.amazon.com/gp/product/9814578509)) 187 | 188 | A graduate-level set of problems and solutions. 189 | 190 | - Furdui. *Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis* ([1e](https://smile.amazon.com/dp/1461467616)) 191 | 192 | - Aliprantis and Burkinshaw. *Problems in Real Analysis* ([2e](https://smile.amazon.com/dp/0120502534)) 193 | 194 | - Kaczor and Nowak. *Problems in Mathematical Analysis* ([Vol I](https://smile.amazon.com/dp/0821820508); [Vol II](https://smile.amazon.com/dp/0821820516); [Vol III](https://smile.amazon.com/dp/0821832980)) 195 | 196 | - Pólya and Szegö. *Problems and Theorems in Analysis* 197 | - Vol I: *Series, Integral Calculus, Theory of Functions* ([Vol I](https://smile.amazon.com/dp/3540636404)) 198 | - Vol II: *Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry* ([Vol II](https://smile.amazon.com/dp/3540636862)) 199 | 200 | - Gasinski and Papageorgiou. 201 | - *Exercises in Analysis: Part 1* ([1e](https://smile.amazon.com/dp/3319061755)) 202 | - *Exercises in Analysis: Part 2: Nonlinear Analysis* ([1e](https://smile.amazon.com/dp/3319278150)) 203 | 204 | A *huge*, brand-new collection of problems on analysis (each book is over 1000 pages). This looks to be the kind of thing you're only interested in if you'll be specializing in real analysis. "This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material." 205 | 206 | - Rădulescu, Rădulescu, Andreescu. *Problems in Real Analysis: Advanced Calculus on the Real Axis* ([1e](https://smile.amazon.com/dp/0387773789)) 207 | 208 | ### Fourier analysis 209 | 210 | - Stein and Shakarchi, *Fourier Analysis: An Introduction* ([1e](https://smile.amazon.com/dp/069111384X)) 211 | - Hubbard, *The World According to Wavelets* ([1e](https://smile.amazon.com/dp/1568810725)) 212 | - Tolstov, *Fourier Analysis* ([Dover](https://smile.amazon.com/dp/0486633179)) 213 | 214 | ### Manifolds 215 | 216 | - Munkres, *Analysis On Manifolds* ([1e](https://smile.amazon.com/dp/0201315963)) 217 | - Spivak, *Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus* ([1e](https://smile.amazon.com/dp/0805390219)) 218 | - Loomis and Sternberg. *Advanced Calculus* ([WS Revised Edition](https://www.amazon.com/dp/9814583936)) 219 | 220 | See also: [Differential Geometry](https://github.com/nculwell/MathStudy/blob/master/GeomTopo.md#differential-geometry). 221 | 222 | ### Complex Analysis 223 | 224 | - Bak and Newman, *Complex Analysis* ([3e](https://smile.amazon.com/dp/1441972870)) 225 | 226 | This has a reputation as a relatively easy introduction to complex analysis, but it covers less material than others. 227 | 228 | - Stein and Shakarchi, *Complex Analysis* ([1e](https://smile.amazon.com/dp/0691113858)) 229 | 230 | A very well-liked intro to complex analysis, and perhaps the best-loved of the S&S series. Still expensive. 231 | 232 | - Ahlfors, *Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable* ([3e](https://smile.amazon.com/dp/0070006571), [3e intl at AbeBooks](http://www.abebooks.com/products/isbn/9780070006577), [3e intl](https://smile.amazon.com/dp/1259064824), [2e](https://smile.amazon.com/dp/0070006563)) 233 | 234 | The traditional textbook for a complex analysis course. Typically considered old and dry these days, but still useful. 235 | 236 | - Flanigan, *Complex Variables: Harmonic and Analytic Functions* ([Dover](https://smile.amazon.com/dp/0486613887)) 237 | 238 | - Conway, *Functions of One Complex Variable* (Vol I: [2e](https://smile.amazon.com/dp/0387903283), [2e intl at AbeBooks](http://www.abebooks.com/products/isbn/9788185015378); Vol II: [1e](https://smile.amazon.com/dp/0387944605)) 239 | 240 | - Needham, *Visual Complex Analysis* ([1e](https://smile.amazon.com/dp/0198534469)) 241 | 242 | An introduction to complex analysis in pictures. 243 | 244 | - Wegert. *Visual Complex Functions: An Introduction with Phase Portraits* ([1e](https://smile.amazon.com/dp/3034801793)) 245 | 246 | Another pictorial intro to complex analysis. 247 | 248 | - Schwerdtfeger, *Geometry of Complex Numbers* ([Dover](https://smile.amazon.com/dp/0486638308)) 249 | 250 | - Gamelin. *Complex Analysis* ([1e](https://smile.amazon.com/dp/0387950699)) 251 | 252 | - Ash and Novinger, *Complex Variables* ([**FREE ONLINE**](http://www.math.uiuc.edu/~r-ash/CV.html), [2e Dover](https://smile.amazon.com/dp/0486462501)) 253 | 254 | Contain solutions. Author's page: 255 | 256 | - Markushevich. *Theory of Functions of a Complex Variable ([AMS Chelsea revised English edition](https://smile.amazon.com/dp/082183780X)) 257 | 258 | - Ablowitz and Fokas. *Complex Variables: Introduction and Applications* ([2e](https://smile.amazon.com/dp/0521534291)) 259 | 260 | ### Functional Analysis 261 | - Stein and Shakarchi, *Functional Analysis: Introduction to Further Topics in Analysis* ([1e](https://smile.amazon.com/dp/0691113874)) 262 | - Akhiezer and Glazman, *Theory of Linear Operators in Hilbert Space* ([Dover](https://smile.amazon.com/dp/0486677486/)) 263 | - Griffel, *Applied Functional Analysis* ([Dover](https://smile.amazon.com/dp/0486422585)) 264 | - Shilov, *Elementary Functional Analysis* ([Dover](https://smile.amazon.com/dp/0486689239/)) 265 | - Rudin, *Functional Analysis* ([McGraw-Hill intl @AbeBooks](http://www.abebooks.com/products/isbn/9780070619883)) 266 | - Halmos, *Introduction to Hilbert Space and the Theory of Spectral Multiplicity* ([Martino](https://smile.amazon.com/dp/1614274711)) 267 | - Halmos, *A Hilbert Space Problem Book* ([2e](https://smile.amazon.com/dp/0387906851)) 268 | - Erdman. *Functional Analysis and Operator Algebras: An Introduction* 269 | - Aliprantis and Border. *Infinite Dimensional Analysis: A Hitchhiker's Guide* ([3e](https://smile.amazon.com/dp/3540326960)) 270 | 271 | ### Dynamical systems 272 | 273 | - Strogatz. *Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering* ([2e](https://smile.amazon.com/dp/0813349109), [1e](https://smile.amazon.com/dp/0738204536)) 274 | - Holmgren. *A First Course in Discrete Dynamical Systems* ([2e](https://smile.amazon.com/dp/0387947809)) 275 | - Devaney. *An Introduction to Chaotic Dynamical Systems* ([2e](https://smile.amazon.com/dp/0813340853)) 276 | - Sternberg. *Dynamical Systems* ([Dover](https://smile.amazon.com/dp/0486477053)) 277 | - Wiggins. *Introduction to Applied Nonlinear Dynamical Systems and Chaos* ([2e](https://smile.amazon.com/dp/0387001778)) 278 | - Glendinning. *Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations* ([2e](https://smile.amazon.com/dp/0521425662)) 279 | - Hirsch, Smale, Devaney. *Differential Equations, Dynamical Systems, and an Introduction to Chaos* ([3e](https://smile.amazon.com/dp/0123820103)) 280 | 281 | ### Asymptotic methods, perturbation theory 282 | 283 | - Bender and Orszag. *Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory* ([1e](https://smile.amazon.com/dp/0387989315)) 284 | - de Bruijn. *Asymptotic Methods in Analysis* ([Dover](https://smile.amazon.com/dp/0486642216)) 285 | - Simmonds and Mann. *A First Look at Perturbation Theory* ([Dover 2e](https://smile.amazon.com/dp/0486675513)) 286 | - Bellman. *Perturbation Techniques in Mathematics, Engineering and Physics* ([Dover](https://smile.amazon.com/dp/0486432580)) 287 | 288 | ### Numerical analysis 289 | 290 | See [Numerical Methods](CS.md#numerical-methods) in the CS section. 291 | -------------------------------------------------------------------------------- /CS.md: -------------------------------------------------------------------------------- 1 | # Computer science 2 | 3 | ## Teach Yourself Computer Science 4 | 5 | Another site that recommends some great resources: https://teachyourselfcs.com/ 6 | 7 | ## Basic programming and intros to CS 8 | 9 | * [*Structure and Interpretation of Computer Programs*](https://mitpress.mit.edu/sicp/full-text/book/book.html) 10 | * Felleisen, Findler, Flatt, Krishnamurthi. *How to Design Programs: An Introduction to Programming and Computing* ([**FREE ONLINE**](http://www.htdp.org/), [1e](https://smile.amazon.com/dp/0262062186)) 11 | * Erwig, 2017. *Once Upon an Algorithm: How Stories Explain Computing* 12 | * Zelle. *Python Programming: An Introduction to Computer Science* 13 | * [*CS Unplugged*](http://csunplugged.org/books/) (for kids) 14 | * Eckel. *Thinking in Java* ([TIJ website](http://www.mindviewinc.com/Books/TIJ4/); old editions are free) 15 | * [Haverbeke. *Eloquent Javascript*](http://eloquentjavascript.net/) 16 | * Downey. *How to Think Like a Computer Scientist* ([C++ Version](http://greenteapress.com/thinkcpp/index.html), [OCaml Version](http://greenteapress.com/thinkocaml/index.html), [Learning with Python](http://greenteapress.com/thinkpython/thinkCSpy/index.html), [Python for Software Design](http://greenteapress.com/thinkpython/pythonsd.html)) 17 | 18 | * Friedman and Felleisen. *The Little Schemer* ([4e](https://smile.amazon.com/dp/0262560992)) 19 | 20 | Sequels: 21 | 22 | * Friedman and Felleisen. *The Seasoned Schemer* ([1e](https://smile.amazon.com/dp/026256100X)) 23 | * Friedman, Byrd, Kiselyov. *The Reasoned Schemer* ([1e](https://smile.amazon.com/dp/0262562146)) 24 | * Friedman and Eastlund. *The Little Prover* ([1e](https://smile.amazon.com/dp/0262527952)) 25 | 26 | ## Theory 27 | 28 | See also: [Logic and Discrete Math](LogicDiscrete.md) 29 | 30 | ### General 31 | 32 | * Sipser, 2012 (3e) / 2006 (2e) / 1996 (1e). *Introduction to the Theory of Computation* 33 | 34 | This is the standard intro to CS theory at many (probably most) universities. 35 | The latest edition is very expensive (even used). Older editions are generally 36 | good alternatives, because in newer editions Sipser added some new sections 37 | but he didn't revise the old ones much. 38 | 39 | * Hopcroft, Ullman, 1979. *Introduction to Automata Theory, Languages and Computation* 40 | * Hopcroft, Motwani, Ullman, 2006. *Introduction to Automata Theory, Languages, and Computation, 3rd Edition* 41 | 42 | A classic and influential introduction to computer science theory. Somewhat more challenging than Sipser. 43 | 44 | * Cohen, 1991. *Introduction to Computer Theory* 45 | 46 | Another classic, this one is known for its readability. Covers formal languages, automata theory and Turing machines. 47 | 48 | * Brookshear, 1989. *Theory of Computation: Formal Languages, Automata, and Complexity* ([1e](https://smile.amazon.com/dp/0805301437)) 49 | 50 | Well-liked for its accessibility. At some times in the past it was hard to find used at a good price, 51 | although currently (2017-09-08) it's pretty affordable. 52 | 53 | * Kinber, Smith, 2001. *Theory of Computing: A Gentle Introduction* 54 | 55 | This is a shorter book, which might be appealing if you're in a hurry. 56 | It covers finite automata, context-free languages, Turing machines, undecidability 57 | and computational complexity, devoting 20-40 pages to each of these topics. 58 | It costs too much, though; for the price, you might as well buy Sipser's 2nd Edition. 59 | 60 | * Kozen, 1997. *Automata and Computability* 61 | 62 | Kozen's intro-level book. Somewhat shorter than others (e.g. Sipser, Hopcroft/Motwani/Ullman). Includes some different topics. Has homework sets, with some select hints and solutions provided. 63 | 64 | * Kozen, 2006. *Theory of Computation* 65 | 66 | Graduate-level. 67 | 68 | * Cutland, 1980. *Computability: An Introduction to Recursive Function Theory* ([1e](https://smile.amazon.com/dp/0521294657)) 69 | 70 | Seems to be the standard introduction to computability. 71 | 72 | * Rogers, 1987. *Theory of Recursive Functions and Effective Computability* ([1e](https://smile.amazon.com/dp/0262680521)) 73 | 74 | More in-depth computability. 75 | 76 | * Davis, Sigal, Weyuker. *Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science* ([2e](https://smile.amazon.com/dp/0122063821)) 77 | 78 | ### Complexity 79 | 80 | * Papadimitriou, *Computational Complexity* 81 | 82 | * Arora and Barak, *Computational Complexity: A Modern Approach* 83 | 84 | ## Data structures and algorithms 85 | 86 | Data structures and algorithms are two sides of the same coin. (In 1976, Niklaus Wirth published a book on the subject called *Algorithms + Data Structures = Programs*.) 87 | 88 | ### Standard topics 89 | 90 | These books cover the basics, that is, the core algorithms that everyone needs to know: sorting, tree traversal, etc. 91 | 92 | * Sedgewick and Wayne, 2011 (4e). *Algorithms* 93 | 94 | This is the latest incarnation of a long series of algorithms books by Robert Sedgewick. 95 | (Wayne joined more recently as co-author.) 96 | There are various other versions that feature specific example languages: 97 | *Algorithms in C++*, *Algorithms in Java*, *Algorithms in C*. 98 | This version uses Java, so I guess it supersedes the previous *Algorithms in Java*. 99 | Its website -- -- 100 | has links to Sedgewick's two free online algorithms courses. 101 | Considering its use of code to illustrate algorithms, its reasonable price and its accompanying 102 | courses, for most people this will probably be the best choice for a first book in algorithms. 103 | And if you're cheap, there are lots of used copies of the various older editions 104 | floating about, since this is a popular series. 105 | (The courses don't require the textbook, by the way. 106 | However, if you're going to be a programmer you really ought to have at least one 107 | algorithms book around anyway, even if it's the only computer book you own.) 108 | 109 | * Cormen, Leiserson, Rivest, Stein, 2009. *Introduction to Algorithms, Third Edition* 110 | 111 | * Cormen, Leiserson, Rivest, Stein, 2001. *Introduction to Algorithms, Second Edition* 112 | * Cormen, Leiserson, Rivest, 1990. *Introduction to Algorithms* 113 | 114 | AKA CLRS. 115 | This is the standard book on algorithms, and it's a big, fat monster: about 1000 large-format pages. 116 | Currently it's pretty reasonably priced, though you can still save money by buying one of the older 117 | editions. There are arguably better approaches for learning the subject, but most people will at 118 | least want to have this one around as a reference. 119 | 120 | * Aho, Hopcroft, Ullman, 1974. *The Design and Analysis of Computer Algorithms* 121 | 122 | A classic book on algorithms. 123 | 124 | * ([3e intl at AbeBooks](http://www.abebooks.com/products/isbn/9780321455369)) 125 | 126 | * Skiena, 2008 (2e). *The Algorithm Design Manual* 127 | 128 | This book focuses somewhat more on how to do and evaluate algorithms vs. how to analyze them mathematically. There is a 1997 1st Edition, but it's hard to find and not a lot cheaper than a used copy of the 2nd Edition. 129 | 130 | * Knuth, *The Art of Computer Programming* 131 | 132 | This collection of bulky tomes is a legendary institution in the field of computer science, as is their author. 133 | It's not the most up-to-date, but it is probably the most complete in-depth examination of algorithms. 134 | I don't think very many people who don't have a Ph.D. in CS have read all of the volumes... 135 | but if you have, it afford certain bragging rights. 136 | 137 | * Manber. *Introduction to Algorithms: A Creative Approach* ([1e](https://smile.amazon.com/dp/0201120372)) 138 | 139 | Focuses on how to design algorithms. 140 | 141 | * Karumanchi. *Data Structure and Algorithmic Thinking with Python: Data Structure and Algorithmic Puzzles* ([1e](https://smile.amazon.com/dp/8192107590)) 142 | 143 | A recent book that takes a relatively practical view (as opposed to mathematical). There are a bunch of mediocre Python-oriented CS books out there, but this one looks to be pretty good. Now that many people are learning Python as a first programming language, there's a pressing need for good books that use Python code to demonstrate concepts, so it's good to see some quality titles finally showing up. 144 | 145 | * Di Pierro. *Annotated Algorithms in Python: with Applications in Physics, Biology, and Finance* 146 | 147 | Another practical Python algorithms book. Covers an impressively wide variety of algorithms, including the basics (data structures, searching and sorting), numerical methods, probability and statistics, random numbers and distributions, Monte Carlo simulations, and parallel algorithms. 148 | 149 | * Groner. *Learning JavaScript Data Structures and Algorithms* ([At PACKT](https://www.packtpub.com/application-development/learning-javascript-data-structures-and-algorithms), [At Amazon](https://smile.amazon.com/dp/1783554878)) 150 | 151 | If Javascript is the only language you know, then you'll need a Javascript-oriented book. This looks like a decent one. 152 | 153 | * Okasaki. *Purely Functional Data Structures* ([1e](https://smile.amazon.com/dp/0521663504)) 154 | * Aho, Ullman, Hopcroft. *Data Structures and Algorithms* ([1e](https://smile.amazon.com/dp/0201000237)) 155 | * Brass. *Advanced Data Structures* ([1e](https://smile.amazon.com/dp/0521880378)) 156 | 157 | ### Specialized algorithms 158 | 159 | These focus on some more specialized areas of algorithms. 160 | 161 | * Motwani and Raghavan, 1995. *Randomized Algorithms* 162 | * Mitzenmacher and Upfal, 2005. *Probability and Computing: Randomized Algorithms and Probabilistic Analysis* 163 | 164 | * Papadimitriou and Steiglitz, 1982. *Combinatorial Optimization: Algorithms and Complexity* (c) 165 | 166 | There's a 1998 Dover edition, which has some corrections but isn't substantially different from the original 1982 version. This book has a unique choice of topics. It starts out with the linear programming problem and the simplex algorithm, a topic usually covered more in applied mathematics. Then, about halfway through, it switches gears and begins to look at graph algorithms. The point, as expressed in the introduction, is to look at the similarities between these continuous and discrete optimization problems, and how the fine differences between them result in dramatic differences in computational complexity. Thus, I think it can be said that, in a sense, this book teaches algorithms as a means to the end of understanding complexity. 167 | 168 | * Bird. *Pearls of Functional Algorithm Design* ([1e](https://smile.amazon.com/dp/0521513383)) 169 | 170 | * Petkovsek, Wilf, Zeilberger. *A = B* ([1e](https://smile.amazon.com/B-Marko-Petkovsek/dp/1568810636)) 171 | 172 | ## Programming language theory 173 | 174 | * Pierce, *Types and Programming Languages* 175 | * Turbak, Gifford, Sheldon, 2008. *Design Concepts in Programming Languages* 176 | * Winskel, *The Formal Semantics of Programming Languages* 177 | * Slonneger, Kurtz, 1995. *Formal Syntax and Semantics of Programming Languages* 178 | * Mitchell, 1996. *Foundations for Programming Languages* 179 | * Pierce (ed), 2004. *Advanced Topics in Types and Programming Languages* 180 | * Stepanov and Rose. *From Mathematics to Generic Programming* ([1e](https://smile.amazon.com/dp/0321942043)) 181 | 182 | ## Compilers and interpreters 183 | 184 | * Krishnamurthi, 2012. *Programming Languages: Application and Interpretation* 185 | 186 | AKA PLAI. 187 | The last version of this incarnation of the book. It goes with an online course, which is available here: 188 | 189 | Together, these make an excellent introduction to the design and implementation of programming languages 190 | using an interpreter. This version of the book (and course) use a Racket language called typed PLAI, 191 | which is a Lisp with strong type inference. 192 | 193 | * Krishnamurthi, 2015. *Programming and Programming Languages* 194 | 195 | From a glance, it looks to me like this is essentially a newer PLAI, retitled and revamped to use 196 | a new implementation language, Pyret. 197 | 198 | This book is under constant revision. Currently the latest stable version is here: 199 | 200 | 201 | * Friedman, Wand, Haynes. *Essentials of Programming Languages* 202 | * Friedman, Wand, Haynes, 1992. *Essentials of Programming Languages* ([1e](https://smile.amazon.com/dp/0262061457), [1e at AbeBooks](http://www.abebooks.com/products/isbn/9780262061452)) 203 | * Friedman, Wand, Haynes, 2001. *Essentials of Programming Languages* ([2e](https://smile.amazon.com/dp/0262062178)) 204 | * Friedman, Wand, 2008. *Essentials of Programming Languages* ([3e](https://smile.amazon.com/dp/0262062798)) 205 | 206 | An more in-depth book about writing interpreters in Scheme. Shriram Krishnamurthi turned me onto this one. 207 | I have the first edition, which is a classic and can often be bought used for under $10. I don't 208 | know how the later editions stack up. Judging from some online reviews, the first might really be the best. 209 | 210 | First edition search info: 211 | 212 | * MIT Press: ISBN 0-262-06145-7 213 | * McGraw-Hill: ISBN 0-07-033442-9 214 | * On Amazon: ASIN 0262061457 215 | 216 | * Aho, Sethi, Ullman, 2006. *Compilers: Principles, Techniques, and Tools, Second Edition* 217 | * Aho, Sethi, Ullman, 1986. *Compilers: Principles, Techniques, and Tools* 218 | 219 | AKA "The Dragon Book" due to its well-known cover illustration. 220 | (1e is "the red dragon book", 2e is "the purple dragon book".) 221 | This is the standard book in the field of compilers, both as an introduction and as a reference. 222 | 223 | * Aho and Ullman, 1977. *Principles of Compiler Design* 224 | 225 | AKA "the green dragon book". 226 | This one is obviously very out-of-date, but the basics are still relevant. 227 | It was well-loved in its day. 228 | 229 | * Cooper and Torczon, 2011. *Engineering a Compiler, Second Edition* 230 | * Cooper and Torczon, 2003. *Engineering a Compiler* 231 | 232 | AKA EAC. 233 | Another beginning-to-end introduction to compiler development. 234 | The 2nd Edition is the most up-to-date compiler book available. 235 | It's the main competitor to The Dragon Book. 236 | 237 | * Mak, 2011. *Writing Compilers and Interpreters: A Software Engineering Approach* (using Java) 238 | * Mak, 1996. *Writing Compilers and Interpreters: An Applied Approach Using C++* 239 | * Mak, 1991. *Writing Compilers and Interpreters: An Applied Approach* (using C) 240 | 241 | Another introduction to compiler writing that focuses more on high-level issues. 242 | The approach is to start out writing an interpreter, then turn it into a compiler. 243 | Mak's books are generally praised for their hands-on approach with concrete code 244 | listings. 245 | 246 | * Appel, 1998. *Modern Compiler Implementation in ML* 247 | 248 | This is a beginning-to-end guide to writing a compiler. The implementation language is Standard ML, 249 | which is a very good language for writing compilers. By the end of the first half of the book, you 250 | have a working compiler. The second half covers advanced topics such as garbage collection, 251 | dataflow analysis and SSA form. I'm not sure how well this would work as a first book on compilers, 252 | but it's very nice as a view of how compilers work from a functional programming perspective, 253 | after you've gone through one of the more standard introductory books. 254 | 255 | * Scott 2015 (4e), 2009 (3e), 2005 (2e), 1999 (1e). *Programming Language Pragmatics* 256 | 257 | This book won't teach you how to build a compiler or interpreter, but it's a great reference on 258 | lots of topics that come up when designing and implementing them. As such, it's a good *second* 259 | book on the subject. 260 | 261 | * Muchnick, 1997. *Advanced Compiler Design and Implementation* 262 | 263 | A guide to more advanced techniques for code analysis and generation. 264 | It focuses more on optimization topics that can't be covered in a first book on compilers. 265 | 266 | * Allen and Kennedy, 2001. *Optimizing Compilers for Modern Architectures: A Dependence-based Approach* 267 | 268 | Focuses on data dependence, vectorization and parallelism. 269 | Very important for taking advantage of the power of modern CPUs. 270 | 271 | * Wolfe, 1996. *High Performance Compilers for Parallel Computing* 272 | 273 | Similar coverage to Allen and Kennedy (but less in-depth), also focuses on data dependence, vectorization and parallelism. 274 | Wolfe also discusses parallelism across multiple machines. 275 | 276 | * Appel, 1992. *Compiling with Continuations* 277 | 278 | This is a book about about continuation-passing style as it applies to compiling functional languages. 279 | (In the context of interpreters, CPS is dicussed in PLAI and EOPL.) One of the nice things about this 280 | book is that, in large part, it describes the design of Standard ML of New Jersey 281 | (AKA SML/NJ: a popular implementation of Standard ML). 282 | Since SML/NJ is open source, you can go to and 283 | see a working example of many of the principles described in the book. 284 | 285 | * Jones, Hosking, Moss, 2011. *The Garbage Collection Handbook: The Art of Automatic Memory Management* 286 | * Jones, Lins, 1996. *Garbage Collection: Algorithms for Automatic Dynamic Memory Management* 287 | 288 | The main reference on garbage collection. 289 | 290 | ## Numerical methods 291 | 292 | ### General 293 | 294 | * Hamming, 1987. *Numerical Methods for Scientists and Engineers* 295 | * Nocedal and Wright, 2006. *Numerical Optimization* 296 | * Isaacson and Keller, 1966. *Analysis of Numerical Methods* 297 | * Higham, 2002 (2e). *Accuracy and Stability of Numerical Algorithms* 298 | * Meikle, 2004. *A New Twist to Fourier Transforms* 299 | * Brigham, 1988. *The Fast Fourier Transform and Its Applications* 300 | * Trefethen, 2012, *Approximation Theory and Approximation Practice* 301 | * Hoffman and Frankel. *Numerical Methods for Engineers and Scientists* ([2e/2001](https://smile.amazon.com/dp/0824704436)) 302 | * Nocedal and Wright. *Numerical Optimization* ([2e](https://smile.amazon.com/dp/0387303030), [1e](https://smile.amazon.com/dp/0387987932)) 303 | * Numerical Recipes: [http://numerical.recipes/](http://numerical.recipes/) 304 | 305 | ### Linear algebra 306 | 307 | - Trefethen and Bau. *Numerical Linear Algebra* ([1e/1997](https://smile.amazon.com/dp/0898713617/)) 308 | - Watkins. *Fundamentals of Matrix Computations* ([3e](https://smile.amazon.com/dp/0470528338/)) 309 | - Stewart. *Matrix Algorithms: Volume I: Basic Decompositions* ([1e](https://smile.amazon.com/dp/0898714141/)) 310 | - Stewart. *Matrix Algorithms, Volume II: Eigensystems* ([1e](https://smile.amazon.com/dp/0898715032/)) 311 | - Demmel. *Applied Numerical Linear Algebra* ([1e](https://smile.amazon.com/dp/0898713897/)) 312 | - Golub and Van Loan. *Matrix Computations* ([4e/2012](https://smile.amazon.com/dp/1421407949), [3e/1996](https://smile.amazon.com/dp/0801854148), [2e/1989](https://smile.amazon.com/dp/0801837391)) 313 | 314 | ## Databases 315 | 316 | * Elmasri and Nevathe. *Fundamentals of Database Systems* ([7e/2015](https://smile.amazon.com/dp/0133970779), [6e/2010](https://smile.amazon.com/dp/0136086209), [5e/2006](https://smile.amazon.com/dp/0321369572)) 317 | 318 | * Ullman and Widom. *A First Course in Database Systems* ([3e/2007](https://smile.amazon.com/dp/013600637X)) 319 | 320 | * Ullman. *Principles of Database & Knowledge-Base Systems* 321 | * *Vol. 1: Classical Database Systems* ([1e/1990](https://smile.amazon.com/dp/0716781581)) 322 | * *Vol. 2: The New Technologies* ([1e/1989](https://smile.amazon.com/dp/071678162X)) 323 | 324 | * Abiteboul, Hull, Vianu. *Foundations of Databases: The Logical Level* ([1e/1994](https://smile.amazon.com/dp/0201537710)) 325 | 326 | AKA The Alice Book. 327 | 328 | * Garcia-Molina, Ullman, Widom. *Database Systems: The Complete Book* ([1e/2001](https://smile.amazon.com/dp/0130319953)) 329 | 330 | * Gray and Reuter. *Transaction Processing: Concepts and Techniques* ([1e/1992](https://smile.amazon.com/dp/1558601902)) 331 | 332 | * Bernstein and Newcomer. *Principles of Transaction Processing* ([2e/2009](https://smile.amazon.com/dp/1558606238)) 333 | 334 | * Maier. *Theory of Relational Databases* ([1e/1983](https://smile.amazon.com/dp/0914894420)) 335 | 336 | * Hellerstein and Stonebraker (eds). *Readings in Database Systems* ([4e/2005](https://smile.amazon.com/dp/0262693143)) 337 | 338 | ## Cryptography 339 | 340 | ### Practical 341 | 342 | * Ferguson, Schneier, Kohno. *Cryptography Engineering: Design Principles and Practical Applications* ([1e/2010](https://smile.amazon.com/dp/0470474246)) 343 | 344 | * Ferguson and Schneier. *Practical Cryptography* ([1e/2003](https://smile.amazon.com/dp/0471223573)) 345 | 346 | A good starting book in crytography. The 2010 book is essentially the second edition of the 2003 one. 347 | 348 | * Schneier. *Applied Cryptography: Protocols, Algorithms, and Source Code in C* ([2e/1996](https://smile.amazon.com/dp/0471117099), [20th Anniversary HC](https://smile.amazon.com/dp/1119096723)) 349 | 350 | The 20th Anniversary edition is just a hardcover reissue of the 1996 second edition, not an update on the content. This is a classic text in cryptography, but the fact that it's 20 years old limits its usefulness. It's more in-depth than Ferguson and Schneier, though. 351 | 352 | * Paar, Pelzl, Preneel. *Understanding Cryptography: A Textbook for Students and Practitioners* ([1e/2010](https://smile.amazon.com/dp/3642041000)) 353 | 354 | * Katz, Lindell. *Introduction to Modern Cryptography* ([2e/2014](https://smile.amazon.com/dp/1466570261)) 355 | 356 | ### Mathematical 357 | 358 | * Klein. *A Cryptography Primer: Secrets and Promises* ([1e](https://smile.amazon.com/dp/1107603455)) 359 | 360 | A short conceptual introduction to cryptography that focuses on the mathematics, but has little in the way of prerequisites. It works through the necessary mathematical topics and then gives an overview of major real-world cryptography systems. 361 | 362 | * Koblitz. *A Course in Number Theory and Cryptography* ([2e](https://smile.amazon.com/dp/0387942939)) 363 | 364 | Assumes an introductory course in number theory. Major topics are public key cryptosystems, primality and factoring, and elliptic curves. 365 | 366 | * Koblitz et al. *Algebraic Aspects of Cryptography* ([1e](https://smile.amazon.com/dp/3540634460)) 367 | 368 | Prereqs include abstract algebra, number theory, algorithms and computational complexity. Covers hidden monomial, combinatorial-algebraic and elliptic and hyperelliptic cryptosystems. An appendix introduces hyperelliptic curves. 369 | 370 | ## Operating Systems 371 | 372 | ### General introductions 373 | 374 | * Stallings. *Operating Systems: Internals and Design Principles* ([8e/2014](https://smile.amazon.com/dp/0133805913), [7e/2011](https://smile.amazon.com/dp/013230998X)) 375 | * Tanenbaum and Bos. *Modern Operating Systems* ([4e/2014](https://smile.amazon.com/dp/013359162X), [3e/2007](https://smile.amazon.com/dp/0136006639)) 376 | * Silberschatz, Galvin, Gagne. *Operating System Concepts* ([9e/2012](https://smile.amazon.com/dp/1118063333), [8e/2008](https://smile.amazon.com/dp/0470128720), [7e/2004](https://smile.amazon.com/dp/0471694665)) 377 | 378 | ### Implementation 379 | 380 | * Tanenbaum and Woodhull. *Operating Systems Design and Implementation* (The MINIX book) ([3e/2006](https://smile.amazon.com/dp/0131429388)) 381 | 382 | ### Specific systems 383 | 384 | * Bach. *The Design of the UNIX Operating System* ([1e/1986](https://smile.amazon.com/dp/0132017997)) 385 | 386 | A classic book that explains the UNIX design philosophy. In its specifics, it is outdated, but it remains important because the UNIX philosophy has been so important in the development of software. 387 | 388 | * Love. *Linux Kernel Development* ([3e](https://smile.amazon.com/dp/0672329468)) 389 | 390 | * McKusick, Neville-Neil, Watson. *The Design and Implementation of the FreeBSD Operating System* ([2e/2014](https://smile.amazon.com/dp/0321968972)) 391 | 392 | * Comer. *Operating System Design: The Xinu Approach* ([2e](https://smile.amazon.com/dp/1498712436)) 393 | 394 | ### Systems programming in userspace 395 | 396 | * Kernighan and Pike. *The Unix Programming Environment* ([1e/1983](https://smile.amazon.com/dp/013937681X)) 397 | 398 | This one is similar to Bach's *The Design of the UNIX Operating System* in that the software it describes is obsolete, but the principles are still very influential. 399 | 400 | * Stevens and Rago. *Advanced Programming in the UNIX Environment* ([3e](https://smile.amazon.com/dp/0321637739)) 401 | 402 | * Kerrisk. *The Linux Programming Interface: A Linux and UNIX System Programming Handbook* ([1e](https://smile.amazon.com/dp/1593272200)) 403 | 404 | * Stevens, Fenner, Rudoff. *Unix Network Programming, Volume 1: The Sockets Networking API* ([3e](https://smile.amazon.com/dp/0131411551)) 405 | 406 | * Stevens. *UNIX Network Programming, Volume 2: Interprocess Communications* ([2e](https://smile.amazon.com/dp/0130810819)) 407 | 408 | * Stevens. *UNIX Network Programming* ([1e](https://smile.amazon.com/dp/0139498761)) 409 | 410 | The original version of the two-volume second edition listed above. 411 | 412 | * Fall and Stevens. *TCP/IP Illustrated, Vol. 1: The Protocols* ([2e/2011](https://smile.amazon.com/dp/0321336313), [1e/1993 [Stevens only]](https://smile.amazon.com/dp/0321336313)) 413 | * Wright and Stevens. *TCP/IP Illustrated, Vol. 2: The Implementation* ([1e/1995](https://smile.amazon.com/dp/020163354X)) 414 | * Stevens. *TCP/IP Illustrated, Vol. 3: TCP for Transactions, HTTP, NNTP, and the UNIX Domain Protocols* ([1e/1996](https://smile.amazon.com/dp/0201634953)) 415 | 416 | * Bryant and O'Hallaron. *Computer Systems: A Programmer's Perspective* ([3e/2015](https://smile.amazon.com/dp/013409266X), [2e/2010](https://smile.amazon.com/dp/0136108040), [1e/2002](https://smile.amazon.com/dp/013034074X)) 417 | 418 | ## Hardware 419 | 420 | * Patterson and Hennessy. *Computer Organization and Design: The Hardware/Software Interface* ([5e/2013](https://smile.amazon.com/dp/0124077269), [4e/2008](https://smile.amazon.com/dp/0123747503), [3e revised/2007](https://smile.amazon.com/dp/0123706068), [2e/1997](https://smile.amazon.com/dp/1558604286)) 421 | 422 | * ARM Edition ([1e/2016](https://smile.amazon.com/dp/0128017333)) 423 | 424 | * Hennessy and Patterson. *Computer Architecture: A Quantitative Approach* ([5e/2011](https://smile.amazon.com/dp/012383872X), [4e/2006](https://smile.amazon.com/gp/product/0123704901), [3e/2002](https://smile.amazon.com/dp/1558605967), [2e/1996](https://smile.amazon.com/dp/1558603298)) 425 | 426 | * Stokes. *Inside the Machine: An Illustrated Introduction to Microprocessors and Computer Architecture* ([1e/2006](https://smile.amazon.com/dp/1593276680)) 427 | 428 | * Weste and Harris. *CMOS VLSI Design: A Circuits and Systems Perspective* ([4e](https://smile.amazon.com/dp/0321547748)) 429 | 430 | * Shen and Lipasti. *Modern Processor Design: Fundamentals of Superscalar Processors* ([1e/2013](https://smile.amazon.com/dp/1478607831)) 431 | 432 | * Harris and Harris. *Digital Design and Computer Architecture* ([2e/2012](https://smile.amazon.com/dp/0123944244)) 433 | 434 | * Dubois (Author), Murali Annavaram (Author), Per Stenström. *Parallel Computer Organization and Design* ([1e/2012](https://smile.amazon.com/dp/0521886759)) 435 | 436 | * Culler, Singh, Gupta. *Parallel Computer Architecture: A Hardware/Software Approach* ([1e](https://smile.amazon.com/dp/1558603433)) 437 | 438 | * Jacob, Ng, Wang. *Memory Systems: Cache, DRAM, Disk* ([1e/2007](https://smile.amazon.com/dp/0123797519)) 439 | 440 | TODO: Systems, FP, AI 441 | -------------------------------------------------------------------------------- /Calculus.md: -------------------------------------------------------------------------------- 1 | ## Calculus 2 | 3 | ### Standard calculus textbooks 4 | 5 | These books are those designed to be the required textbook for a standard high school or university calculus course. Many of them have had a large number of revisions, which makes it likely that you can find slightly older but still perfectly useful copies on the used market. They try to have everything -- proofs, intuitive explanations, illustrations, problems -- but they aren't necessarily great at anything. These books are widely derided by math majors, though I suspect this to be in part motivated by elitism and by grad students' dislike of teaching lower-level math courses. In any case, these are useful even if you just want a cheap source of problems to practice with. 6 | 7 | The OpenStax series follows a very common sequencing of topics, which I list here as a representative of what you can expect to find in the books in this section. OpenStax splits these into three separate books, but most series combine them all into one huge book of about 1000 pages. It's also common to see 1 & 2 combined, and a separate book for 3. 8 | 9 | - Volume 1: functions, limits, derivatives, integration. 10 | - Volume 2: [more] integration, differential equations, sequences and series, parametric equations, polar coordinates. 11 | - Volume 3: parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, second-order differential equations. 12 | 13 | Here are some books in this category, including the most popular ones that I 14 | know of. I've tried to link mainly to the best-priced editions so you can get 15 | a book for $5-10 (though prices change). 16 | 17 | - OpenStax: Strang, Herman et al. *Calculus*. (**FREE ONLINE**: [Vol 1](https://openstax.org/details/calculus-volume-1); [Vol 2](https://openstax.org/details/calculus-volume-2); [Vol 3](https://openstax.org/details/calculus-volume-3)) 18 | - Strang, *Calculus* (**FREE ONLINE**: [Website](http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/), [Direct link to PDF](http://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf)) 19 | - Simmons. *Calculus with Analytic Geometry* ([2e](https://smile.amazon.com/dp/0070576424)) 20 | - Stewart. *Calculus: Early Transcendentals* ([5e](https://www.amazon.com/dp/0534393217)) -- Has huge adoption in both high schools and universities. 21 | - Leithold. ([TC7](https://www.amazon.com/dp/0673469131); [TCWAG 6](https://www.amazon.com/dp/0060441070)) -- I've seen Louis Leithold credited as the creator of the modern "standard" calculus textbook. 22 | - Larson, Hostetler, Edwards. *Calculus* ([8e](https://www.amazon.com/dp/061850298X/); [7e](https://www.amazon.com/dp/0618141804); [6e](https://www.amazon.com/dp/0395869749)) 23 | - Thomas et al. *Thomas' Calculus* ([12e](https://smile.amazon.com/dp/0321587995); [Upd 10e](https://smile.amazon.com/dp/0201755270); [9e](https://smile.amazon.com/dp/0201531747)) -- Thomas retired in 1978, and editions since then have different co-authors, principally Ross Finney. 24 | - Lial, Greenwell et al. *Calculus with Applications* ([9e](https://www.amazon.com/dp/0321421329)) 25 | - Anton, Bivens and Davis. *Calculus* ([7e](https://www.amazon.com/dp/047138156X); [7e Student Resource Manual](https://www.amazon.com/dp/0471441724); [9e multivariable](https://www.amazon.com/dp/0470183462)) 26 | - Marsden and Weinstein. *Calculus* (Vol I: [2e](https://smile.amazon.com/dp/0387909745); Vol II: [2e](https://smile.amazon.com/dp/0387909753); Vol III: [2e](https://smile.amazon.com/dp/0387909850)) 27 | - Rogawski. *Calculus: Early Transcendentals* ([2e](https://smile.amazon.com/dp/1429208384)) 28 | - Briggs and Cochran. *Calculus: Early Transcendentals* ([1e](https://smile.amazon.com/dp/0321570561)) 29 | - Bittinger and Ellenbogen. *Calculus and Its Applications* ([9e](https://smile.amazon.com/dp/0321395344)) 30 | 31 | ### Elite calculus textbooks 32 | 33 | These are books that math majors get enthusiastic about. They are typically used in elite universities and honors courses. They emphasize theory from the ground up beginning with the real number system, but they have fewer calculation problems and applications problems (no applications, in some cases). Note that many, maybe most students who read these books do not actually *start* calculus with them: often they've seen calculus before, maybe they've even had a course or two. 34 | 35 | - Spivak, *Calculus* ([4e](https://smile.amazon.com/dp/0914098918); [3e](https://smile.amazon.com/dp/0521867444); [3e/4e answer book](https://smile.amazon.com/dp/0914098926)) 36 | 37 | Spivak is the most revered of this class of textbooks. It's also the most current: its fourth edition was published in 2008. Spivak has a chatty, conversational style. The book begins by establishing the properties of the real number system, and covers limits, differential and integral calculus, and infinite sequences. Unlike the books that follow, Spivak does not deal with calculus of several variables, so you need another book for that. (He has written a book on that subject, *Calculus on Manifolds*, but it's not considered an introductory book.) Spivak's book has been called an introduction to analysis; you might also call it "calculus for mathematicians". 38 | 39 | - Apostol, *Calculus*, volumes I and II ([Vol I](https://smile.amazon.com/dp/0471000051), [Vol I intl](https://smile.amazon.com/dp/8126515198/), [Vol II](https://smile.amazon.com/dp/0471000078), [Vol II intl](https://smile.amazon.com/dp/8126515201)) 40 | 41 | Apostol is, according to my own rather cursory research, the most widely used of this class of textbooks in college classrooms. Volume I in particular is excellent. The language is much more typical "math-speak" than Spivak's, but the approaches to the material are unusual. Apostol begins with integration before covering limits and differential calculus. This approach works, but it is incovenient if you're trying to use it in combination with another textbook or an online course, since almost all other courses follow the order limits-derivatives-integrals. Apostol's problem sets are excellent, perhaps the best of the bunch. Chapter 1 in particular is a crash course in proof by induction that will very quickly get you comfortable with manipulating sums. 42 | 43 | Volume II introduces linear algebra and calculus of several variables. It seems to be regarded as not as good as Volume I, particularly because its presentation of linear alegebra is dated. However, it does cover some interesting topics not often seen in a calculus textbook: systems of differential equations, probability, and numerical analysis (i.e. approximation methods). 44 | 45 | The standard edition of these books is, unfortunately, exhorbitantly expensive. However, at least the physical quality of the books is extremely good (the one I have is, at least). 46 | 47 | - Courant, *Differential and Integral Calculus*, volumes I and II 48 | 49 | - Courant (Wiley 2nd edition). [Vol I](https://smile.amazon.com/dp/0471608424) [Vol II](https://smile.amazon.com/dp/0471178535) 50 | - Courant and John (Springer). [Vol I](https://smile.amazon.com/gp/product/354065058X), [Vol II/1](https://smile.amazon.com/gp/product/3540665692), [Vol II/2](https://smile.amazon.com/gp/product/3540665706/) 51 | - Courant (original). [Vol II](https://smile.amazon.com/dp/487187835X) 52 | - Courant (1937/1936 Blackie edition, printed 1961). At Archive.org: [Vol I](https://archive.org/details/DifferentialIntegralCalculusVolI), [Vol II](https://archive.org/details/DifferentialIntegralCalculusVol2) 53 | 54 | Richard Courant, who died in 1972, was a highly respected German-American mathematician. With Herbert Robbins, he also wrote *What is Mathematics?*, a remarkable work that attempts to explain a large swathe of mathematics to a popular audience. This calculus textbook is particularly noted for its wealth of physics applications, making it by far the most "applied" of this group. However, its problems are also notoriously difficult, so much so that they're not really appropriate for a learner at this level, at least not without a supplement of easier problems to practice with. 55 | 56 | Since Courant has been dead for several decades, a newer edition was published (by Springer) with Fritz John as co-author. That edition is also highly respected. The most notable difference is that Courant and John splits Volume II into two parts and adds several sections of new material. 57 | 58 | - Shahriari, *Approximately Calculus* ([1e](https://smile.amazon.com/dp/0821837508)) 59 | 60 | A more recent book of this style. It's intended as a second book on calculus. It's full of difficult problems that push your theoretical understanding of calculus, approaching the topic in unusual ways. 61 | 62 | ### Other textbooks of note 63 | 64 | These books don't fit cleanly into the categories that I described above. 65 | 66 | #### Intuitive approaches 67 | 68 | These take the attitude that emphasis on rigorous proofs gets in the way of understanding calculus. 69 | 70 | - Ash and Ash, *The Calculus Tutoring Book* ([1e paperback](https://www.amazon.com/dp/0780310446) [1e hardcover](https://www.amazon.com/dp/0879421835)) 71 | 72 | This book just doesn't bother with theorems or proofs unless they are necessary. It focuses on giving you an intuitive grasp of calculus. I like it a lot. I wouldn't advocate it as your only book on calculus, but I think it would make a very good *first* book. It covers the standard calculus curriculum as I decribed in the "Standard calculus textbooks" section above. Although it focuses heavily on pedagogy, I think that this may *not* be a good book "for dummies", so to speak. It may be that stronger math students are the ones who benefit the most from this approach, because they are used to learning by understanding rather than by memorizing rules. Though I mention that proofs are largely dispensed with here, they are not entirely absent: I found that, when they were included, it was most often in support of a statement that I wasn't sure if I believed, which seems the perfect balance. Doesn't cover a few standard topics, such as differential equations or parametric equations. The paperback seems a bit flimsy, so if you're planning to use this you might want to get the hardcover edition. This book is out of print, so get a used copy while you still can! 73 | 74 | - Thompson and Gardner, *Calculus Made Easy* ([Revised](https://smile.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480)) 75 | 76 | An intuitive introduction to calculus. This isn't thorough enough to be a course textbook, but it makes a good companion to a textbook. It's for someone who's just beginning calculus. The original version (by just Thompson) is in the public domain. It's shorter and some people feel that it does a better job of keeping things simple. Keep in mind that it's old! It was published in 1914. Its casual style emphasizes its old-fashionedness. Some might find this charming, others annoying. You can get it online here: 77 | 78 | - Kline, *Calculus: An Intuitive and Physical Approach* ([Dover](https://smile.amazon.com/dp/0486404536)) 79 | 80 | The title pretty much says what this is. It's older (originally published in 1967, updated in 1977), and was written by Morris Kline, a prolific writer on mathematics (and critic of math education) who authored several books for a popular audience. 81 | 82 | - Blåsjö. *Intuitive Infinitesimal Calculus* ([**FREE ONLINE**](http://intellectualmathematics.com/calculus/)) 83 | 84 | Focuses on supporting calculus with geometric and physical explanations, and motivating it with the historical problems that motivated the development of calculus. Problems focus on understanding. Early emphasis on differential equations. 85 | 86 | - Zeldovich and Yaglom. *Higher Math for Beginners* ([Archive.org](https://archive.org/details/ZeldovichYaglomHigherMathematics)) 87 | 88 | ##### Others 89 | 90 | - Thomas, *Calculus and Analytic Geometry* (c) [3rd Alternate](https://smile.amazon.com/dp/B000K1UMJS) 91 | 92 | This entry refers to the original series of textbooks written by George B. Thomas himself, up to the Fourth Edition (1969). As of 2015 they can still be bought used (quite cheap!), and thanks to the durable hardback bindings they used in those days, you can probably still find them in good condition. (Just hope some jerk didn't scribble all over your copy.) Depending on who you ask, the pinnacle of the series was either the 4th Edition or the 3rd Alternate Edition. 93 | 94 | As advertised, there is a strong emphasis here on analytic geometry and applications. Thomas taught at MIT, and this is clearly a "calculus for engineers" approach. 95 | 96 | - The calculus book from [The Art of Problem Solving series](SchoolLevel.md#the-art-of-problem-solving). 97 | 98 | - Lang, *A First Course in Calculus* ([5e](https://smile.amazon.com/dp/0387962018), [Short Calculus](https://smile.amazon.com/dp/0387953272), [4e @AbeBooks](http://www.abebooks.com/products/isbn/9780201041491)) 99 | 100 | Serge Lang is famous for his difficult graduate-level texts in a dozen different subjects, but he has also put his hand to writing a handful of textbooks for lower levels of math. Of those, probably the most successful is this, his calculus book. 101 | 102 | This book is really distinct from all the others here. It is relatively short. It ignores applications to focus on equations, but it is not really a rigorous textbook either. It has proofs, but only the ones that Lang thought were essential. It simply covers the topics of calculus in a clear and straightforward manner. There have been five editions, and each added more material (getting longer), until Lang actually brought back the original edition under the title *Short Calculus*. I have the Fourth Edition. 103 | 104 | Because of its focus on the standard topics without a bunch of fuss over applications, this is currently my preferred reference for anything that it covers. 105 | 106 | - Körner, *Calculus for the Ambitious* ([1e](https://smile.amazon.com/dp/1107063922)) 107 | 108 | CUP's promotion says, "In a lively and easy-to-read style, Professor Körner uses approximation and estimates in a way that will easily merge into the standard development of analysis. By using Taylor's theorem with error bounds he is able to discuss topics that are rarely covered at this introductory level." I haven't seen this book in the flesh yet, but it's inexpensive. 109 | 110 | - Stein. *Calculus in the First Three Dimensions* ([Dover](https://smile.amazon.com/dp/0486801144); [Solutions manual (PDF)](http://www.doverpublications.com/solutions/801144.pdf)) 111 | 112 | - Kiesler. *Elementary Calculus: An Infinitesimal Approach* ([**FREE ONLINE**](https://www.math.wisc.edu/~keisler/calc.html); [Dover](https://smile.amazon.com/dp/0486484521)) 113 | 114 | - Lax and Terrell. *Calculus With Applications* 115 | 116 | ### Free books 117 | 118 | - 119 | - 120 | 121 | ### Online calculus resources 122 | 123 | MIT OCW has a series of online lectures for calculus. The lecturing isn't outstanding, but the material covered is good for the most part. The lectures can be watched on YouTube here: 124 | - 125 | - 126 | 127 | Other online lecture offerings include ones from [Ohio State](https://mslc.osu.edu/online/lessons) and [Khan Academy](https://www.khanacademy.org/math/). Both seemed a bit slow and basic for my taste, whereas MIT's was more my speed, but then again I'd already taken some calculus in high school so I wasn't starting from scratch. 128 | 129 | The University of Wisconsin-Madison also has free calculus texts that you can get online; they don't look at all adequate as stand-alone texts for self study, but they do have problems with some solutions included. Whitman College also has free calculus texts. 130 | 131 | - [UW-Madison calculus students' page](https://www.math.wisc.edu/undergraduate/calcstudentpage), with links to PDFs of the latest texts 132 | - [Source code for the UW-Madison texts](https://github.com/SigurdAngenent/wisconsin-calculus) 133 | - [Whitman College's Community Calculus page](https://www.whitman.edu/mathematics/multivariable/) 134 | - [Fremlin's problems with solutions (several subjects, Latex files)](https://www.essex.ac.uk/maths/people/fremlin/materials/index.htm) 135 | - 136 | 137 | ### Vector calculus 138 | 139 | For multivariate calculus, there seems to be a general consensus that the texts that teach "all" of calculus don't do a great job with it. (Leithold, for example, stops giving so many proofs at that point in the curriculum and states that they belong in a book dedicated to the subject.) The following texts are dedicated to this part of the calculus curriculum in particular (arranged in descending order according to my impression of their usefulness): 140 | 141 | - Hubbard and Hubbard, *Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach* ([5e at Matrix Editions](http://matrixeditions.com/5thUnifiedApproach.html), [5e at Amazon](https://smile.amazon.com/dp/0971576688), [4e at Amazon](https://smile.amazon.com/dp/B008VRPQV2)) 142 | - Schey, *Div, Grad, Curl and All That* ([4e](https://smile.amazon.com/dp/0393925161), [3e](https://smile.amazon.com/dp/0393969975), [2e](https://smile.amazon.com/dp/0393962512), [1e](https://smile.amazon.com/dp/0393093670)) 143 | - Baxandall and Liebeck, *Vector Calculus* ([Dover](https://smile.amazon.com/dp/0486466205)) 144 | - Friedman, *Advanced Calculus* ([Dover](https://smile.amazon.com/dp/0486457958)) 145 | - C. E. Edwards. *Advanced Calculus of Several Variables* ([1e](https://smile.amazon.com/dp/0486683362)) 146 | - H. M. Edwards. *Advanced Calculus: A Differential Forms Approach* ([3e, 2014 reissue](https://www.amazon.com/dp/0817684115), [3e, 1994](https://www.amazon.com/dp/0817637079)) 147 | - Shifrin, *Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds* ([1e](https://smile.amazon.com/dp/047152638X)) 148 | - Corral, *Vector Calculus* ([**FREE ONLINE**](http://mecmath.net/index.html)) 149 | - Marsden and Tromba. *Vector Calculus* ([5e](https://smile.amazon.com/dp/0716749920), [4e](https://smile.amazon.com/dp/0716724324)) 150 | - Colley. *Vector Calculus* ([2e](), [1e](https://smile.amazon.com/dp/0131492047), [2e](https://smile.amazon.com/dp/0131858742)) 151 | - Matthews. *Vector Calculus* ([1e](https://smile.amazon.com/dp/3540761802)) 152 | - Bressoud. *Second Year Calculus: From Celestial Mechanics to Special Relativity* ([1e](https://smile.amazon.com/dp/038797606X)) 153 | - Flanigan and Kazdan. *Calculus Two: Linear and Nonlinear Functions* ([2e](https://smile.amazon.com/dp/0387973885)) 154 | - Bray. *Multivariable Calculus* ([1e at CreateSpace](https://www.createspace.com/4173421), [1e](https://smile.amazon.com/dp/1482550741)) Author's page: 155 | - Shurman. *Calculus and Analysis in Euclidean Space* 156 | - Lax and Terrell. *Multivariable Calculus with Applications* 157 | - Callahan. *Advanced Calculus: A Geometric View* 158 | 159 | *The Feynman Lectures* also discuss vector calculus in the context of electromagnetism, which is supposedly a great way to tie it in with your understanding of the physical, if you already have some background in physics. See [Physics](Sciences.md#physics). 160 | 161 | ### Calculus problem books 162 | 163 | It may be that the problems in whatever textbook you're using don't give you as much practice as you want. One option is to get another textbook and do the problems from that, too. However, there are a number of books dedicated to providing problems. One advantage to these is that they generally tend to give you explanations of how to solve them as well. 164 | 165 | - Demidovich, *Problems in mathematical analysis* [can be found online] 166 | - Maron, *Problems in Calculus of One Variable* (c) 167 | - Mendelson, *Schaum's 3,000 Solved Problems in Calculus* (c) [reportedly has some errors] 168 | - Kelley, *The Humongous Book of Calculus Problems* (c) 169 | - Bluman, *Problem Book for First Year Calculus* 170 | - Jones, *Calculus: 1,001 Practice Problems For Dummies* ([1e](https://smile.amazon.com/dp/111849671X)) -- By PatrickJMT of YouTube fame. 171 | - REA. *The Calculus Problem Solver* ([Unspecified edition](https://smile.amazon.com/dp/0878915052)) 172 | 173 | John Erdman of Portland State University has posted a number of free problem books as PDFs on his website (answers to odd-numbered exercises given): 174 | 175 | This site has links to lots of other sites with problem sets and practice exams: 176 | 177 | ## Differential Equations 178 | 179 | ### Combined 180 | 181 | - Simmons. *Differential Equations with Applications and Historical Notes* ([3e](https://smile.amazon.com/dp/1498702597), [2e](https://smile.amazon.com/dp/0070575401)) 182 | 183 | - Boyce and DiPrima, *Elementary Differential Equations and Boundary Value Problems* ([9e](https://smile.amazon.com/dp/0470383348), [8e](https://smile.amazon.com/dp/0471433381)) 184 | 185 | - Edwards and Penney. *Differential Equations and Linear Algebra* ([2e](https://smile.amazon.com/dp/0131481460)) 186 | 187 | - Edwards, Penney, Calvis. *Differential Equations and Boundary Value Problems: Computing and Modeling* ([5e](https://smile.amazon.com/dp/0321796985), [4e (Edwards/Penney)](https://smile.amazon.com/dp/0131561073)) 188 | 189 | - Piskunov, *Differential and Integral Calculus* (Vol I: [Mir/CBS](https://smile.amazon.com/dp/8123904924); Vol II: [Mir/CBS](https://smile.amazon.com/dp/8123904932)) 190 | 191 | From what I gather, this pair of volumes is legendary for its quality (though problems are too easy), but the physical quality of this edition is terrible. 192 | 193 | ### ODEs 194 | - Tenenbaum, *Ordinary Differential Equations* ([Dover](https://smile.amazon.com/dp/0486649407)) 195 | - Hurewicz, *Lectures on Ordinary Differential Equations* ([Dover](https://smile.amazon.com/dp/0486664201)) 196 | - Coddington, *An Introduction to Ordinary Differential Equations* ([Dover](https://smile.amazon.com/dp/0486659429)) 197 | - Brauer and Nohel. *The Qualitative Theory of Ordinary Differential Equations: An Introduction* ([Dover](https://smile.amazon.com/dp/0486658465)) 198 | - Arnold. *Ordinary Differential Equations* ([MIT Press, tr. Silverman](https://smile.amazon.com/dp/0262510189), [Springer, tr. Cooke](https://smile.amazon.com/dp/3540345639)) - Springer is a later version. 199 | - Coddington and Levinson, *Theory of Ordinary Differential Equations* ([Krieger 1984](https://smile.amazon.com/dp/0898747554)) 200 | - Imhoff, *Differential Equations in 24 Hours: with Solutions and Historical Notes* ([1ed, 2015](https://smile.amazon.com/gp/product/1478765224)) 201 | - Logan. *A First Course in Differential Equations* 202 | 203 | ### PDEs 204 | 205 | #### Basic 206 | 207 | - Strauss. *Partial Differential Equations: An Introduction* ([1e](https://smile.amazon.com/dp/0471548685), [2e](https://smile.amazon.com/dp/0470054565)) 208 | - Farlow. *Partial Differential Equations for Scientists and Engineers* ([Dover](https://smile.amazon.com/dp/048667620X)) 209 | - Logan. *Applied Partial Differential Equations* ([3e](https://smile.amazon.com/dp/3319124927), [2e](https://smile.amazon.com/dp/0387209530)) 210 | - John. *Partial Differential Equations* ([4e](https://smile.amazon.com/dp/0387906096)) 211 | - Bleecker and Csordas. *Basic Partial Differential Equations* ([1e](https://smile.amazon.com/dp/1571460365)) 212 | - Zachmanoglou and Thoe. *Introduction to Partial Differential Equations with Applications* ([Dover](https://smile.amazon.com/dp/0486652513)) 213 | - Asmar. *Partial Differential Equations with Fourier Series and Boundary Value Problems* ([3e Dover](https://smile.amazon.com/dp/0486807371)) 214 | - Hillen, Leonard, van Roessel. *Partial Differential Equations: Theory and Completely Solved Problems* ([1e](https://smile.amazon.com/dp/1118063309)) 215 | - Olver. *Introduction to Partial Differential Equations* 216 | - Logan. *Applied Partial Differential Equations* 217 | 218 | #### Advanced (more prequisites) 219 | 220 | - Vasy. *Partial Differential Equations: An Accessible Route Through Theory and Applications( ([1e](https://smile.amazon.com/dp/1470418819)) 221 | - Gustafson. *Introduction to Partial Differential Equations and Hilbert Space Methods* ([Dover](https://smile.amazon.com/dp/0486612716)) 222 | - Taylor. *Partial Differential Equations* (Vol I: *Basic Theory* [2e](https://smile.amazon.com/dp/1441970541); Vol II: *Qualitative Studies of Linear Equations* [2e](https://smile.amazon.com/dp/1441970517); Vol III: *Nonlinear Equations* [2e](https://smile.amazon.com/dp/1441970487)) 223 | - Evans. *Partial Differential Equations: Second Edition* ([2e](https://smile.amazon.com/dp/0821849743)) 224 | - Folland. *Introduction to Partial Differential Equations* ([2e](https://smile.amazon.com/dp/0691043612)) 225 | - McOwen. *Partial Differential Equations: Methods and Applications* ([2e](https://smile.amazon.com/dp/0130093351)) 226 | 227 | ## Advanced Calculus 228 | 229 | The term "advanced calculus" seems to be somewhat vague. Sometimes it means calculus of several variables, sometimes it means analysis, sometimes it means applications that become possible after you have a couple of years of calculus under your belt. The ones I list here straddle the line between calculus and analysis. 230 | 231 | - Buck. *Advanced Calculus* ([3e](https://smile.amazon.com/dp/1577663020)) 232 | - Hildebrand. *Advanced Calculus for Applications* ([Dover 2e](https://www.amazon.com/dp/0130111899)) 233 | - Widder. *Advanced Calculus* ([Dover](https://smile.amazon.com/dp/0486661032)) 234 | 235 | ## Calculus of variations 236 | 237 | 238 | 239 | 240 | -------------------------------------------------------------------------------- /GeomTopo.md: -------------------------------------------------------------------------------- 1 | 2 | ## Geometry 3 | 4 | There are various English-language editions of Euclid available at archive.org. [Search here](https://archive.org/search.php?query=creator%3A%28euclid%29%20elements&and[]=languageSorter%3A%22English%22). 5 | 6 | ### Euclidean 7 | 8 | #### Introductory 9 | 10 | - Euclid, tr. Heath. *The Elements*. Dover. ([Vol I / Books 1-2](https://smile.amazon.com/dp/0486600882), [Vol II / Books 3-9](https://smile.amazon.com/dp/0486600890), [Vol III / Books 10-13](https://smile.amazon.com/Euclid-Thirteen-Books-Elements-10-13/dp/0486600904)) 11 | - Euclid, tr. Heath. *The Elements* Green Lion Press. ([Single volume](https://smile.amazon.com/dp/1888009195)) 12 | - Euclid books 1-6, tr. Byrne. This one is neat because the diagrams have colors. Archive.org links: https://archive.org/details/firstsixbooksofe00eucl | https://archive.org/details/firstsixbooksel00byrn | https://archive.org/details/firstsixbooksofe00byrn 13 | - Lang and Murrow. *Geometry: A High School Course* ([2e](https://smile.amazon.com/dp/0387966544), [Solutions manual](https://smile.amazon.com/dp/0387941819)) 14 | - Kiselev and Givental. *Kiselev's Geometry* (Vol I: [Sumizdat 1e](https://smile.amazon.com/dp/0977985202); Vol II: [Sumizdat 1e](https://smile.amazon.com/dp/0977985210)) - Look for seller "sumizdat_dot_org", that's the publisher. 15 | - Coxeter. *Introduction to Geometry* ([Wiley 2e](https://smile.amazon.com/dp/0471504580/), [2e HC [OOP]](https://smile.amazon.com/gp/product/0471182834)) 16 | - Birkhoff and Beatley. *Basic Geometry* ([AMS Chelsea ed](https://smile.amazon.com/gp/product/0821821016), [At AMS store](http://bookstore.ams.org/chel-120/); [Manual for Teachers [at AMS store]](http://bookstore.ams.org/chel-34/), [Manual for Teachers [at AbeBooks]](http://www.abebooks.com/products/isbn/9780821826928); [Answer book [at AMS store]](http://bookstore.ams.org/chel-162/), [Answer Book [at AbeBooks]](http://www.abebooks.com/products/isbn/9780828401623)) 17 | - Brannan, Esplen, Gray. *Geometry* (2014, ISBN 978-1118679197, [Worldcat](https://www.worldcat.org/isbn/9781118679197), [Amazon](https://smile.amazon.com/dp/1118679199)) 18 | - Meyer. *Geometry and Its Applications* (2e, 2006: ISBN 978-0123694270, [Worldcat](https://www.worldcat.org/oclc/212425111), [Amazon](https://smile.amazon.com/dp/0123694272)) 19 | - Augros. The Arts of Liberty, *Introductory Geometry and Arithmetic*. ([Web page](https://artsofliberty.udallas.edu/geometry-and-arithmetic/), [PDF](https://artsofliberty.udallas.edu/wp-content/uploads/2017/04/Introductory-Geometry-and-Arithmetic.pdf)) 20 | - Harpur. 1894 interpretation of Euclid. https://www.google.com/books/edition/_/PkHP78BglQMC?hl=en&gbpv=0 21 | - Africk, Elementary College Geometry. This is a typewritten, hand-illustrated text. It introduces two-dimensional geometry, with a focus on finding numerical solutions rather than proving theorems. https://open.umn.edu/opentextbooks/textbooks/elementary-college-geometry 22 | - Lozanovski, A Beautiful Journey Through Olympiad Geometry. Free PDF, form asks for information before downloading. https://www.olympiadgeometry.com/the-book.html 23 | 24 | #### Beyond introductory 25 | 26 | - Coxeter. *Geometry Revisited* ([MAA 1967](https://smile.amazon.com/dp/0883856190/)) 27 | - Johnson. *Advanced Euclidean Geometry* ([Dover](https://smile.amazon.com/dp/0486462374/)) 28 | - Casey, 1886. *A Sequel to the First Six Books of the Elements of Euclid* ([At archive.org](https://archive.org/details/sequeltofirstsix00caserich)) 29 | - Altshiller-Court. *College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle* ([2e Dover](https://smile.amazon.com/dp/0486458059/)) 30 | - Coxeter. *Regular Polytopes* ([3e](https://smile.amazon.com/Regular-Polytopes-H-S-Coxeter/dp/0486614808/)) 31 | - Petrunin. *Euclidean plane and its relatives; a minimalist introduction* (https://arxiv.org/abs/1302.1630) - covers elementary geometry and beyond, assumes knowledge up to basic calculus 32 | 33 | ### Euclidean and non-euclidean 34 | 35 | - Hartshorne. *Geometry: Euclid and Beyond* ([1e](https://smile.amazon.com/dp/0387986502)) 36 | - Moise. *Elementary Geometry From An Advanced Viewpoint* ([3e](https://smile.amazon.com/dp/0201508672), [2e](https://smile.amazon.com/dp/0201047934)) 37 | - Greenberg. *Euclidean And Non-Euclidean Geometries* ([4e](https://smile.amazon.com/dp/0716799480)) 38 | - Coxeter. *Non-Euclidean Geometry* ([6e](https://smile.amazon.com/dp/0883855224/)) 39 | - Hilbert and Cohn-Vossen. *Geometry and the Imagination* ([AMS Chelsea](https://smile.amazon.com/gp/product/0821819984)) 40 | - Leonard, Lewis, Liu, Tokarsky. *Classical Geometry: Euclidean, Transformational, Inversive, and Projective* (1e 1997: [ISBN 978-0760706602](https://www.worldcat.org/isbn/978-0760706602), [Amazon](https://smile.amazon.com/dp/0760706603); 2e 2003: [ISBN 978-1592441303](https://www.worldcat.org/isbn/978-1592441303), [Amazon](https://smile.amazon.com/dp/1592441300)) 41 | - Stillwell. *Numbers and Geometry* (1e, 1997: ISBN 978-0387982892, [Worldcat](https://www.worldcat.org/oclc/468834725), [Amazon](https://smile.amazon.com/dp/0387982892)) 42 | - Stillwell. *The Four Pillars of Geometry* (1e 2005: ISBN 978-0387255309, [Worldcat](https://www.worldcat.org/oclc/209834142), [Amazon](https://smile.amazon.com/dp/0387255303)) 43 | - McDaniel. *Geometry by Construction: Object Creation and Problem-solving in Euclidean and Non-Euclidean Geometries* 44 | 45 | #### Focusing on projective geometry 46 | 47 | - Coxeter. *Projective Geometry* ([2e](https://smile.amazon.com/dp/0387406239/)) 48 | - Cremona, 1885. *Elements Of Projective Geometry* ([At archive.org](https://archive.org/details/elementsproject02cremgoog)) 49 | - Meserve. *Fundamental Concepts of Geometry* ([Dover](https://smile.amazon.com/dp/0486634159)) 50 | - Veblen and Young. *Projective Geometry* (At archive.org: [Vol 1](https://archive.org/details/in.ernet.dli.2015.152722), [Vol 2](https://archive.org/details/in.ernet.dli.2015.461814), [Search](https://archive.org/search.php?query=creator%3A%28veblen%20young%29%20projective%20geometry)) 51 | 52 | ## Computational Geometry 53 | 54 | - de Berg, Cheong, van Kreveld, Overmars. *Computational Geometry: Algorithms and Applications* ([3e](https://smile.amazon.com/dp/3540779736)) 55 | - Edelsbrunner. *A Short Course in Computational Geometry and Topology* ([1e](https://smile.amazon.com/dp/3319059564)) 56 | - O'Rourke. *Computational Geometry in C* ([2e](https://smile.amazon.com/dp/0521649765)) 57 | - Cheng, Dey, Shewchuk. *Delaunay Mesh Generation* ([1e](https://smile.amazon.com/Delaunay-Generation-Chapman-Computer-Information/dp/1584887303)) 58 | - Botsch, Kobbelt, Pauly, Alliez, Levy. *Polygon Mesh Processing Hardcover* ([1e](https://smile.amazon.com/dp/1568814267)) 59 | 60 | ## General Topology 61 | 62 | - Munkres. *Topology* ([2e intl](https://smile.amazon.com/dp/8120320468), [2e](https://smile.amazon.com/dp/B004DX5K5K)) 63 | 64 | The standard text. Also includes basic algebraic topology. 65 | 66 | - Mendelson. *Introduction to Topology* ([3e Dover](https://smile.amazon.com/dp/0486663523)) 67 | 68 | A brief introduction, available cheap. 69 | 70 | - Gamelin and Greene. *Introduction to Topology* ([2e Dover](https://smile.amazon.com/dp/0486406806)) 71 | 72 | Another cheap alternative. One of Alan Hatcher's recommendations. 73 | 74 | - Crossley. *Essential Topology* ([1e corr](https://smile.amazon.com/dp/1852337826)) 75 | 76 | An introductory text with a reputation for easy reading. 77 | 78 | - Willard. *General Topology* ([Dover](https://smile.amazon.com/dp/0486434796)) 79 | 80 | Another affordable introduction. Maybe too much information for a true first book. 81 | 82 | - Jänich. *Topology* ([1e](https://smile.amazon.com/dp/0387908927)) 83 | 84 | Another of Alan Hatcher's recommendations, he calls it "a pleasure to read." 85 | 86 | - Kelley. *General Topology* ([At Archive.org](https://archive.org/details/GeneralTopology), [Springer hardcover 1975](https://www.amazon.com/dp/0387901256), [Ishi Press 2008](https://smile.amazon.com/dp/0923891552), [Van Nostrand 1955](https://smile.amazon.com/dp/B00462BLBA)) 87 | 88 | The classic introduction (1955). 89 | 90 | - Simmons. *Introduction to Topology and Modern Analysis* ([Krieger 2003](https://smile.amazon.com/dp/1575242389)) 91 | 92 | - Croom. *Principles of Topology* ([Dover](https://smile.amazon.com/dp/0486801543)) 93 | 94 | A gentle introduction for beginners. 95 | 96 | - Prasolov. *Intuitive Topology* ([1e](https://smile.amazon.com/dp/0821803565)) 97 | 98 | An extremely gentle introduction for extreme beginners. 99 | 100 | - Steen and Seebach. *Counterexamples in Topology* ([Dover](https://smile.amazon.com/dp/048668735X)) 101 | 102 | - Henle. *A Combinatorial Introduction to Topology* 103 | 104 | Goes straight into algebraic topology with minimal coverage of point-set topology. 105 | 106 | ## Algebraic Topology 107 | 108 | - Hatcher. *Algebraic Topology* (f) ([CUP Paperback](https://smile.amazon.com/dp/0521795400/), [**FREE ONLINE**](https://www.math.cornell.edu/~hatcher/AT/ATpage.html)) 109 | - Bredon. *Topology and Geometry* ([1e](https://smile.amazon.com/Topology-Geometry-Graduate-Texts-Mathematics/dp/0387979263/)) 110 | - Stillwell. *Classical Topology and Combinatorial Group Theory* ([2e](https://smile.amazon.com/dp/0387979700)) 111 | - Rotman. *An Introduction to Algebraic Topology* ([1e](https://smile.amazon.com/dp/0387966781/)) 112 | - Fulton. *Algebraic Topology: A First Course* ([1e](https://smile.amazon.com/dp/0387943277/)) 113 | - May. *A Concise Course in Algebraic Topology* ([1e](https://smile.amazon.com/dp/0226511839)) 114 | - May and Ponto. *More Concise Algebraic Topology: Localization, Completion, and Model Categories* ([1e](https://smile.amazon.com/dp/0226511782)) 115 | - Lee. *Introduction to Topological Manifolds* ([2e](https://smile.amazon.com/dp/1441979395)) 116 | 117 | ## Differential Geometry 118 | 119 | - Pressley. *Elementary Differential Geometry* ([2e/2010](https://smile.amazon.com/dp/184882890X)) 120 | - Tu. *An Introduction to Manifolds* ([2e/2011](https://smile.amazon.com/dp/1441973990)) 121 | - Guillemin and Pollack. *Differential Topology* ([AMS Chelsea](https://smile.amazon.com/dp/0821851934)) 122 | - Millman and Parker. *Elements of Differential Geometry* ([1e](https://smile.amazon.com/dp/0132641437)) 123 | - O'Neill. *Elementary Differential Geometry* ([2e](https://smile.amazon.com/dp/0120887355)) 124 | - Milnor. *Topology from the Differentiable Viewpoint* ([PUP revised](https://smile.amazon.com/dp/0691048339)) 125 | - Kreyszig. *Differential Geometry* ([Dover](https://smile.amazon.com/dp/0486667219)) 126 | - Spivak. *A Comprehensive Introduction to Differential Geometry* (in 6 volumes) ([Vol I, 3e](https://smile.amazon.com/dp/0914098705); [Vol II, 3e](https://smile.amazon.com/dp/0914098713); etc.) 127 | - Guggenheimer. *Differential Geometry* ([Dover](https://smile.amazon.com/dp/0486634337)) 128 | - Bishop & Goldberg. *Tensor Analysis on Manifolds* ([Dover](https://smile.amazon.com/dp/0486640396)) 129 | - Lee. *Introduction to Smooth Manifolds* ([1e](https://smile.amazon.com/dp/0387954481)) 130 | - Lee. *Riemannian Manifolds: An Introduction to Curvature* ([1e](https://smile.amazon.com/dp/0387983228)) 131 | - Do Carmo. *Riemannian Geometry* ([1e](https://smile.amazon.com/dp/0817634908)) 132 | - Do Carmo. *Differential Geometry of Curves and Surfaces* ([2e Dover](https://smile.amazon.com/dp/0486806995), [1e](https://smile.amazon.com/dp/0132125897)) 133 | - Matsumoto. *An Introduction to Morse Theory* ([1e](https://smile.amazon.com/dp/0821810227)) 134 | - Kosinski. *Differential Manifolds* ([Dover](https://smile.amazon.com/dp/0486462447)) 135 | - Lovelock and Rund. *Tensors, Differential Forms, and Variational Principles* ([Dover](https://smile.amazon.com/dp/0486658406)) 136 | - Struik. *Lectures on Classical Differential Geometry* ([Dover](https://www.amazon.com/dp/0486656098)) 137 | - McInerney. *First Steps in Differential Geometry: Riemannian, Contact, Symplectic* 138 | - Tapp. *Differential Geometry of Curves and Surfaces* 139 | 140 | ## Applied and Computational Topology 141 | 142 | - Ghrist. *Elementary Applied Topology* ([At CreateSpace](https://www.createspace.com/4978477), [At Amazon](https://smile.amazon.com/dp/1502880857)) 143 | - Edelsbrunner and Harer. *Computational Topology: An Introduction* ([1e](https://smile.amazon.com/dp/0821849255)) 144 | - Zomorodian. *Topology for Computing* ([1e](https://smile.amazon.com/dp/0521136091)) 145 | - Kaczynski, Mischaikow, Mrozek. *Computational Homology* ([1e](https://smile.amazon.com/dp/0387408533)) 146 | 147 | ## Algebraic geometry 148 | 149 | ### Introductions 150 | - Beltrametti, Carletti, Gallarati, Bragadin. *Lectures on Curves, Surfaces and Projective Varieties* ([1e](https://smile.amazon.com/dp/3037190647/)) 151 | - Garrity et al. *Algebraic Geometry: A Problem Solving Approach* ([1e](https://smile.amazon.com/gp/product/0821893963)) 152 | - Shafarevich, Reid. *Basic Algebraic Geometry 1: Varieties in Projective Space* ([3e](https://smile.amazon.com/dp/3642379559/)) 153 | - Shafarevich, Reid. *Basic Algebraic Geometry 2: Schemes and Complex Manifolds* ([3e](https://smile.amazon.com/dp/3642380093/)) 154 | - Holme. *A Royal Road to Algebraic Geometry* ([1e](https://smile.amazon.com/dp/3642192246/)) 155 | - Fulton. [*Algebraic Curves, an Introduction to Algebraic Geometry*](http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf) 156 | - Gathmann. [Algebraic Geometry (SS 2014)](http://www.mathematik.uni-kl.de/agag/mitglieder/professoren/gathmann/notes/alggeom/) 157 | - Smith, 2014. *Introduction to Algebraic Geometry* ([1e Paperback](https://www.amazon.com/dp/1503381536), [**FREE ONLINE**](http://www.five-dimensions.org/Textbooks/)) 158 | - Vakil. *The Rising Sea: Foundations Of Algebraic Geometry Notes* ([main page](http://virtualmath1.stanford.edu/~vakil/216blog/), [blog](https://math216.wordpress.com/), [Ravi Vakil's homepage](http://virtualmath1.stanford.edu/~vakil/)) 159 | 160 | ### Classical (pre-Grothendieck) 161 | 162 | - Lang, 1958. *Introduction to Algebraic Geometry* ([Martino](https://smile.amazon.com/dp/1614276277)) 163 | - Weil, 1946, 1962. *Foundations of algebraic geometry* ([](https://smile.amazon.com/dp/B0007DO3Q2)) 164 | - Lefschetz, 1953. *Algebraic Geometry* ([Dover](https://smile.amazon.com/dp/0486446115)) 165 | - Hodge and Pedoe, 1947. *Methods of Algebraic Geometry* ([Vol I](https://smile.amazon.com/dp/0521469007), [Vol II](https://smile.amazon.com/gp/product/0521469015), [Vol III](https://smile.amazon.com/dp/0521467756)) 166 | - Baker, 1922-1925. *Principles of Geometry* (At archive.org: [Vol 1](https://archive.org/details/principlesofgeom01bake), [Vol 2](https://archive.org/details/principlesofgeom02bake), [Vol 3](https://archive.org/details/principlesofgeom03bake), [Vol 4](https://archive.org/details/principlesofgeom04bake), [Vol 5](https://archive.org/details/principlesofgeom05bake), [Vol 6](https://archive.org/details/principlesofgeom06bake)) 167 | 168 | ### Beyond 169 | - Hartshorne. *Algebraic Geometry* ([1e](https://smile.amazon.com/dp/0387902449/)) 170 | - Liu. *Algebraic Geometry and Arithmetic Curves* ([1e](https://smile.amazon.com/dp/0199202494/) 171 | - Griffiths, Harris. *Principles of Algebraic Geometry* ([Intl ed @AbeBooks](http://www.abebooks.com/products/isbn/9788126546510)) 172 | - Görtz, Wedhorn. *Algebraic Geometry I, Schemes with Examples and Exercises* ([1e](https://smile.amazon.com/dp/3834806765/)) 173 | - Vakil. [The Rising Sea: Foundations Of Algebraic Geometry Notes](https://math.stanford.edu/~vakil/216blog/) 174 | - Eisenbud and Harris. *3264 and All That: A Second Course in Algebraic Geometry* ([1e](https://smile.amazon.com/dp/1107602726)) 175 | 176 | -------------------------------------------------------------------------------- /IndiaRussia.md: -------------------------------------------------------------------------------- 1 | # India 2 | 3 | 4 | 5 | ## India and Russia 6 | 7 | India and Russia both built reputations in the 20th Century for producing great 8 | mathematicians. What many people in the USA probably don't know is that the two 9 | countries have also been close partners geopolitically, and that one way this 10 | partnership has played out is that Indians have become fans of Russian math 11 | texts. The result is that a large portion of the Russian math texts translated 12 | into English are really only available in the Indian market. 13 | 14 | ## Russian texts 15 | 16 | Site with info about Mir books: 17 | 18 | On the Internet Archive: 19 | 20 | Information about many Soviet publications: 21 | 22 | URSS: 23 | 24 | - https://www.amazon.in/Problem-Book-Algebra-V-Krechmar/dp/9351448320 25 | - https://www.amazon.in/Problems-CALCULUS-ONE-VARIABLE-Maron/dp/9351762599 26 | - https://www.amazon.in/Problems-MATHEMATICS-Hints-Solutions-Govorov/dp/9351762556 27 | - https://www.amazon.in/Problem-Book-MATHEMATICAL-ANALYSIS/dp/9351762548 28 | - https://www.amazon.in/Problem-Book-Algebra-V-Krechmar/dp/9351448320 29 | - https://www.amazon.in/Problems-Mathematics-Solutions-V-Govorov/dp/8123904878 30 | - https://www.amazon.in/Elementary-Mathematics-G-Dorofeev/dp/8123908423 31 | - https://www.amazon.in/Problems-Elementary-Physics-Bukhovtsev/dp/8123910142 32 | 33 | - https://archive.org/details/Problem-Book-In-High-School-Mathematics 34 | 35 | Irodov 36 | - https://www.amazon.in/Problems-GENERAL-PHYSICS-I-Irodov/dp/9351762564 37 | - https://www.amazon.in/Problem-General-Physics-GKP/dp/9351448177 38 | - https://www.amazon.in/Fundamental-Laws-Mechanics-IE-IRODOV/dp/9350943166 39 | - https://www.amazon.in/Basic-Laws-Electromagnetism-IE-IRODOV/dp/9350943182 40 | - https://www.amazon.in/Science-Everyone-Aptitude-Problem-Physics/dp/9350941449 41 | 42 | ## British texts 43 | 44 | Hall and Knight 45 | - https://www.amazon.in/Algebra-Beginners-Hall/dp/9350943204 46 | - https://www.amazon.in/Elementary-Algebra-Schools-H-S-Hall/dp/9350943255 47 | - https://www.amazon.in/SCHOOL-GEOMETRY-H-S-Hall/dp/9350943476 48 | - 49 | - https://www.amazon.in/Higher-Algebra-Knight-ORIGINAL-MASPTERPIECE/dp/9385966677 50 | - https://www.amazon.in/Complete-Solutions-Knights-Algebra-Questions/dp/9351405575 51 | 52 | - Loney, The Elements of Coordinate Geometry. 53 | - [Library of India](https://archive.org/details/in.ernet.dli.2015.136385) 54 | - [U of California](https://archive.org/details/elementscoordin02lonegoog) 55 | 56 | S. L. Loney 57 | - Plane Trigonometry 1: 58 | - The Elements of COORDINATE GEOMETRY Part-1 Cartesian Coordinates: 59 | - The Elements of STATISTICS & DYNAMICS Part-I Statics 60 | - The Elements of STATISTICS & DYNAMICS Part-II Dynamics 61 | 62 | Joseph Edwards 63 | - https://www.amazon.in/Differential-Calculus-Beginners-Joseph-Edwards/dp/9350942461 64 | - https://www.amazon.in/Integral-Calculus-Beginners-Joseph-Edwards/dp/9350941457 65 | - https://www.amazon.in/Integral-Calculus-Beginners-Joseph-Edwards/dp/8174731245 66 | 67 | Misc 68 | - https://www.amazon.in/Higher-Algebra-Barnard/dp/9350943190 69 | - https://www.amazon.in/Skills-Mathematics-TRIGONOMETRY-Main-Advanced/dp/9351761444 70 | 71 | ## Indian publications 72 | 73 | - https://www.amazon.in/Concepts-Physics-1-H-C-Verma/dp/8177091875 74 | - https://www.amazon.in/Concepts-Physics-2-H-C-Verma/dp/8177092324 75 | - https://www.amazon.in/Modern-Approach-Chemical-Calculations-Mukerjee/dp/8177096419 76 | 77 | School books 78 | - https://www.amazon.in/Mathematics-Class-Based-NCERT-Syllabus/dp/9383182490 79 | 80 | JEE prep 81 | - https://www.amazon.in/Play-Graphs-JEE-Main-Advanced/dp/9311126128 82 | - https://www.amazon.in/Understanding-Physics-Main-Advanced-Mechanics/dp/9311125288 83 | - https://www.amazon.in/Differential-Calculus-JEE-Main-Advanced/dp/931112611X 84 | - https://www.amazon.in/Integral-Calculus-JEE-Main-Advanced/dp/9311126225 85 | - https://www.amazon.in/Algebra-Main-Advanced-S-K-Goyal/dp/9311126594 86 | - https://www.amazon.in/Coordinate-Geometry-JEE-Main-Advanced/dp/9311127612 87 | - https://www.amazon.in/Comprehensive-Algebra-Vol-Vinay-Kumar/dp/1259064220 88 | - https://www.amazon.in/Skills-Mathematics-TRIGONOMETRY-Main-Advanced/dp/9351761444 89 | - https://www.amazon.in/Objective-Mathematics-Advanced-Engineering-Examinations/dp/8193233409 90 | 91 | Current NCERT textbooks can be viewed and downloaded here: 92 | 93 | Elementary 94 | - NCERT Math Magic 95 | - Class 1: [Amazon India](https://www.amazon.in/dp/8174504761), [Amazon](https://smile.amazon.com/dp/8174504761) 96 | - Class 1 workbook: 97 | - Class 2: https://www.amazon.in/Math-Magic-Textbook-Mathematics-Class/dp/8174506799 98 | - Class 2 workbook: 99 | - Class 3: https://www.amazon.in/Math-Magic-Textbook-Mathematics-Class/dp/8174505105 100 | - Class 3 workbook: 101 | - https://www.amazon.in/International-Mathematics-Olympiad-Work-Book/dp/9386379864 102 | - https://www.amazon.in/S-Chands-Mental-Mathematics-Class/dp/8121931258 103 | - https://www.amazon.in/BMAs-Olympiad-Mock-Test-20-20/dp/9382058761 104 | - https://www.amazon.in/Class-Learning-Mathematics-Smarter-Life/dp/9385875272 105 | - https://www.amazon.in/New-Composite-Mathematics-Class-2/dp/9352534832 106 | 107 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | CC0 1.0 Universal 2 | 3 | Statement of Purpose 4 | 5 | The laws of most jurisdictions throughout the world automatically confer 6 | exclusive Copyright and Related Rights (defined below) upon the creator and 7 | subsequent owner(s) (each and all, an "owner") of an original work of 8 | authorship and/or a database (each, a "Work"). 9 | 10 | Certain owners wish to permanently relinquish those rights to a Work for the 11 | purpose of contributing to a commons of creative, cultural and scientific 12 | works ("Commons") that the public can reliably and without fear of later 13 | claims of infringement build upon, modify, incorporate in other works, reuse 14 | and redistribute as freely as possible in any form whatsoever and for any 15 | purposes, including without limitation commercial purposes. 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Affirmer understands and acknowledges that Creative Commons is not a 112 | party to this document and has no duty or obligation with respect to this 113 | CC0 or use of the Work. 114 | 115 | For more information, please see 116 | 117 | 118 | -------------------------------------------------------------------------------- /LinearAlgebra.md: -------------------------------------------------------------------------------- 1 | # Linear Algebra 2 | 3 | ## Introductions 4 | 5 | ### Applied focus 6 | 7 | - Strang. *Introduction to Linear Algebra* (with OCW lectures) ([4e](https://smile.amazon.com/dp/0980232716/)) 8 | 9 | The latest incarnation of Gilbert Strang's linear algebra textbook. I haven't seen this one myself, but it goes with his highly-regarded online LA course. It is reportedly somewhat more elementary than his older *Linear Algebra and its Applications*. 10 | 11 | - Strang. *Linear Algebra and its Applications* ([4e](https://smile.amazon.com/Linear-Algebra-Its-Applications-4th/dp/0030105676/), [4e intl](https://smile.amazon.com/Linear-Algebra-Its-Applications-India/dp/8131501728/), [3e](https://smile.amazon.com/Linear-Algebra-Its-Applications-3rd/dp/0155510053/)) 12 | 13 | Strang's older book. 14 | 15 | - Hefferon. ([**FREE ONLINE**](http://joshua.smcvt.edu/linearalgebra/), [Dec 2014 paperback](https://smile.amazon.com/Linear-Algebra-Jim-Hefferon/dp/0989897567/)) 16 | 17 | Jim Hefferon wrote this free (GFDL/CC BY-SA 2.5) linear algebra text [http://joshua.smcvt.edu/linearalgebra/] which is available as a PDF file or as Latex source. It has exercises with worked answers. 18 | 19 | - Klein. *Coding the Matrix* (With Brown/Coursera course; great course but not much use as a stand-alone text. Also, it's not required for the course.) 20 | 21 | - Lay. *Linear Algebra and Its Applications* ([3e upd](https://smile.amazon.com/Linear-Algebra-Applications-Updated-CD-ROM/dp/0321287134/), [4e](https://smile.amazon.com/Linear-Algebra-Its-Applications-4th/dp/0321385179/), [5e](https://smile.amazon.com/Linear-Algebra-Its-Applications-5th/dp/032198238X/)) 22 | 23 | - Poole. *Linear Algebra: A Modern Introduction* ([3e](https://smile.amazon.com/Linear-Algebra-Introduction-Available-Enhanced/dp/0538735457/)) 24 | 25 | A colorful "modern textbook" approach to linear algebra. Don't bother with the 4th Edition, as it's very expensive and largely the same as the Third Edition. 26 | 27 | - Singh. *Linear Algebra: Step by Step* ([1e](https://smile.amazon.com/dp/0199654441)) 28 | 29 | A recent book. Looks like it has a lot of good diagrams (which are often lacking in older textbooks). 30 | 31 | - Meyer. *Matrix Analysis and Applied Linear Algebra Book and Solutions Manual* 32 | 33 | A good book, but expensive. This used to be available online for free, but the author took it down due to unspecified abuses of the license agreement. 34 | 35 | - Andreescu. *Essential Linear Algebra with Applications: A Problem-Solving Approach* ([1e](https://smile.amazon.com/dp/0817643605)) 36 | 37 | ### Abstract focus 38 | 39 | These are texts in the old style, aimed at mathematicians. Some of them are older texts that have stood the test of time. 40 | 41 | - Hoffman and Kunze. *Linear Algebra* ([2e](https://smile.amazon.com/dp/0135367972/), [2e intl ed](https://smile.amazon.com/Linear-Algebra-2nd-Hoffman-Kunze/dp/8120302702/)) 42 | 43 | For many years this was the standard LA textbook, though it seems it's not as popular as it used to be. It has good, thorough coverage of the core of undergraduate linear algebra. It's a bit old, however, and leans toward the abstract. I don't think it even mentions the Singular Value Decomposition (SVD). 44 | 45 | - Shilov. *Linear Algebra* ([Dover ed](https://smile.amazon.com/dp/048663518X/)) 46 | 47 | A Russian approach to linear algebra. Like many Russian textbooks, it jumps right in and makes no attempt to hold your hand. Even though the content may be appropriate for first-time learners, many students in the US won't be prepared for a book like this when they start LA. Also tends toward the abstract and doesn't cover the SVD. Includes hints and solutions for exercises. 48 | 49 | - Friedberg, Insel, Spence. *Linear Algebra* ([4e](https://smile.amazon.com/dp/0130084514/), [4e intl](https://smile.amazon.com/dp/9332549648/), [3e](https://smile.amazon.com/dp/0132338599/)) 50 | 51 | - Lang. *Linear Algebra* ([3e](https://smile.amazon.com/dp/0387964126/), [Solutions](https://smile.amazon.com/dp/0387947604)) 52 | 53 | - Treil. *Linear Algebra Done Wrong* 54 | 55 | The title is a play on Axler's *Linear Algebra Done Right*. Free online at the author's page: 56 | 57 | 58 | - Beezer. *A First Course in Linear Algebra* ([**FREE ONLINE**](http://linear.ups.edu/)) 59 | 60 | Another free (GFDL) linear algebra textbook, by Robert Beezer of University of Puget Sound. There are many experimental aspects in this book, including its style of "numbering" (everything is referred to by alphabetic abbreviations instead of numbers) and its web-oriented organization. I have no idea how this would work as a text but it seems intriguing as a companion to a more traditional text. (If you're going the free route, Hefferon would probably make a good companion.) 61 | 62 | Some calculus books include an introduction to linear algebra. Among these are Apostol's *Calculus* and Hubbard and Hubbard's *Vector Calculus*. (Most calculus books include *some* introduction to linear algebra but it's usually cursory.) 63 | 64 | ## Axler 65 | 66 | I put this book in its own category because it's a bit unique in its appeal. It fills a need that is particular to the current mathematics curriculum. The ordinary intro books these days do not cover enough advanced material for students to comfortably go directly on to the more advanced books listed below. What's more, many students don't have enough exposure to reading and writing proofs yet. Axler's book serves as both a course in abstract linear algebra that covers the essential topics, and a course in proof-reading and proof-writing. However, its contents might be superfluous for someone who started using one of the more thorough introductory books such as Hoffman and Kunze or Shilov. 67 | 68 | - Axler. *Linear Algebra Done Right* ([3e](https://smile.amazon.com/dp/3319110799/), [2e](https://smile.amazon.com/dp/0387982582/), [ERRATA](http://linear.axler.net/)) 69 | 70 | An outstanding introduction to an *abstract* approach to linear algebra. This book is all about proofs, you won't find calculations here. It is intended as a second course in linear algebra, to follow a more computation-oriented course, and I agree that this is its best use. You *could* start LA here, but you'd end up having read a whole book and still not knowing how to solve a linear equation. One of the distinctive things about Axler's approach is that he introduces the theory of eigenvalues without using determinants (preferring instead to use the fundamental theorem of algebra). Determinants are then introduced in the last chapter. Also, the quality of the Third Edition hardcover is supposedly really nice. 71 | 72 | ## Problems 73 | 74 | - Erdman. *Exercises and Problems in Linear Algebra* 75 | - Zhang. *Linear Algebra: Challenging Problems for Students* ([1e](https://smile.amazon.com/dp/0801854598)) 76 | - Lipschutz. Schaum's *3,000 Solved Problems in Linear Algebra* ([1e](https://smile.amazon.com/dp/0070380236)) 77 | - Lipschutz and Lipson. *Schaum's Outline of Linear Algebra* ([5e](https://smile.amazon.com/dp/0071794565), [4e](https://smile.amazon.com/dp/007154352X)) 78 | - Halmos. *Linear Algebra Problem Book* ([1e](https://smile.amazon.com/dp/0883853221)) 79 | 80 | ## Advanced linear algebra (beyond a first course) 81 | 82 | Most of these will probably be more accessible to someone who has read one of the above intro books, *and* Axler's *Linear Algebra Done Right*. 83 | 84 | - Halmos. *Finite-Dimensional Vector Spaces* ([Martino ed](https://smile.amazon.com/dp/1614272816/), [Benediction ed](https://smile.amazon.com/dp/178139573X/), [Springer hardcover (OOP)](https://smile.amazon.com/dp/B004HOYQX2/)) 85 | 86 | This is another abstract approach to LA that emphasizes connections to analysis and intends to prepare the student for a course in functional analysis. Interesting problems and a colorful exposition. Martino Fine Books has a good reputation for their physical product, but I don't know anything about the physical quality of the Benediction Classics edition. (My own copy is the old Springer hardcover.) 87 | 88 | - Horn and Johnson. *Matrix Analysis* ([2e](https://smile.amazon.com/dp/0521548233/), [1e](https://smile.amazon.com/Matrix-Analysis-Roger-Horn/dp/0521386322/)) 89 | 90 | - Horn and Johnson. *Topics in Matrix Analysis* ([1e](https://smile.amazon.com/dp/052130587X/)) 91 | 92 | - Lax. *Linear Algebra and Its Applications* ([2e](https://smile.amazon.com/dp/0471751561/)) 93 | 94 | This is a grad-level abstract linear algebra text by *Peter Lax*, not the introductory book by *David Lay*! The "applications" here are the pure mathematician's idea of a "application", which means applying the theory to a problem in mathematics, not applying mathematics to the real world. 95 | 96 | - Roman. *Advanced Linear Algebra* ([3e](https://smile.amazon.com/dp/0387728287/), [3e intl at AbeBooks](http://www.abebooks.com/products/isbn/9788132202974)) 97 | 98 | Another grad-level abstract linear algebra book. In spirit it is similar to Axler's *Linear Algebra Done Right*, but from a more advanced perspective. 99 | 100 | - Gantmacher. *Applications of the Theory of Matrices* ([Dover ed](https://smile.amazon.com/dp/0486445542/)) 101 | 102 | - Loehr. *Advanced Linear Algebra* ([1e](https://smile.amazon.com/dp/1466559012)) 103 | 104 | Explores linear algebra in conjunction with many topics in algebra and some in analysis. 105 | 106 | - Franklin. *Matrix Theory* ([Dover ed](https://smile.amazon.com/dp/0486411796/)) 107 | 108 | A physics-oriented overview of matrix theory, followed by a chapter on physics applications and a chapter on numerical methods. 109 | 110 | - Erdman. *Elements of Linear and Multilinear Algebra 111 | 112 | Free notes: 113 | 114 | Others: 115 | - Gentle. *Matrix Algebra: Theory, Computations, and Applications in Statistics* 116 | - Bernstein. *Matrix Mathematics: Theory, Facts, and Formulas* 117 | - Macdonald. *Linear and Geometric Algebra* 118 | - Kaplansky. *Linear Algebra and Geometry: A Second Course* 119 | 120 | ## Numerical linear algebra 121 | 122 | See [Numerical Methods](CS.md#numerical-methods) in the CS section. 123 | 124 | ## Random matrix theory 125 | 126 | - Anderson, Guionnet, Zeitouni. *An Introduction to Random Matrices* ([1e](https://smile.amazon.com/dp/0521194520)) 127 | - Baik, Deift, Suidan. *Combinatorics and Random Matrix Theory* ([1e](https://smile.amazon.com/dp/0821848410)) 128 | - Tao. *Topics in Random Matrix Theory* ([1e](https://smile.amazon.com/dp/0821874306)) 129 | -------------------------------------------------------------------------------- /LogicDiscrete.md: -------------------------------------------------------------------------------- 1 | # Logic and Discrete Math 2 | 3 | ## Logic 4 | 5 | A nice guide to studying logic: 6 | 7 | ### Philosophical logic 8 | 9 | * Gensler, *Introduction to Logic* ([2e](https://smile.amazon.com/dp/0415996511), [1e](https://smile.amazon.com/dp/0415226759)) 10 | 11 | This is a really nice first course in logic, which covers all the core material 12 | that you'd want to see in a first course, gives a tour of major philosophical applications of logic, 13 | and also has a nice overview of less mainstream types of logics. 14 | 15 | * Copi and Cohen. *Introduction to Logic* ([12e](https://smile.amazon.com/dp/0131898345), [11e](https://smile.amazon.com/dp/0130337358)) 16 | * Hurley. *A Concise Introduction to Logic* ([10e](https://www.amazon.com/dp/0495503835), [9e](https://www.amazon.com/dp/0534585051)) 17 | 18 | ### Mathematical logic 19 | 20 | * Keisler, Kunen, Millar, Miller, Robbin, *Mathematical Logic and Computability* 21 | 22 | Free online here: 23 | 24 | * Enderton, *A Mathematical Introduction to Logic* ([2e](https://smile.amazon.com/dp/0122384520), [1e at AbeBooks](http://www.abebooks.com/products/isbn/9780122384509)) 25 | * Chiswell and Hodges. *Mathematical Logic* ([1e](https://smile.amazon.com/dp/0199215626)) 26 | * Goldrei. *Propositional and Predicate Calculus: A Model of Argument* ([1e](https://smile.amazon.com/dp/1852339217)) 27 | * Lover. *Elementary Logic: For Software Development* ([1e](https://smile.amazon.com/dp/1848000812)) 28 | * Smullyan. *First-order logic* ([Dover](https://smile.amazon.com/dp/0486683702)) 29 | * Tarski. *Introduction to logic* ([Dover 2e revised](https://smile.amazon.com/dp/048628462X), [4e [with Jan Tarski]](https://smile.amazon.com/dp/019504472X)) 30 | * van Dalen, *Logic and Structure* ([5e](https://smile.amazon.com/dp/1447145577), [4e](https://smile.amazon.com/dp/3540208798), [3e](https://smile.amazon.com/dp/3540578390)) 31 | * Manin and Zilber, tr. Koblitz. *A Course in Mathematical Logic for Mathematicians* ([2e/2010](https://smile.amazon.com/dp/1461424798)) 32 | * Kleene. *Mathematical Logic* ([1e](https://smile.amazon.com/dp/0486425339)) 33 | * Kleene. *Introduction to Metamathematics* ([1e](https://smile.amazon.com/dp/0923891579)) 34 | * Schöning. *Logic for Computer Scientists* 35 | * Robbin. *Mathematical Logic: A First Course* ([Dover](https://smile.amazon.com/dp/048645018X)) 36 | * Boolos, Burgess, Jeffrey. *Computability and Logic* ([5e](https://smile.amazon.com/dp/0521701465)) 37 | * Shapiro. *Foundations without Foundationalism: A Case for Second-Order Logic* ([1e](https://smile.amazon.com/dp/0198250290)) 38 | * Hedman. *A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity* ([1e](https://smile.amazon.com/dp/0198529813)) 39 | 40 | #### Modal Logic 41 | 42 | * Girle. *Modal Logics and Philosophy* ([2e](https://smile.amazon.com/dp/0773536531)) 43 | * Blackburn, de Rijke, and Venema. *Modal Logic* ([1e](https://smile.amazon.com/dp/0521527147)) 44 | * van Benthem. *Modal Logic for Open Minds* ([1e](https://smile.amazon.com/dp/157586598X)) 45 | * Cocchiarella, Freund. *Modal Logic: An Introduction to its Syntax and Semantics* ([1e](https://smile.amazon.com/dp/0195366573)) 46 | 47 | #### Model Theory 48 | 49 | * Manzano. *Model Theory* ([1e](https://smile.amazon.com/dp/0198538510)) 50 | * Chang and Keisler. *Model Theory* ([3e Dover](https://smile.amazon.com/dp/0486488217)) 51 | * Hodges. *A Shorter Model Theory* ([1e](https://smile.amazon.com/dp/0521587131)) 52 | * Hodges. *Model Theory* ([1e](https://smile.amazon.com/dp/0521066360)) 53 | * Marker. *Model Theory: An Introduction* ([1e](https://smile.amazon.com/dp/0387987606)) 54 | 55 | #### Proof Theory 56 | 57 | * Takeuti. *Proof Theory* ([2e Dover](https://smile.amazon.com/dp/0486490734)) 58 | 59 | #### Topos Theory 60 | 61 | * Johnstone. *Topos Theory* ([Dover](https://smile.amazon.com/dp/0486493369)) 62 | * Goldblatt. *Topoi: The Categorial Analysis of Logic* ([Dover](https://smile.amazon.com/dp/0486450260)) 63 | 64 | #### Type Theory 65 | 66 | * Nederpelt and Geuvers. *Type Theory and Formal Proof: An Introduction* ([1e](https://smile.amazon.com/dp/110703650X)) 67 | * Hindley. *Basic Simple Type Theory* ([1e](https://smile.amazon.com/dp/0521054222)) 68 | 69 | #### Misc logic 70 | 71 | * Goldblatt, *Logics of Time and Computation* ([1e](https://smile.amazon.com/dp/0937073946)) 72 | * Baier and Katoen, *Principles of Model Checking* ([1e](https://smile.amazon.com/dp/026202649X)) 73 | * Harel, Kozen, Tiuryn, *Dynamic Logic* ([1e](https://smile.amazon.com/dp/0262527669)) 74 | * Franzén, *Gödel's Theorem: An Incomplete Guide to Its Use and Abuse* ([1e](https://smile.amazon.com/dp/1568812388)) 75 | 76 | #### Logic course notes 77 | 78 | * Simpson: 79 | 80 | Mathematical Logic; Incompleteness and Undecidability; Foundations of Mathematics; Model Theory; Computability, Unsolvability, and Randomness; some "topics" courses. 81 | 82 | * Simmons and Schalk. *An introduction to lambda-calculi and arithmetic* 83 | * Simmons. *An introduction to Good old fashioned model theory* (incomplete) 84 | * Simmons. *Basic Model Theory* 85 | 86 | ## Set Theory 87 | 88 | * Halmos. *Naive Set Theory* ([Martino](https://smile.amazon.com/dp/1614271313), [Springer HC [OOP]](https://smile.amazon.com/dp/0387900926)) 89 | * Pinter. *Set Theory* ([Dover](https://smile.amazon.com/dp/0486497089)) 90 | * Suppes. *Axiomatic Set Theory* ([Dover](https://smile.amazon.com/dp/0486616304)) 91 | * Enderton. *Elements of Set Theory* ([1e](https://smile.amazon.com/dp/0122384407)) 92 | * Goldrei. *Classic Set Theory: For Guided Independent Study* ([1e](https://smile.amazon.com/dp/0412606100)) 93 | * Kunen. *Set Theory* ([1e](https://smile.amazon.com/dp/1848900503)) 94 | * Jech. *Set Theory* ([3e](https://smile.amazon.com/dp/3540440852)) 95 | * Moore. *Zermelo's Axiom of Choice: Its Origins, Development, and Influence* ([Dover](https://smile.amazon.com/dp/0486488411) 96 | * Jech. *The Axiom of Choice* ([Dover](https://smile.amazon.com/dp/0486466248)) 97 | * Cohen. *Set Theory and the Continuum Hypothesis* ([Dover](https://smile.amazon.com/dp/0486469212)) 98 | 99 | ## Category Theory 100 | 101 | * Mac Lane. *Categories for the Working Mathematician* ([2e](https://smile.amazon.com/dp/0387984038)) 102 | 103 | The classic introduction by one of the creators of category theory. 104 | 105 | * Awodey. *Category Theory* ([2e](https://smile.amazon.com/dp/0199237182)) 106 | 107 | * Spivak. *Category Theory for the Sciences* ([1e](https://smile.amazon.com/dp/0262028131)) 108 | 109 | Note that this is by David Spivak, not Michael Spivak of [*Calculus*](Calculus.md#elite-calculus-textbooks) fame. A pre-publication version, before final editing and without solutions, is available online here: 110 | 111 | 112 | 113 | * Pierce. *Basic Category Theory for Computer Scientists* ([1e](https://smile.amazon.com/dp/0262660717)) 114 | 115 | * Lawvere and Schanuel. *Conceptual Mathematics: A First Introduction to Categories* ([2e](https://smile.amazon.com/dp/052171916X)) 116 | 117 | * Simmons. *An Introduction to Category Theory* ([1e](https://smile.amazon.com/dp/0521283043)) 118 | 119 | ### Course notes 120 | 121 | * Simmons and Schalk. *Category theory in four easy movements* 122 | * Simmons. *Category Theory by Magic* 123 | 124 | ## Discrete Math 125 | 126 | ### Introductions 127 | 128 | #### Discrete math for computer science 129 | 130 | These are generally grab-bags of topics relevant for beginning CS students: logic, proofs, number theory, boolean algebra, combinatorics, graph theory. I only list older, cheap editions. These books tend to be relatively elementary and shallow, because they are devoted to brief coverage of a large variety of topics, but on the other hand they are widely available, polished in their presentation and they have lots of exercises. 131 | 132 | Typical topics are: logic and proof, set theory, functions, introduction to algorithms, basic number theory, mathematical induction, counting and discrete probability, other topics in combinatorics, graphs and trees, basic automata theory. 133 | 134 | * Lehman, Leighton, Meyer. *Mathematics for Computer Science* (FREE [Harvard CS 20 notes](https://www.seas.harvard.edu/courses/cs20/MIT6_042Notes.pdf)) 135 | * Rosen. *Discrete Mathematics and its Applications* ([6e](https://smile.amazon.com/dp/0073229725), [5e](https://smile.amazon.com/dp/0072424346), [5e solns [odd problems only]](https://smile.amazon.com/dp/0072474777)) - Probably the most popular book of this type. 136 | * Epp. *Discrete Mathematics with Applications* ([3e](https://smile.amazon.com/dp/0534359450), [3e solns](https://smile.amazon.com/Student-dp/0534360289), [2e](https://smile.amazon.com/dp/0534944469), [ERRATA](http://condor.depaul.edu/sepp/DMwA3e.htm)) - Noted for its clarity. Seems to be well-liked by struggling students. 137 | * Grimaldi. *Discrete and Combinatorial Mathematics: An Applied Introduction* ([4e](https://smile.amazon.com/dp/0201199122), [3e](https://smile.amazon.com/dp/B00404GGWI), [2e](https://smile.amazon.com/dp/0201119544)) - Older. Concludes with an introduction to abstract algebra with applications including cryptography. 138 | * Hunter. *Essentials Of Discrete Mathematics* ([2e](https://smile.amazon.com/dp/1449604420)) - Has some interesting applications outside of computer science (DNA, social networks, language, music). 139 | * Bender and Williamson. *Mathematics for Algorithm and Systems Analysis* ([Dover](https://smile.amazon.com/dp/0486442500)) - A somewhat less-flashy DM for computer science. 140 | 141 | #### Discrete math with a different focus 142 | 143 | * Scheinerman. *Mathematics: A Discrete Introduction* ([3e](https://smile.amazon.com/dp/0840049420), [2e](https://smile.amazon.com/dp/0534398987)) - Covers a similar range of topics, but is aimed more at math majors. 144 | * Ross. *Topics in Finite and Discrete Mathematics* ([1e Dover](https://www.amazon.com/dp/052177571X)) - Unusual topics include finance, linear programming and statistical inference. No coverage of logic or proofs. 145 | 146 | #### More advanced approaches to discrete math for computer science 147 | 148 | * Aho and Ullman, 1994. *Foundations of Computer Science: C Edition* ([**FREE ONLINE**](http://infolab.stanford.edu/~ullman/focs.html), [1e](https://smile.amazon.com/dp/0716782847)) - Combines discrete math with programming. 149 | 150 | * Graham, Knuth, Patashnik. *Concrete Mathematics: A Foundation for Computer Science* ([2e](https://smile.amazon.com/dp/0201558025)) - One of the most well-loved books in math and computer science. 151 | 152 | ### Combinatorics 153 | 154 | #### Beginning 155 | 156 | * Lovász, Pelikán, Vesztergombi. *Discrete Mathematics: Elementary and Beyond* ([1e](https://smile.amazon.com/dp/0387955852)) 157 | * Brualdi. *Introductory Combinatorics* ([4e](https://smile.amazon.com/dp/0131001191), [3e](https://smile.amazon.com/dp/0131814885); [4e errata](https://www.math.wisc.edu/~brualdi/4ederrata.pdf)) 158 | * Niven. *The Mathematics of Choice: How to Count Without Counting* ([MAA 1e](https://smile.amazon.com/dp/0883856158)) 159 | * Martin. *Counting: The Art of Enumerative Combinatorics* ([1e](https://smile.amazon.com/dp/038795225X)) 160 | * Chen and Koh. *Principles and Techniques in Combinatorics* ([1e](https://smile.amazon.com/dp/9810211392)) 161 | * Bogart. [*Combinatorics Through Guided Discovery*](https://math.dartmouth.edu/news-resources/electronic/kpbogart/) 162 | * Wilf. *generatingfunctionology* ([**2e FREE ONLINE**](https://www.math.upenn.edu/~wilf/DownldGF.html) [3e](https://smile.amazon.com/generatingfunctionology-Third-Herbert-S-Wilf/dp/1568812795/)) 163 | * Stanley. *Enumerative Combinatorics* ([Vol I, 2e](https://smile.amazon.com/dp/1107602629), [Vol II, 1e](https://smile.amazon.com/dp/B00HMUGS4S)) 164 | * Cameron. *Combinatorics: Topics, Techniques, Algorithms* ([1e](https://smile.amazon.com/dp/0521457610)) 165 | * Bona. *Combinatorics of Permutations* ([2e](https://smile.amazon.com/dp/1439850518)) 166 | * Bona. *A Walk through Combinatorics: An Introduction to Enumeration and Graph Theory* ([3e](https://smile.amazon.com/dp/9814460001)) 167 | * Bona. *Introduction to Enumerative and Analytic Combinatorics* ([2e](https://smile.amazon.com/dp/148224909X)) 168 | * Bona. *Handbook of Enumerative Combinatorics* ([1e](https://smile.amazon.com/dp/1482220857)) 169 | * Lovász. *Combinatorial Problems and Exercises* ([AMS Chelsea](https://smile.amazon.com/dp/0821842625)) 170 | * Flajolet and Sedgewick. *Analytic Combinatorics* ([1e](https://smile.amazon.com/dp/0521898064)) 171 | * Stanley. *Algebraic Combinatorics: Walks, Trees, Tableaux, and More* ([1e](https://smile.amazon.com/dp/146146997X)) 172 | * Stanley. *Catalan Numbers* ([1e](https://smile.amazon.com/dp/1107427746)) 173 | * Aigner. *A Course in Enumeration* ([1e](https://smile.amazon.com/dp/3540390324)) 174 | * Jukna. *Extremal Combinatorics: With Applications in Computer Science* ([2e](https://smile.amazon.com/dp/3642173632)) 175 | * Mansour. *Combinatorics of Set Partitions* ([1e](https://smile.amazon.com/dp/1439863334)) 176 | * Bollobás. *Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability* ([1e](https://smile.amazon.com/dp/0521337038)) 177 | * Anderson. *Combinatorics of Finite Sets* ([Dover](https://smile.amazon.com/dp/0486422577)) 178 | * Matousek, Nešetřil, Pellegrini, eds. *Geometry, Structure and Randomness in Combinatorics* ([1e](https://smile.amazon.com/dp/8876425241)) 179 | 180 | ### Graph Theory 181 | 182 | #### Introductions 183 | 184 | * Trudeau. *Introduction to Graph Theory* ([Dover](https://smile.amazon.com/dp/0486678709)) 185 | 186 | * Chartrand, 1984. *Introductory Graph Theory* ([Dover](https://smile.amazon.com/dp/0486247759)) 187 | 188 | * Chartrand, Zhang, 2012. *A First Course in Graph Theory* ([Dover](https://smile.amazon.com/dp/0486483681)) 189 | 190 | More in-depth than Chartrand's other intro book. Includes solutions to odd-numbered exercises. 191 | 192 | * Hartsfield and Ringel. *Pearls in Graph Theory: A Comprehensive Introduction* ([Dover ed](https://smile.amazon.com/dp/0486432327/)) 193 | 194 | #### Beyond 195 | 196 | * Diestel. *Graph Theory* ([4e](https://smile.amazon.com/dp/3642142788), [3e](https://smile.amazon.com/dp/3540261834)) 197 | 198 | Can be previewed free online. See: 199 | 200 | * Bollobás. *Modern Graph Theory* ([1e](https://smile.amazon.com/dp/0387984887)) 201 | * Bollobás. *Extremal Graph Theory* ([Dover](https://smile.amazon.com/dp/0486435962)) 202 | * Bondy and Murty. *Graph Theory* ([1e](https://smile.amazon.com/dp/1846289696)) 203 | * Bollobás. *Random Graphs([2e](https://smile.amazon.com/gp/product/0521797225)) 204 | 205 | See also: [random matrix theory](https://github.com/nculwell/MathStudy/blob/master/LinearAlgebra.md#random-matrix-theory) 206 | -------------------------------------------------------------------------------- /OnlineCourses.md: -------------------------------------------------------------------------------- 1 | Right now, this is just a jumble of links. I plan to organize it later. 2 | 3 | Frederic Schuller, Lectures on Quantum Theory 4 | 5 | 6 | Frederic Schuller, Lectures on the Geometric Anatomy of Theoretical Physics 7 | 8 | 9 | Discrete math 10 | 11 | 12 | Abstract algebra 13 | 14 | 15 | 16 | Intro to CS 17 | 18 | -------------------------------------------------------------------------------- /Picks.md: -------------------------------------------------------------------------------- 1 | # Picks 2 | 3 | Some suggestions for a sequence of study. 4 | 5 | Prealgebra: OpenStax 6 | 7 | High school algebra/trig sequence: OpenStax A&T or Axler *Precalculus* 8 | 9 | Calculus: Lang; Spivak; Hubbard and Hubbard 10 | 11 | Linear Algebra: Strang *LAAIA* 3; Axler *LADR*; Tretethen and Bau; Hoffman and Kunze; Horn and Johnson 12 | 13 | CS: Sedgewick; Sipser 2e; Papadimitriou and Steiglitz; EOPL 14 | 15 | Probability: Ross *FCIP* 16 | 17 | Analysis: Schramm; Stromberg; Churchill; Flanigan; Taylor; Royden; Conway; Akhiezer and Glazman; Munkres *AOM* 18 | 19 | Algebra: Pinter; Artin; Mac Lane and Birkhoff 20 | 21 | Topology: Gamelin and Greene; Munkres *T*; Hatcher 22 | 23 | Algebraic Geometry: Garrity; Shafarevich; Harsthorne 24 | -------------------------------------------------------------------------------- /ProbStats.md: -------------------------------------------------------------------------------- 1 | 2 | ## Probability 3 | 4 | #### General introductions 5 | 6 | - Pitman, *Probability* ([1e](https://smile.amazon.com/dp/0387979743)) 7 | 8 | Considered by many to be the best introduction to probability. 9 | 10 | - Ross, *A First Course in Probability* ([6e](https://smile.amazon.com/dp/0130338516)) 11 | 12 | Lots of great problems. 13 | 14 | - Morin. *Probability: For the Enthusiastic Beginner* ([At Createspace](https://www.createspace.com/5987678), [At Amazon](https://smile.amazon.com/dp/1523318678)) 15 | 16 | An excellent-looking non-calculus introduction to probability. As a non-calculus approach, it focuses on discrete distributions, but it discusses the Gaussian distribution from the perspective of discrete approximation. (I think this is a pretty useful way to do it.) The author's website has some sample chapters (including TOC) that you can view: 17 | 18 | - Ash. *The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists* ([Revised paperback](https://smile.amazon.com/dp/0780310519), [Original hardcover](https://smile.amazon.com/dp/0879422939)) 19 | 20 | - Feller, *An Introduction to Probability Theory and its Applications* (Vol I: [3e](https://smile.amazon.com/dp/0471257087), [3e intl](https://smile.amazon.com/dp/8126518057); Vol II: [2e](https://smile.amazon.com/dp/B000OOHXDO), [2e intl](https://smile.amazon.com/dp/8126518065)) 21 | 22 | The most classic entry in this section. Many still consider it to be the best. Vol I is introductory (though maybe it would go down smoother after another book in this list), while Vol II is considered grad-level as it involves measure theory. 23 | 24 | - Pishro-Nik. *Introduction to Probability, Statistics, and Random Processes* ([1e](https://smile.amazon.com/dp/0990637204), [1e solns](https://smile.amazon.com/dp/0990637212)) 25 | 26 | - Blitzstein and Hwang. *Introduction to Probability* ([1e](https://smile.amazon.com/dp/1466575573)) 27 | 28 | - Bertsekas and Tsitsiklis. *Introduction to Probability* ([2e](https://smile.amazon.com/dp/188652923X), [1e](https://smile.amazon.com/dp/188652940X)) - Goes with MIT OCW course [6.041/6.431 "Probabilistic Systems Analysis and Applied Probability"](http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/). 29 | 30 | #### Further 31 | 32 | - Ross, *Introduction to Probability Models* ([9e](https://smile.amazon.com/dp/0125980620)) 33 | 34 | #### Stochastic processes (without measure theory) 35 | 36 | - Ross, *Stochastic Processes* ([2e](https://smile.amazon.com/dp/0471120626), [2e intl](https://smile.amazon.com/dp/8126517573), [2e intl @AbeBooks](http://www.abebooks.com/products/isbn/9780471120629/16832454196), [1e @AbeBooks](http://www.abebooks.com/products/isbn/9780471099420/16098583380)) 37 | - Karlin and Taylor, *A First Course in Stochastic Processes* ([2e](https://smile.amazon.com/dp/0123985528)) (used price fluctuates a lot but can sometimes be in the $15-30 range) 38 | - Karlin and Taylor, *A Second Course in Stochastic Processes* ([2e](https://smile.amazon.com/dp/0123986508)) (used price fluctuates a lot but can sometimes be in the $20-30 range) 39 | - Karlin and Taylor, *An Introduction to Stochastic Modeling* (3e preferred: [3e](https://smile.amazon.com/dp/0126848874)) 40 | - Gallager. *Stochastic Processes: Theory for Applications* ([1e](https://smile.amazon.com/dp/1107039754)) - Goes with MIT OCW courses [6.262 "Discrete Stochastic Processes"](http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-262-discrete-stochastic-processes-spring-2011/) and [6.432 "Stochastic Processes, Detection, and Estimation"](http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-262-discrete-stochastic-processes-spring-2011/). 41 | 42 | #### Applied 43 | - Trivedi. *Probability and Statistics with Reliability, Queueing, and Computer Science Applications* ([2e](https://smile.amazon.com/dp/0471333417)) 44 | - Mitzenmacher & Upfal, *Probability and Computing: Randomized Algorithms and Probabilistic Analysis* ([1e](https://smile.amazon.com/dp/0521835402)) 45 | - Ross, *Applied Probability Models with Optimization Applications* ([Dover](https://smile.amazon.com/dp/0486673146)) 46 | 47 | #### With measure theory 48 | 49 | Modern probability theory builds its mathematical foundation on measure theory, which is generally regarded as an intermediate-to-advanced topic in real analysis. Some of these books assume exposure to it, others aim to teach it as they go. 50 | 51 | - Rosenthal, *A First Look at Rigorous Probability Theory* ([2e](https://smile.amazon.com/dp/9812703713)) 52 | 53 | This is, in particular, an introduction to measure theory. It assumes a background in undergraduate-level probability (e.g. Ross or Feller) and analysis (e.g. Rudin's *Principles of Mathematical Analysis*). 54 | 55 | - Schilling, *Measures, Integrals and Martingales* ([1e](https://smile.amazon.com/dp/0521615259)) 56 | 57 | Another book that teaches measure theory in the context of probability, assuming undergraduate-level probability and analysis. 58 | 59 | - Dudley, *Real Analysis and Probability* ([2e](https://smile.amazon.com/dp/0521007542)) 60 | 61 | A well-regarded introduction to measure theory from a probability perspective. 62 | From the introduction: 63 | "The first half of the book gives an exposition of real analysis: basic set 64 | theory, general topology, measure theory, integration, an introduction to functional 65 | analysis in Banach and Hilbert spaces, convex sets and functions, 66 | and measure on topological spaces. The second half introduces probability 67 | based on measure theory, including laws of large numbers, ergodic theorems, 68 | the central limit theorem, conditional expectations, and martingale convergence. 69 | A chapter on stochastic processes introduces Brownian motion and the 70 | Brownian bridge." 71 | 72 | - Williams, *Probability with Martingales* ([1e](https://smile.amazon.com/dp/0521406056)) 73 | 74 | Very popular book at the lower end of measure-theoretic probability. 75 | 76 | - Ross and Peköz, *A Second Course in Probability* ([1e](https://smile.amazon.com/dp/0979570409)) - Introduces measure theory. (Seems not very popular.) 77 | 78 | - Shiryaev, *Probability* ([2e](https://smile.amazon.com/dp/0387945490), [3e Vol I](https://smile.amazon.com/dp/038772205X)) 79 | 80 | Considered one of the best textbooks for graduate students coming to grips with rigorous probability theory. 81 | The third edition splits the book into two volumes. 82 | 83 | - Chung, *A Course in Probability Theory* ([3e](https://smile.amazon.com/dp/0121741516), [2e](https://smile.amazon.com/dp/0121741516)) 84 | 85 | Another of the best rigorous probability textbooks. 86 | 87 | - Billingsley, *Probability and measure* ([3e preferred](https://smile.amazon.com/dp/8126517719)) 88 | 89 | Classic, very popular graduate text on measure-theoretic probability. 90 | 91 | - Durrett, *Probability: Theory and Examples* ([4e](https://smile.amazon.com/dp/0521765390)) 92 | 93 | Another very standard graduate text on measure-theoretic probability. 94 | This seems to be one of those books that a lot of people don't like, but it's so important that they have to read it anyway. 95 | 96 | - Kallenberg, *Foundations of Modern Probability* ([2e](https://smile.amazon.com/dp/0387953132)) 97 | 98 | Encyclopedic reference to probability theory at the advanced level. 99 | 100 | ## Statistics 101 | 102 | - Freedman, Pisani and Purves, *Statistics* ([4e](https://smile.amazon.com/dp/0393929728), [3e](https://smile.amazon.com/dp/0393970833), [4e intl](https://smile.amazon.com/dp/8130915871)) 103 | 104 | Conceptual introduction to statistics with minimal math. Widely viewed as the best introduction to how to think about statistics. 105 | 106 | - Diez, Barr, Çetinkaya-Rundel. *OpenIntro Statistics* (f) 107 | 108 | Get it free online (or order it) here: 109 | 110 | There are also a couple of other editions that de-emphasize math in order to teach students who have less background. (You can find them as well via the link above.) 111 | 112 | - OpenStax, *Introductory Statistics* (f) 113 | 114 | - Free PDF: 115 | - Buy on Amazon: 116 | 117 | - DeGroot and Schervish, *Probability and Statistics* ([2e](https://smile.amazon.com/dp/020111366X), [3e](https://smile.amazon.com/dp/B01FETPSRG), [4e](https://smile.amazon.com/dp/0321500466), [4e intl at AbeBooks](http://www.abebooks.com/products/isbn/9780321500465)) 118 | 119 | A popular introduction to mathematical statistics. 120 | 121 | - McElreath. *Statistical Rethinking: A Bayesian Course with Examples in R and Stan* ([1e](https://smile.amazon.com/dp/1482253445)) 122 | 123 | An overview of the philosophical and practical aspects of statistics from a modern beyesian perspective. "The principle audience is researchers in the natural and social sciences, whether new PhD students or seasoned professionals, who have had a basic course on regression but nevertheless remain uneasy about statistical modeling." 124 | 125 | - Cassela and Berger, *Statistical Inference* ([2e](https://smile.amazon.com/dp/0534243126), [2e intl](https://smile.amazon.com/dp/8131503941)) 126 | 127 | A standard grad-level introduction to mathematical/theoretical statistics. 128 | 129 | - Schervish, *Theory of Statistics* ([1e](https://smile.amazon.com/dp/0387945466)) 130 | 131 | More advanced and complete book on theoretical statistics. 132 | 133 | - Bickel and Doksum, *Mathematical Statistics: Basic Ideas and Selected Topics* ([1e 1977 at AbeBooks](http://www.abebooks.com/products/isbn/9780816207848); Vol I: [2e CRC 2015](https://smile.amazon.com/dp/1498723802), [2e PH 2006 updated PB](https://www.amazon.com/dp/0132306379); Vol II: [2e CRC 2015](https://smile.amazon.com/dp/1498722687), [2e PH 2006](https://smile.amazon.com/Mathematical-Statistics-Basic-Selected-Topics/dp/0132306379); Set [2e CRC 2015](https://smile.amazon.com/Mathematical-Statistics-Selected-Volumes-Statistical/dp/1498740316)) 134 | 135 | Standard grad-level text on mathematical statistics. 136 | 137 | - Gelman et al, *Bayesian Data Analysis* ([3e](https://smile.amazon.com/dp/1439840954), [2e](https://smile.amazon.com/dp/158488388X)) 138 | 139 | Good first book on Bayesian analysis. 140 | 141 | - Gelman and Hill, *Data Analysis Using Regression and Multilevel/Hierarchical Models* ([1e](https://smile.amazon.com/dp/052168689X)) 142 | 143 | Good first book on multilevel/hierarchical models 144 | 145 | - Fleiss, *The Design and Analysis of Clinical Experiments* (x) 146 | 147 | Standard book on clinical study design. 148 | 149 | - Mandel, *The Statistical Analysis of Experimental Data* (c) 150 | 151 | - Robert, *The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation* ([2e](https://smile.amazon.com/dp/0387715983)) 152 | 153 | - Erich Lehmann books 154 | 155 | These are classic standards, but somewhat old now (and, I think, out of print). 156 | 157 | - Lehmann and Casella. *Theory of Point Estimation* ([2e](https://smile.amazon.com/dp/0387985026)) 158 | - Lehmann and Romano. *Testing Statistical Hypotheses* ([3e](https://smile.amazon.com/dp/0387988645)) 159 | 160 | #### Biostats 161 | 162 | - Wassertheil-Smoller. *Biostatistics and Epidemiology: A Primer for Health and Biomedical Professionals* ([3e](https://smile.amazon.com/dp/0387402926)) 163 | - Glantz. *Primer of Biostatistics* ([6e](https://smile.amazon.com/dp/0071435093)) 164 | 165 | ## Machine Learning 166 | 167 | AKA statistical learning, data mining, predictive modeling. 168 | 169 | ### The free books 170 | 171 | * James, Witten, Hastie and Tibshirani, 2013. *An Introduction to Statistical Learning: with Applications in R* 172 | 173 | AKA ISL or ISLR. Probably the most popular introduction to maching learning. 174 | 175 | 176 | * Hastie, Tibshirani and Friedman, 2009. *The Elements of Statistical Learning: Data Mining, Inference, and Prediction* 177 | 178 | AKA ESL. The standard textbook for serious machine learning courses. 179 | 180 | 181 | * Goodfellow, Bengio and Courville, forthcoming/online. *Deep Learning* 182 | 183 | Due for publication in 2016 (or 2017?). This book isn't even out in paper form yet (MIT Press will publish it soon), but you can read it for free online here: 184 | 185 | * Barber, 2012. *Bayesian Reasoning and Machine Learning* 186 | 187 | AKA BRML. A popular machine learning textbook from a Bayesian viewpoint. 188 | 189 | 190 | * MacKay, 2003. *Information Theory, Inference, and Learning Algorithms* 191 | 192 | An older, but respected, introduction to ML from an information theory viewpoint. 193 | 194 | 195 | * Boyd and Vandenberghe, *Convex Optimization* 196 | 197 | While this book is not exactly about machine learning, many (most?) ML techniques rely on the optimization techniques covered here. The book's web page also links to a free online course. 198 | 199 | 200 | 201 | ### Other big books 202 | 203 | * Kuhn and Johnson, 2013. *Applied Predictive Modeling* ([1e](https://smile.amazon.com/dp/1461468485)) 204 | 205 | This is a guide to machine learning at the level of detail necessary to implement techniques in R. Much attention is paid to how to make each method perform well. The body of each chapter is a description of the techniques involved, then at the end of the chapter is a "Computing" section which describes how to do what you just learned in R. The author's approach is to tell you just as much as you need to know to use the techniques, then point you to primary literature where you can read the details. 206 | 207 | 208 | 209 | * Reed and Marks, 1999. *Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks* ([1e](https://smile.amazon.com/dp/0262181908)) 210 | 211 | This one is old, not particularly in-depth and only covers a limited subset of NN techniques, but it remains one of the better introductions to the topic of neural networks. It's also relatively short and affordable. 212 | 213 | * Murphy, 2012. *Machine Learning: a Probabilistic Perspective* ([1e](https://smile.amazon.com/dp/0262018020)) 214 | 215 | 216 | 217 | * Izenman, 2008. *Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning* ([1e](https://smile.amazon.com/dp/0387781889)) 218 | 219 | This book is statistics-oriented, but it largely covers ML techniques. 220 | 221 | * Bishop, 2006. *Pattern Recognition and Machine Learning* ([1e](https://smile.amazon.com/dp/0387310738)) 222 | 223 | AKA PRML. Bayesian viewpoint. This book used to be very influential but it's getting a bit dated, and I get the impression that it's generally regarded as not the best-written ML book around. 224 | 225 | 226 | * Bishop, 1996. *Neural Networks for Pattern Recognition* ([1e](https://smile.amazon.com/dp/0198538642)) 227 | 228 | Old but still relevant (because there aren't a lot of in-depth books about neural networks). 229 | 230 | * Abu-Mostafa, Magdon-Ismail, Lin, 2012. *Learning From Data* ([1e](https://smile.amazon.com/dp/1600490069)) 231 | 232 | Now out of print? Goes with an online course from Caltech: 233 | 234 | * Mohri, Rostamizadeh, Talwalkar, 2012. *Foundations of Machine Learning* ([1e](https://smile.amazon.com/dp/026201825X)) 235 | 236 | * Koller, Friedman, 2009. *Probabilistic Graphical Models: Principles and Techniques* ([1e](https://smile.amazon.com/dp/0262013193)) 237 | 238 | This is the reigning book on PGMs, but it demands more mathematical background (e.g. abstract algebra) than a lot of the other books listed here. It's also a very physically imposing volume (1280 pages). 239 | 240 | * Korb and Nicholson, *Bayesian Artificial Intelligence* ([2e](https://amazon.com/dp/1439815917)) 241 | 242 | Bayesian network techniques. 243 | 244 | ## Natural language processing 245 | 246 | * Jurafsky and Martin, 2008. *Speech and Language Processing* ([2e](https://smile.amazon.com/dp/0131873210)) 247 | 248 | The main book on NLP. A 3rd edition is in progress, and the draft can be seen here: 249 | 250 | * Manning and Schütze, 1999. *Foundations of Statistical Natural Language Processing* ([1e](https://smile.amazon.com/dp/0262133601)) 251 | 252 | Older, but still the other big book in this field. 253 | 254 | ## Information retrieval 255 | 256 | * Manning, Raghavan, Schütze, 2008. *Introduction to Information Retrieval* ([1e](https://smile.amazon.com/dp/0521865719)) 257 | 258 | Free on the web: 259 | 260 | * Büttcher, Clarke, Cormack, 2010. *Information Retrieval: Implementing and Evaluating Search Engines* ([1e](https://smile.amazon.com/dp/0262528878)) 261 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # MathStudy 2 | 3 | Info on resources for studying math, stats, CS, etc. 4 | 5 | I created this list for my own studies. I haven't read most of the books here yet, and probably never will read most of them. I've made it visible to the public, though, in case anyone else finds it useful. I make no promises: it may be full of bad advice and it probably contains some erroneous statements about points of fact. 6 | 7 | Keep in mind that I'm not very familiar with some of these subjects, so my organization might not make any sense. I usually start out by just collecting a bunch of titles, then I organize them as I begin to figure out how a typical sequence of study in that subfield should proceed. 8 | 9 | I hope to make the list more complete in the future, but for now, there are some subjects that are left out for no good reason. I also hope in the future to present a simpler list of "here's a list of books you can work through to cover all these subjects without repeating the same material too much or spending too much money". 10 | 11 | ## Sections 12 | 13 | I'm not sure how well I chose the sections here, but at least they break the list up into more manageable chunks. 14 | 15 | ### [Calculus](Calculus.md) 16 | ### [Analysis](Analysis.md) 17 | ### [Probability, Statistics and Machine Learning](ProbStats.md) 18 | ### [Linear Algebra](LinearAlgebra.md) 19 | ### [Algebra](Algebra.md) 20 | ### [Geometry and Topology](GeomTopo.md) 21 | ### [Logic and Discrete Math](LogicDiscrete.md) 22 | ### [Computer Science](CS.md) 23 | ### [School level (pre-calculus) mathematics](SchoolLevel.md) 24 | ### [Sciences](Sciences.md) 25 | 26 | ## Lists of free resources 27 | 28 | - - A list similar to this one that links to many free books. 29 | - Open Textbook Library (Minnesota): 30 | - UPS list: 31 | - OpenStax: 32 | - George Cain (GA Tech): 33 | - Green Tea Press (Free books by Allen Downey): 34 | 35 | ## Annotations 36 | 37 | [I've stopped bothering with this, since now I just link to Amazon or other listings for the books where you can see prices, but there are still some annotations hanging around so I'm leaving the legend here for now.] 38 | 39 | - (u) - This book is very expensive (price > $100), but used copies can be bought for a reasonable price. 40 | - (x) - This book is very expensive (price > $100), and used copies *cannot* [at the time of writing] be bought for a reasonable price. 41 | - (f) - This book is available free online. 42 | - (i) - This book is very expensive (price > $100), but there is an affordable international edition. 43 | - (c) - This book is relatively inexpensive (price < $30) when bought new. 44 | - (o) - An acceptable edition of this book that's previous to the current one but not terribly out of date can be bought for considerably cheaper than the current edition. 45 | -------------------------------------------------------------------------------- /SchoolElem.md: -------------------------------------------------------------------------------- 1 | # Grade school math 2 | 3 | # Elementary 4 | 5 | ## Problems 6 | 7 | - Borac. *Competitive Mathematics for Gifted Students - Level 1 Combo: ages 7-9* (2014, [ISBN 978-0692240076](https://www.worldcat.org/isbn/978-0692240076), [Amazon](https://smile.amazon.com/Competitive-Mathematics-Gifted-Students-Level/dp/0692240071)) 8 | - 9 | - https://smile.amazon.com/Hard-Elementary-School-Glenn-Ellison/dp/1489507175 10 | - https://smile.amazon.com/Hard-Math-Elementary-School-Workbook/dp/1484843010 11 | - https://smile.amazon.com/Primary-Grade-Challenge-Edward-Zaccaro/dp/0967991536 12 | - https://smile.amazon.com/Math-Gifted-Student-Challenging-Activities/dp/1411434331 13 | - https://smile.amazon.com/Hard-Math-Middle-School-IMLEM/dp/1453814450 14 | - https://smile.amazon.com/Hard-Math-Middle-School-Workbook/dp/1542835089 15 | 16 | - 17 | 18 | ## For parents, or reference for kids 19 | 20 | - Great Source math series 21 | 22 | I've looked over the first three books in this series and they look really 23 | good. They are designed as references rather than books that you work through 24 | from start to finish. They don't have any exercises at all since they are not 25 | intended to be primary textbooks. 26 | 27 | If you compare the table of contents of each subsequent volume, they appear 28 | redundant. This is only partly true, however, as the later volumes present 29 | review material more concisely. For example, the measurement section in Math 30 | to Learn devotes two pages to customary units (i.e. SAE/imperial) and two to 31 | metric units, with a number of illustrations dedicated to each and a little 32 | guide showing you how to line up a ruler when measuring something; Math to 33 | Know shortens each of these two one page each; and Math at Hand presents both 34 | customary and metric units on a single page. 35 | 36 | - Grades 1-2: Math to Learn (2e 2006, ISBN 978-0669535983, [Worldcat](https://www.worldcat.org/isbn/978-0669535983), [Amazon](https://smile.amazon.com/dp/0669535982)) 37 | - Grades 3-4: Math to Know (2006, ISBN 978-0669508178, [Worldcat](https://www.worldcat.org/isbn/978-0669508178), [Amazon](https://smile.amazon.com/dp/0669535982)) 38 | - Grades 5-6: Math at Hand (2e 2003, ISBN 978-0669508178, [Worldcat](https://www.worldcat.org/isbn/978-0669508178), [Amazon](https://smile.amazon.com/dp/0669535966)) 39 | - Grades 7-8: Math on Call (2e 2003, ISBN 978-0669508192, [Worldcat](https://www.worldcat.org/isbn/978-0669508192), [Amazon](https://smile.amazon.com/dp/0669508195)) 40 | - Algebra to Go (2000, ISBN 978-0669471519, [Worldcat](https://www.worldcat.org/isbn/978-0669471519), [Amazon](https://smile.amazon.com/dp/0669471518)) 41 | - Geometry to Go (2001, ISBN 978-0669481297, [Worldcat](https://www.worldcat.org/isbn/978-0669481297), [Amazon](https://smile.amazon.com/dp/0669481297)) 42 | 43 | - Everything You Need to Ace Math in One Big Fat Notebook: The Complete Middle School Study Guide 44 | (2016, [ISBN 978-0761160960](https://www.worldcat.org/isbn/978-0761160960), 45 | [Amazon](https://smile.amazon.com/dp/0761160965)) 46 | - Barron's E-Z Arithmetic 47 | - Lewis, Help Your Kids with Math 48 | (DK 2014, [ISBN 978-1465421661](https://www.worldcat.org/isbn/978-1465421661),\ 49 | [Amazon](https://smile.amazon.com/dp/1465421661)) - 50 | An extremely visual approach to math. This would probably be helpful for 51 | finding a visual explanation for things but I find it lacking in words. 52 | - No-Nonsense Algebra - 53 | Summarizes pre-algebra and introductory algebra. 54 | 55 | ## Enrichment: math excursions, puzzles, etc. 56 | 57 | Books that aren't intended to be systematic curricula, and are more colorful than just practice problems. 58 | 59 | - Amazing Visual Math (DK ) - A geometry lift-the-flap book. 60 | - How to Be Good at Math (DK ) 61 | - Weltman, This is Not a Maths Book: A Smart Art Activity Book (2015, ISBN 978-1782402053, [Amazon](https://smile.amazon.com/dp/1782402055)) - Drawing activities with straight-edge and compass. 62 | - Another: 63 | - Science (actually pretty mathematical): 64 | - 65 | - 66 | - 67 | - 68 | - 69 | - 70 | - 71 | - 72 | 73 | ## US textbooks 74 | 75 | ### Major lines of school books 76 | 77 | - Scott Foresman 78 | - Go Math! 79 | - Harcourt 80 | - McGraw-Hill My Math 81 | - Math Connects 82 | 83 | ### UCSMP 84 | 85 | I'm interested in what I've read about these, so I include them here. However, 86 | I'm disturbed by the sheer size of them. That is a very bad sign IMO, as there 87 | just isn't that much content to teach at this level. I withhold judgement until 88 | I get my hands on them as see what's in all those pages. 89 | 90 | #### Everyday Mathematics 91 | 92 | - 93 | 94 | #### 6-12 95 | 96 | - Pre-Transition (pre-pre-algebra) 97 | - Transition (pre-algebra) 98 | 99 | ### Activate Science (Oxford) 100 | 101 | I just saw it online and it looked interesting. 102 | 103 | - Vol 1 104 | - Vol 2 105 | 106 | ## Foreign textbooks 107 | 108 | ### Singapore Math 109 | 110 | Singapore Math is an adaptation of the Singapore math textbooks to the US 111 | market. ("Singapore Math" also refers to the US company that has done this and 112 | sells the books.) There are a few different versions: "US", "Standards" and 113 | "Common Core". From reading the summaries, I gather that the "US" edition has 114 | the least changes from the original, whereas the others add topics to match US 115 | standards. As such, the US version is probably the best, because the point of 116 | these Asian curricula is largely to avoid loading little kids with so many 117 | topics. (The current US edition is older, though, and the books aren't all in 118 | color like the other editions, if that matters. I think it doesn't.) 119 | 120 | Official website: 121 | 122 | You can find them elsewhere but the official site seems as good a place as any 123 | to get them. (It seems that they don't sell through distributors/retailers, so 124 | any books you find elsewhere are probably secondhand.) 125 | 126 | Here are some other series that appear to be Singapore Math knockoffs: 127 | 128 | - 129 | - 130 | - 131 | - 132 | 133 | ### Shanghai Mathematics 134 | 135 | New English-language editions of the math books used in Shanghai, produced for 136 | use in the UK. They emphasize fewer topics in more depth compared to western 137 | approaches. This project looks intriguing but there aren't any reports out yet 138 | about the results of using them in British schools. 139 | 140 | #### Real Shanghai Mathematics 141 | 142 | Series from Collins. 143 | 144 | Official website: 145 | 146 | These are sold through retailers and you can buy them on Amazon. 147 | 148 | #### Shanghai Maths Project 149 | 150 | Looks like this was published in 2015. These books are the 1st year set: 151 | 152 | - Learner book 1: 153 | - Practice book 1A: 154 | - Practice book 1B: 155 | - Teacher's guide 1: 156 | 157 | ### India NCERT textbooks 158 | 159 | India has a government program to produce standard textbooks that can be 160 | reproduced inexpensively. (At least this is what I infer from what I've read on 161 | the website.) 162 | 163 | You can preview them here: 164 | 165 | This site actually lets you download the entire books as PDFs, or read them in 166 | the browser, but the PDFs have watermarks. 167 | 168 | These books can be bought on Amazon but the copies available in the USA are 169 | expensive. They're cheap in India but I don't know a way to get them shipped to 170 | the USA. 171 | 172 | # Science and Engineering 173 | 174 | This isn't math, I'm just throwing it in here until I get it broken out into another page. 175 | 176 | - 177 | - 178 | - 179 | 180 | # Curricula (not just math) 181 | 182 | ## NGAC award-winning units 183 | 184 | 185 | 186 | ## The College of William and Mary's Center for Gifted Eduction 187 | 188 | 189 | 190 | ### K-1 191 | 192 | 193 | 194 | 195 | ### 1-2 196 | 197 | ### 2-X 198 | 199 | 200 | ### 3-4 201 | 202 | 203 | 204 | 205 | ## Kendall Hunt store 206 | 207 | https://k12.kendallhunt.com/product-listing?f[0]=field_program_term%3A1544 208 | 209 | ## Math Enrichment 210 | 211 | 212 | 213 | 214 | 215 | 216 | 217 | ## Contest/challenge problems 218 | 219 | 220 | ## Math Puzzles 221 | 222 | 223 | 224 | -------------------------------------------------------------------------------- /SchoolLevel.md: -------------------------------------------------------------------------------- 1 | # Grade school math 2 | 3 | ## High school math subjects 4 | 5 | The standard US textbooks used by schools are pretty widely derided, although I 6 | do give links to some of them near the bottom of this document. I've focused on 7 | other alternatives here. I begin with Pre-Algebra (basically a one-year 8 | overview of all mathematics that is expected to be mastered before beginning 9 | algebra) because, although it's not usually considered high school level, it is 10 | the first course that has many adult-style textbooks dedicated to it. 11 | 12 | ### Series that cover all subjects 13 | 14 | See below for more information about these. 15 | 16 | - The Art of Problem Solving ([At AoPS](https://artofproblemsolving.com/store/item/intro-geometry)) 17 | - OpenStax 18 | - Japanese Mathematics (translations from University of Chicago) 19 | 20 | 21 | ### Pre-algebra 22 | 23 | - The Art of Problem Solving: Volumes 1 and 2 24 | - Dolciani. *Pre-Algebra: An Accelerated Course* [1987](https://smile.amazon.com/dp/039543050X) 25 | 26 | ### Introductory algebra 27 | 28 | - The Art of Problem Solving: Algebra 29 | - Gelfand, Algebra 30 | - Foerster, Algebra (2006 Classic Edition: [ISBN 978-0131657083](https://www.worldcat.org/isbn/978-0131657083), [Amazon](https://smile.amazon.com/dp/020132458X); 1999 Classic Edition: [ISBN 978-0201324587](https://www.worldcat.org/isbn/978-0201324587), [Amazon](https://smile.amazon.com/dp/020132458X); 1994 Classic Edition: [ISBN 978-0201860948](https://www.worldcat.org/isbn/978-0201860948), [Amazon](https://smile.amazon.com/dp/0201860945)) 31 | 32 | ### Continuing algebra and trigonometry 33 | 34 | Encompassing the portion of the US curriculum referred to by the terms Algebra 2, Trigonometry and Precalculus. 35 | 36 | - The Art of Problem Solving: Intermediate Algebra 37 | - The Art of Problem Solving: Precalculus 38 | - OpenStax Algebra and Trigonometry 39 | - Lang, Basic Mathematics 40 | - Gelfand, Trigonometry 41 | - Axler, Precalculus. (1e: [Amazon](https://smile.amazon.com/dp/0470180722); 2e: [Amazon](https://smile.amazon.com/dp/047064804X)) 42 | - Simmons, Precalculus in a Nutshell 43 | - Foerster, Algebra and Trigonometry (2005 Classics Edition: [ISBN 978-0131657106](https://www.worldcat.org/isbn/978-0131657106), [Amazon](https://smile.amazon.com/dp/0131657100)) 44 | - 45 | 46 | ### Geometry 47 | 48 | - The Art of Problem Solving: Introduction to Geometry 49 | - Lang and Murrow, *Geometry: A High School Course* ([2e](https://smile.amazon.com/dp/0387966544), [Solutions manual](https://smile.amazon.com/dp/0387941819)) 50 | - Kiselev's Geometry I 51 | - Meyer. *Geometry and Its Applications* (2e, 2006: ISBN 978-0123694270, [Worldcat](https://www.worldcat.org/oclc/212425111), [Amazon](https://smile.amazon.com/dp/0123694272)) 52 | 53 | #### Might work 54 | 55 | - Stillwell. *The Four Pillars of Geometry* (1e 2005: ISBN 978-0387255309, [Worldcat](https://www.worldcat.org/oclc/209834142), [Amazon](https://smile.amazon.com/dp/0387255303)) 56 | - Leonard, Lewis, Liu, Tokarsky. *Classical Geometry: Euclidean, Transformational, Inversive, and Projective* 57 | (1e 1997: [ISBN 978-0760706602](https://www.worldcat.org/isbn/978-0760706602), 58 | [Amazon](https://smile.amazon.com/dp/0760706603); 59 | 2e 2003: [ISBN 978-1592441303](https://www.worldcat.org/isbn/978-1592441303), 60 | [Amazon](https://smile.amazon.com/dp/1592441300)) 61 | 62 | ## Sources for texts and resources 63 | 64 | ### UCSMP 65 | 66 | 67 | 68 | ### CME 69 | 70 | - 71 | - 72 | 73 | ### Connected Mathematics (CMP) 74 | 75 | Seems to be the most widely used constructivist mathematics series for middle schools. 76 | 77 | - Project home: 78 | - Wikipedia: 79 | - Pearson's CMP3 page: 80 | - Pearson's CMP2 page: 81 | 82 | Constructivist mathematics approaches math by asking the students to solve 83 | problems that allow them to "construct" mathematical concepts for themselves. 84 | Research generally indicates that this is a good way to do things, because 85 | thinking about things is what makes you learn them (as opposed to repeating 86 | what you're told to do, which is far less effective and thus requires more 87 | hours of studying to achieve the same results). The big caveat is that the 88 | constructivist approach requires a competent teacher to supervise learning and 89 | make sure students don't get off track: the teacher's job largely becomes one 90 | of recognizing and correcting misconceptions. 91 | 92 | These features make constructivist books inappropriate as a primary resource 93 | for self study (because you have no teacher to correct your misconceptions), 94 | but they might still be useful in combination with another text as a source of 95 | problems. 96 | 97 | For a look at the thinking behind constructivist mathematics instruction, 98 | *Concept-rich Mathematics Instruction* 99 | ([ISBN 978-1416603597](https://www.worldcat.org/isbn/9781416603597), 100 | [Amazon](https://smile.amazon.com/dp/141660359X)) is a useful overview. 101 | 102 | ### OpenStax 103 | 104 | The OpenStax project offers free, high-quality textbooks for a variety of subjects. Here's the link to the math section: 105 | 106 | 107 | 108 | Print copies have been available on Amazon but many are on longer in print and there aren't a lot of used copies floating around. 109 | 110 | Currently, they offer textbooks for Pre-algebra, College Algebra, Algebra-Trigonometry, Precalculus and Calculus I-III. Notably, there is no Geometry text. 111 | 112 | As is typical with such sequences, *College Algebra*, *Algebra and Trigonometry* and *Precalculus* are essentially the same book with a slightly different beginning and ending point for each. Thus, there's no point in owning all of them. 113 | 114 | As far as I can tell, *College Algebra* contains a strict subset of the chapters of *Algebra and Trigonometry*, and *Precalculus* is the same as *Algebra-Trigonometry* except that it omits the first two chapters ("Prerequisites" and "Equations and Inequalities"), it has slightly different coverage of trigonometry (one section removed that I noticed) and it adds a new chapter called "Introduction to Calculus". 115 | 116 | For self-study purposes, *Algebra and Trigonometry* seems to be the most desirable to have, since the material in the "Introduction to Calculus" chapter from *Precalculus* can be found in any calculus textbook. 117 | 118 | Note that these books have two PDF versions: the "OP" version that is linked to from the main math books page, and the "Print Edition" version that can be found in a link on the details page. I'm not sure what the difference is, but I've noticed that the OP version is a larger file, whereas the Print Edition contains the student answer key (solutions for odd-numbered exercises). 119 | 120 | Since the OpenStax website is annoying to use, I provide some direct links here, although these might be out-of-date in the future: 121 | 122 | - [*Algebra and Trigonometry*, Print Edition PDF](https://d3bxy9euw4e147.cloudfront.net/oscms-prodcms/media/documents/AlgebraAndTrigonometry-Print-Edition.pdf) 123 | (includes the student answer key in the back of the book) 124 | 125 | - [*Algebra and Trigonometry*, information page](https://openstax.org/details/algebra-and-trigonometry) 126 | 127 | This page includes a link to an errata page, and additional resources that are available exclusively for instructors. 128 | 129 | - [*Algebra and Trigonometry* on Amazon](https://www.amazon.com/Algebra-Trigonometry-OpenStax/dp/1938168372) 130 | 131 | ### Sheldon Axler 132 | 133 | Sheldon Axler is a university professor who has written a number of math textbooks for undergraduates. These offer a no-nonsense presentation for an adult audience. Axler doesn't try to entertain you (much), but he does offer a lot of helpful tips about how to think about math as you learn it. Reading his books gives me the sense that he's taught a lot of undergraduates in his time and he has a pretty good idea of what he can and can't expect them to figure out on their own. He is also careful to give you an idea about why he's telling you something, instead of taking the "it will make sense when you get there" attitude that many math professors adopt in writing their books. 134 | 135 | - *Algebra and Trigonometry* ([1e](https://smile.amazon.com/dp/047047081X)) 136 | - *Precalculus* ([1e](https://smile.amazon.com/dp/0470180722), [2e](https://smile.amazon.com/dp/047064804X)) 137 | 138 | These two books overlap quite a bit; I'm not sure if there is any substantive difference between them besides the sequencing of topics. His other book at this level, *College Algebra*, is superfluous because it is entirely contained within *Algebra and Trigonometry* (and it's only slightly cheaper). 139 | 140 | I suggest buying a decent-quality copy of whichever edition is cheapest. As of this writing, this one is the cheapest option to buy used: 141 | 142 | - [Axler's *Precalculus*, first edition, on Amazon](https://smile.amazon.com/Precalculus-Prelude-Calculus-Sheldon-Axler/dp/0470180722) 143 | 144 | Note that the covers of these paperback books are not especially strong and they tend to curl up. 145 | 146 | ### The Art of Problem Solving 147 | 148 | I gather this series began as two books by Richard Rusczyk, 149 | *The Art of Problem Solving* volumes 1 and 2, which cover the pre-algebra 150 | curriculum and are aimed at [Mathcounts](http://www.mathcounts.org/) 151 | contestants. However, the series has been expanded to include textbooks from 152 | pre-algebra through all of high school mathematics. People rave about them, so 153 | they're probably pretty good. I've only looked at *Introduction to Algebra*, 154 | but I found it interesting and thorough in its explanations. 155 | 156 | - *Prealgebra* 157 | - *Introduction to Algebra* 158 | - *Introduction to Geometry* 159 | - *Introduction to Number Theory* 160 | - *Introduction to Counting and Probability* 161 | - *Intermediate Algebra* 162 | - *Intermediate Counting and Probability* 163 | - *Precalculus* 164 | - *Calculus* 165 | 166 | The main high school curriculum subjects covered here (*Prealgebra*, 167 | *Introduction to Algebra*, *Intermediate Algebra*, *Introduction to Geometry*, 168 | *Precalculus*), aren't usually given a challenging treatment in the other 169 | available books, so these make very attractive alternatives. 170 | 171 | I don't know if there's as much need for the calculus book, as students already 172 | have lots of different options for that (as detailed on my other books page), 173 | but what I like about it judging from the samples available online is that it 174 | gives nice, detailed walkthroughs of more complex problems than you see in the 175 | worked examples of a typical textbook. 176 | 177 | Since there is often a lot of overlap between courses on "Algebra II" and 178 | "Precalculus", I compared the contents of *Intermediate Algebra* and 179 | *Precalculus*. They are mostly different, with *Intermediate Algebra* focusing 180 | polynomials, other functions, and series, whereas *Precalculus* is almost 181 | entirely devoted to trigonometry and an introduction to linear algebra. 182 | 183 | AoPS also has a set of books called *Beast Academy* which is planned to cover 184 | grades 2-5, although currently only grades 3 and 4 are complete. I have no idea 185 | if those are any good. 186 | 187 | These can be found here: 188 | 189 | The Art of Problem Solving website also offers online courses that go with 190 | these books. 191 | 192 | ### The Russian texts 193 | 194 | #### Gelfand 195 | 196 | Israel M. Gelfand (Гельфанд) wrote a series of books to teach fundamental mathematics to grade school students as part of a correspondence program. The resulting series of books covers from algebra through precalculus: 197 | 198 | - Gelfand and Shen. *Algebra* ([Birkhäuser 1993](https://smile.amazon.com/dp/0817636773)) 199 | - Gelfand, Glagoleva, Kirillov. *The Method of Coordinates* ([Dover 2002](https://smile.amazon.com/dp/0486425657)) 200 | - Gelfand, Glagoleva, Shnol. *Functions and Graphs* ([Dover 2002](https://smile.amazon.com/dp/0486425649)) 201 | - Gelfand and Saul. *Trigonometry* ([Birkhäuser 2001](https://smile.amazon.com/dp/0817639144)) 202 | - S. I. Gelfand, Gerver, Kirillov, Konstantinov. *Sequences, Combinations, Limits* 203 | 204 | Rutgers still runs the Extended Gelfand Correspondence Program in Mathematics (http://www.egcpm.com/), which allows you to have your exercises graded. You could just do them by yourself of course, but no answers are provided. The program accepts students of ages 13-17. 205 | 206 | Gelfand's books seem like a pretty interesting way to introduce high-school material to motivated students. They aren't as dry as most American textbooks, though they lack color and gloss. However, I'm not sure if they really go into enough depth in some areas, so you might need to supplement them with a book like Axler's. 207 | 208 | #### Kiselev 209 | 210 | Andrei P. Kiselev (Киселёв, also written Kiselyov) wrote a book called Geometry, which was the standard text in Russia for many decades (and was revised many times during that period). It is available in English in two volumes, *Planimetry* and *Stereometry*, which were translated and adapted for the USA by Alexander Givental. 211 | 212 | - [Kiselev's Geometry, Book I: Planimetry](https://smile.amazon.com/dp/0977985202) 213 | - [Kiselev's Geometry, Book II: Stereometry](https://smile.amazon.com/dp/0977985210) 214 | 215 | *Volume I: Planimetry* covers lines, circles, similarity, regular polygons and areas. *Volume II: Stereometry* covers figures in three dimensions: lines and planes, polyhedra and round solids; then it wraps up with an introduction to vectors and then an overview of the history of geometry and a brief introduction to non-Euclidean geometry. *Volume II* in particular goes well beyond what high school students in the US are expected to learn from a geometry course, and it gets very dense. 216 | 217 | #### Others 218 | 219 | Yakolev, High School Mathematics. ([Worldcat](http://www.worldcat.org/title/high-school-mathematics/oclc/39209913)) 220 | Dorofeev, Elementary Mathematics 221 | Vygodsky, Mathematical Handbook: Elementary Mathematics 222 | Govorov, Problems in Mathematics: with Hints and Solutions 223 | Bukhovtsev, Problems In Elementary Physics 224 | 225 | ### Harold Jacobs 226 | 227 | Jacobs books combine entertaining commentary and careful exposition. He aims to convince people who "don't like math" that really it's an interesting subject. These books are copiously illustrated, with lots of well-chosen images that help illustrate and reinforce the mathematical content. 228 | 229 | - *Mathematics: A Human Endeavor* ([3e](https://smile.amazon.com/dp/071672426X), [2e](https://smile.amazon.com/dp/0716713268)) 230 | - *Elementary Algebra* ([1e](https://smile.amazon.com/dp/0716710471)) 231 | - *Geometry: Seeing, Doing, Understanding* ([3e](https://smile.amazon.com/dp/0716743612), [2e](https://smile.amazon.com/dp/071671745X)) 232 | 233 | *Elementary Algebra* and *Geometry* are fairly standard secondary school curricula for those subjects. *A Human Endeavor* is a "topics" type book that would be appropriate for anyone at the pre-algebra level on up who isn't already familiar with the topics. The topics it presents aren't particularly advanced, but they are important ones, and many of them (e.g. statistics, topology) are not covered in a standard high school curriculum. 234 | 235 | A number of the topics covered in *A Human Endeavor* (e.g. symmetry) are ones that are typically introduced in the pre-algebra curriculum, then ignored for so long that students wonder why they were ever brought up until they re-emerge in an abstract algebra course a decade later for any students whose studies make it that far. But that's an entirely different discussion. 236 | 237 | ## Barbeau 238 | 239 | A quote from the introduction of Barbeau's *Polynomials*: 240 | 241 | > This book is not a textbook. Nor is its topic being particularly recommended for inclusion, indiscriminately, into the school curriculum. However, it should convey some of the breadth and depth found close to the traditional school and college curricula, and encourage the reader not only to follow up on some of the historical and technical references, but to pull out pen and paper to tackle some problems of special interest. Some of the mathematics will be difficult, but I believe that it will all be accessible. 242 | > 243 | > The intended audience consists of students at both high school and college who wish to go beyond the usual curriculum, as well as teachers who wish to broaden their mathematical experience and discover possible material for use with their regular or enriched students. In particular, I am concerned about two groups of students. There are those who romp through the school curriculum in mathematics while they have yet to complete other subjects. A standard response to this situation is to accelerate them, either into calculus or into college prematurely. 244 | > 245 | > While this is undoubtedly appropriate for some, my experience is that very often such acceleration is counterproductive and leads to an unsettled academic experience. Then there are those who get caught up in contest activity. It is now possible to spend much of the spring semester preparing for and writing contests, and this may have some value. However, there are some for whom contests are not congenial and others who emphasize the short-term goal of solving problems and winning contests at the expense of proper mathematical growth. 246 | > 247 | > What seems to be needed is a mathematical enrichment which starts with school mathematics, broadens it and yet is sufficiently down-to-earth that the student can explore it in an elementary way with pencil and paper or calculator. 248 | 249 | This book covers algebra, but it covers it much more deeply than typical high school courses. It would be appropriate, as Barbeau suggests, as enrichment reading for a high school student who is too advanced for the usual curriculum but has not been accelerated through it. It would help to remedy one of the failings of the typical high school curriculum, which is that algebra is typically not taught very thoroughly, then when it comes time to learn calculus, students' algebra skills are weak and their calculus skills suffer for it. 250 | 251 | Many of the problems are taken from various math contests. 252 | 253 | As an example of what you get in this book, it includes methods for solving cubic equations, which, while not really hard, are more involved than methods for quadratic equations and aren't normally taught to high school students. In addition to being useful (cubic equations do come up and not knowing how to solve one is embarrassing), I find these techniques to be very instructive as examples of how you could go about solving problems. 254 | 255 | Barbeau has another book, *Pell's Equation*, that is similar in spirit, and (unsurprisingly) explores Pell's equation. 256 | 257 | ## Old books in the public domain 258 | 259 | Leonhard Euler wrote an introduction to algebra called (in English) Elements of Algebra: 260 | 261 | - Free online 262 | - Scott Hecht's MS Word typesetting: https://archive.org/details/ElementsOfAlgebraLeonhardEuler2015 263 | - Copies of 1800's editions of Hewlett's translation: 264 | 265 | 266 | 267 | - Print editions 268 | - Springer hardcover facsimile print: 269 | - Scott Hecht's MS Word typesetting: 270 | - Looks to be printed from an Archive.org photocopy (original typesetting but poor quality with marks and underlining): 271 | 272 | These are apparently still really popular in India. Since they are in the public domain, you can find them available online for free. PDFs are available on archive.org, probably elsewhere as well. They are still in print, though not always as cheap as you'd hope given that the copyrights have expired. Be warned that since they're old, the writing style isn't what you'd expect from a contemporary book. 273 | 274 | - Hall and Knight, *Elementary Algebra for Schools* ([@Archive.org (Michigan)](https://archive.org/details/elementaryalgeb00kniggoog)) 275 | - Hall and Knight, *Higher Algebra* ([@Archive.org (Michigan)](https://archive.org/details/higheralgebraas00kniggoog), [@Archive.org (Wellesley)](https://archive.org/details/higheralgebraseq00hall), [Solutions @Archive.org (Cornell)](https://archive.org/details/cu31924105225399)) 276 | - Hall and Knight, *Elementary Trigonometry* ([@Archive.org (Boston College)](https://archive.org/details/elementarytrigon00hall), [Solutions @Archive.org (UC)](https://archive.org/details/solutionsofexamp00hallrich)) 277 | - Loney, *Plane Trigonometry* ([@Archive.org (Michigan)](https://archive.org/details/planetrigonomet03lonegoog)) 278 | - Chrystal, *Introduction to Algebra: For the Use of Secondary Schools and Technical Colleges* ([@Archive.org (UC)](https://archive.org/details/introductiontoal00chryrich)) 279 | - Chrystal, *Algebra: an Elementary Text-book* (two volumes) ([Vol I @Archive.org (Toronto)](https://archive.org/details/algebraelementar01chryuoft), [Vol II @Archive.org (Toronto)](https://archive.org/details/algebraelementar02chryuoft); [Vol I @Archive.org (Michigan)](https://archive.org/details/algebraanelemen09chrygoog), [Vol II @Archive.org (Michigan)](https://archive.org/details/algebraanelemen08chrygoog)) 280 | 281 | *Elementary Algebra for Schools* is probably unnecessary these days. It covers roughly the equivalent of Algebra I and maybe Algebra II in US high schools, but modern textbooks do a better job with the material. 282 | 283 | On the other hand, *Higher Algebra* is still a very useful book because much of the material that it covers is ignored by modern curricula. Some of what it covers is similar to Barbeau's *Polynomials* (e.g. Hall and Knight cover Cardano's method for solving cubic equations). Other topics in here, like continued fractions, are rarely discussed in modern textbooks. 284 | 285 | The famous Indian mathematician Ramanujan read Hall and Knight's *Higher Algebra* and cited it in his notebooks, and this association may account for its continuing fame in India, as Ramanujan is somewhat of a national hero. 286 | 287 | Loney's *Plane Trigonometry* has a lot of information, but I'm not sure how useful it is anymore as a textbook. This may be just a personal bias of mine, but I don't find trigonometry interesting enough to dedicate this much time and energy to all by itself. A book like Gelfand's or Axler's gives you the basics you need, and the rest is generally covered elsewhere (e.g. in calculus and analysis) when it's needed. If you really want to know a lot about trig, though, Loney might be what you want. 288 | 289 | Hall and Knight and Loney are available from Indian publishers for fairly cheap. Try searching AbeBooks to buy them if you're in the USA. I can't vouch for the quality of those cheap editions, but I've heard they're better than you might expect (unlike the terrible Indian editions published by companies like Wiley). 290 | 291 | Chrystal's *Introduction to Algebra* and *Algebra: an Elementary Text-book* form an elementary and advanced pair similar to Hall and Knight's *Elementary Algebra for Schools* and *Higher Algebra*, and similarly, the elementary one isn't of much interest. Chrystal's advanced text, *Algebra: an Elementary Text-book* (misleadingly titled), begins with the basic principles of algebra but it is not really a beginner's book, and it progresses quickly to a great variety of topics that are rarely taught these days, or are only taught at higher levels of algebra and analysis. Chrystal's books offer a lot of challenging problems. 292 | 293 | I don't know if anyone still uses these other old books or not, but some people like them. 294 | 295 | - Charles Smith. *A Treatise on Algebra* 296 | - Wells. *A First Course in Algebra* 297 | - Wells. *Second Course in Algebra* 298 | - Wells. *University Algebra* 299 | - Todhunter. *Algebra for beginners* ([1880 ed @Archive.org (Toronto)](https://archive.org/details/algebraforbeginn00todhuoft)) 300 | - Todhunter. *Algebra For the Use of Colleges and Schools* ([1889 ed @Archive.org (Toronto)](https://archive.org/details/algebraforuseofc00todhuoft)) 301 | 302 | ### Newer classic texts, not yet in the public domain 303 | 304 | - Durell and Robson. *Advanced Trigonometry* ([Dover](https://smile.amazon.com/dp/0486432297)) 305 | - Levi. *Elements of Algebra* ([AMS Chelsea](https://smile.amazon.com/dp/0828401039)) 306 | - Fine. *College Algebra* ([AMS Chelsea](https://smile.amazon.com/dp/0821838636)) 307 | 308 | ## Schaum's Outlines 309 | 310 | Schaum's has several of their "outlines" which are appropriate for this level. Schaum's outlines are full of worked problems, which you can use to study or to practice. (The answers are right there, though, so you have to cover them up if you want to use them for practice.) The outlines also provide some explanation of the topics, so in theory you could even use them as textbooks, though that isn't really what they're designed for. 311 | 312 | - *Elementary Algebra* 313 | - *Intermediate Algebra* 314 | - *Trigonometry* 315 | - *College Algebra* 316 | - *Geometry* 317 | - *Precalculus* 318 | 319 | # Others 320 | 321 | ## Free 322 | 323 | - Corral. *Trigonometry* 324 | 325 | ## More-or-less standard curriculum 326 | 327 | - David Rayner 328 | - *Essential Mathematics* ([Book 1](https://smile.amazon.com/dp/0199146616), [Book 2](https://smile.amazon.com/dp/0199146624), [Book 3](https://smile.amazon.com/dp/0199146632)) 329 | - *General Mathematics* ([1e](https://smile.amazon.com/dp/0199142785)) 330 | - Esty, Precalculus ([6e](https://smile.amazon.com/dp/1256671207)) 331 | - Foerster, Algebra and Trigonometry ([Classics ed](https://smile.amazon.com/dp/0131657100)) 332 | - Lang and Murrow, *Geometry: A High School Course* ([2e](https://smile.amazon.com/dp/0387966544), [Solutions manual](https://smile.amazon.com/dp/0387941819)) 333 | - Moise, *Elementary Geometry from an Advanced Standpoint* ([3e PB](https://smile.amazon.com/dp/0201508672), [2e HC](https://smile.amazon.com/dp/0201047934)) 334 | - Moise and Downs. *Geometry* [3e](https://smile.amazon.com/dp/0201253356) 335 | 336 | ## Enrichment 337 | 338 | - Ellison, *Hard Math for Elementary School* 339 | - Halmos, *Naive Set Theory* 340 | - Cofman, *Numbers and Shapes Revisited* 341 | - Rademacher, *Higher mathematics from an elementary point of view* 342 | - Lang, *Basic Mathematics* 343 | - Vilenkin, *Stories About Sets* 344 | - Krause, *Taxicab Geometry: An Adventure in Non-Euclidean Geometry* (c) 345 | - Richeson, *Euler's Gem: The Polyhedron Formula and the Birth of Topology* ([PUP HC](https://smile.amazon.com/dp/0691126771), [PUP PB](https://smile.amazon.com/dp/0691154570)) 346 | - Stroud and Booth, *Engineering Mathematics* ([7e](https://smile.amazon.com/dp/0831134704), [6e](https://smile.amazon.com/dp/0831133279), [5e](https://smile.amazon.com/dp/0831131527)) 347 | 348 | ## Problem books, problem solving, math competition prep 349 | 350 | - Tanton. *Trigonometry: A Clever Study Guide* ([1e](https://smile.amazon.com/Trigonometry-Clever-Study-Guide-Problem/dp/0883858363)) 351 | - Math Olympiad Contest Problems 352 | - Vol 1: For Elementary and Middle Schools 353 | - Vol 2: 354 | - Vol 3: 355 | - Stanford Mathematics Problem Book 356 | - Posamentier, Salkind. Challenging Problems in Algebra (Dover 1996, ISBN 978-0486691480, [Amazon](https://smile.amazon.com/dp/0486691489)) 357 | - Posamentier, Salkind. Challenging Problems in Geometry (Dover 1996, ISBN 978-0486691541, [Amazon](https://smile.amazon.com/dp/0486691543)) 358 | - Yaglom and Yaglom. Challenging Mathematical Problems With Elementary Solutions 359 | (Volume I, Dover 1987: ISBN 978-0486655369, [Amazon](0486655369); 360 | Volume II, Dover 1987: ISBN 978-0486655376, [Amazon](0486655377)) 361 | 362 | - 363 | - 364 | - 365 | - 366 | - 367 | - 368 | - 369 | - 370 | - 371 | - 372 | - 373 | - 374 | - 375 | - 376 | - 377 | - 378 | - 379 | - 380 | - 381 | - 382 | - 383 | - 384 | - 385 | - 386 | - 387 | 388 | ### AMS Mathematical World series 389 | 390 | From the AMS website: "This accessible series brings the beauty and wonder of mathematics to the advanced high school student, the mathematics teacher, the scientist or engineer, and the lay reader with a strong interest in mathematics. Mathematical World features well-written, challenging expository works that illustrate the fascination and usefulness of mathematics." 391 | 392 | Here's a link to the whole series on the AMS website: 393 | 394 | Some titles that have caught my attention: 395 | 396 | - Prasolov, *Intuitive Topology* 397 | - Farmer, *Groups and Symmetry: A Guide to Discovering Mathematics* 398 | - Farmer and Stanford, *Knots and Surfaces: A Guide to Discovering Mathematics* 399 | 400 | ## Cambridge reading list (pre-university) 401 | 402 | 403 | 404 | ## Sequences from major publishers 405 | 406 | I don't know if these are good, but they are affordable. 407 | 408 | - Dolciani *Structure and Method* 1970-76: [Algebra](https://smile.amazon.com/dp/0395142555), [Algebra and Trigonometry](https://smile.amazon.com/dp/0395142563) 409 | - Dolciani *Structure and Method* 1977-80: [Algebra](https://smile.amazon.com/dp/0395266378), [Algebra and Trigonometry](https://smile.amazon.com/dp/0395244102) 410 | - Dolciani. *Pre-Algebra: An Accelerated Course* [1987](https://smile.amazon.com/dp/039543050X) 411 | - McDougal Littell 1994-2000: [Algebra](https://smile.amazon.com/dp/0395977223), [Algebra and Trigonometry](https://smile.amazon.com/dp/039567610X), [Geometry](https://smile.amazon.com/dp/0395977274) 412 | - Addison Wesley 1993-94: [Algebra](https://smile.amazon.com/dp/0201812487), [Algebra teacher's](https://smile.amazon.com/dp/0201812495), [Geometry](https://smile.amazon.com/dp/0201812606), [Geometry teacher's](https://smile.amazon.com/dp/0201812614), [Algebra and Trigonometry](https://smile.amazon.com/dp/0201812525), [Algebra and Trigonometry teacher's](https://smile.amazon.com/dp/0201812533) 413 | - McGraw-Hill Glencoe 2004-05: [Algebra 1](https://smile.amazon.com/dp/0078651131), [Geometry](https://smile.amazon.com/dp/0078651069), [Algebra 2](https://smile.amazon.com/dp/0078656095) 414 | - Prentice-Hall 2003-2007: [Pre-algebra](https://smile.amazon.com/dp/0130686085), [Algebra](https://smile.amazon.com/dp/013052316X), [Algebra 2](https://smile.amazon.com/dp/013062568X), [Geometry](https://smile.amazon.com/dp/0131339974) 415 | - Bliter. Introductory & Intermediate Algebra for College Students 416 | (4e 2012: [Amazon](https://smile.amazon.com/dp/0321758943)) 417 | - Blitzer. Introductory Algebra for College Students 418 | (5e 2008: [Amazon](https://smile.amazon.com/dp/0132356791)) 419 | - Rockswold, Krieger. Beginning and Intermediate Algebra with Applications & Visualization (2e 2006: ) 420 | 421 | -------------------------------------------------------------------------------- /Sequence.md: -------------------------------------------------------------------------------- 1 | # A sequence of study 2 | 3 | ## Mathematics 4 | 5 | * Axler, *Precalculus* 6 | * [MIT OCW Calculus I (Jerison)](https://www.youtube.com/watch?v=7K1sB05pE0A&list=PL0361E2871852F969) 7 | * Spivak, *Calculus* 8 | * [MIT OCW Linear Algebra (Strang)](https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715CB9EF31D) 9 | * Strang, *Linear Algebra and its Applications* or *Introduction to Linear Algebra* 10 | * Axler, *Linear Algebra Done Right* (optional) 11 | * [MIT OCW Calculus II (Auroux)](https://www.youtube.com/watch?v=PxCxlsl_YwY&list=PL4C4C8A7D06566F38) 12 | * Hubbard and Hubbard, *Vector Calculus, Linear Algebra and Differential Forms* 13 | * Pinter, *A Book of Abstract Algebra* (optional) 14 | * Artin, *Algebra* 15 | * Stromberg, *An Introduction to Classical Real Analysis* 16 | * Rudin, *Principles of Mathematical Analysis* (optional) 17 | * Dummit and Foote, *Abstract Algebra* (optional, topics not in Artin) 18 | * Cox, Little, O'Shea, *Ideals, Varieties, and Algorithms* 19 | * Churchill, *Complex Variables and Applications* (optional) 20 | * Flanigan, *Complex Variables* 21 | * Akhiezer and Glazman, *Theory of Operators in Hilbert Space* 22 | 23 | ## University web pages that present possible courses of study 24 | 25 | * 26 | --------------------------------------------------------------------------------