├── README.md ├── build_toc.py └── contributing.md /README.md: -------------------------------------------------------------------------------- 1 | # Awesome Math [![Awesome](https://cdn.rawgit.com/sindresorhus/awesome/d7305f38d29fed78fa85652e3a63e154dd8e8829/media/badge.svg)](https://github.com/sindresorhus/awesome) 2 | 3 | A curated list of awesome mathematics resources. 4 | 5 | All resources are freely available except those with a 💲 icon. 6 | 7 | # Contents 8 | 9 | 10 | 11 | * [Contents](#contents) 12 | * [General Resources](#general-resources) 13 | * [Learning Platforms](#learning-platforms) 14 | * [Learn to Learn](#learn-to-learn) 15 | * [Youtube Series](#youtube-series) 16 | * [Tools](#tools) 17 | * [Questions and Answers](#questions-and-answers) 18 | * [Encyclopedia](#encyclopedia) 19 | * [Books](#books) 20 | * [Magazines](#magazines) 21 | * [Blogs](#blogs) 22 | * [Meetings and Conferences](#meetings-and-conferences) 23 | * [Misc](#misc) 24 | * [Branches of Mathematics](#branches-of-mathematics) 25 | * [Foundations of Mathematics](#foundations-of-mathematics) 26 | * [Transition To Pure Rigour Math](#transition-to-pure-rigour-math) 27 | * [Set Theory](#set-theory) 28 | * [Logic](#logic) 29 | * [Category Theory](#category-theory) 30 | * [Type Theory](#type-theory) 31 | * [Homotopy Type Theory](#homotopy-type-theory) 32 | * [Surreal Numbers](#surreal-numbers) 33 | * [Number Theory](#number-theory) 34 | * [Algebraic Number Theory](#algebraic-number-theory) 35 | * [Analytic Number Theory](#analytic-number-theory) 36 | * [Algebra](#algebra) 37 | * [Abstract Algebra](#abstract-algebra) 38 | * [Group Theory](#group-theory) 39 | * [Linear Algebra](#linear-algebra) 40 | * [Ring Theory](#ring-theory) 41 | * [Galois Theory](#galois-theory) 42 | * [Lie Algebras](#lie-algebras) 43 | * [Combinatorics](#combinatorics) 44 | * [Graph Theory](#graph-theory) 45 | * [Geometry and Topology](#geometry-and-topology) 46 | * [Differential Geometry](#differential-geometry) 47 | * [Algebraic Geometry](#algebraic-geometry) 48 | * [Algebraic Statistics](#algebraic-statistics) 49 | * [Topology](#topology) 50 | * [Algebraic Topology](#algebraic-topology) 51 | * [Analysis](#analysis) 52 | * [Real Analysis](#real-analysis) 53 | * [Harmonic Analysis](#harmonic-analysis) 54 | * [Complex Analysis](#complex-analysis) 55 | * [Functional Analysis](#functional-analysis) 56 | * [Measure Theory](#measure-theory) 57 | * [Ordinary Differential Equations](#ordinary-differential-equations) 58 | * [Partial Differential Equations](#partial-differential-equations) 59 | * [Probability and Statistics](#probability-and-statistics) 60 | * [Probability Theory](#probability-theory) 61 | * [Statistics](#statistics) 62 | * [Statistical Learning](#statistical-learning) 63 | * [Stochastic processes](#stochastic-processes) 64 | * [Numerical Analysis](#numerical-analysis) 65 | * [Signal processing](#signal-processing) 66 | * [Mathematics for Computer Science](#mathematics-for-computer-science) 67 | * [Mathematical Biology](#mathematical-biology) 68 | * [Mathematical Physics](#mathematical-physics) 69 | * [Students Lecture Notes](#students-lecture-notes) 70 | * [Related Awesome Lists](#related-awesome-lists) 71 | * [License](#license) 72 | 73 | 74 | 75 | # General Resources 76 | 77 | ## Learning Platforms 78 | 79 | * [Khan Academy](https://www.khanacademy.org/math) 80 | * [Coursera](https://www.coursera.org/courses?query=mathematics&languages=en) 81 | * [MIT OpenCourseWare](http://ocw.mit.edu/courses/mathematics/) 82 | * [edX](https://www.edx.org/course/subject/math) 83 | * [Brilliant](https://brilliant.org/courses/#math-foundational) 84 | * [WooTube](https://misterwootube.com/) 85 | * [Mathigon](https://mathigon.org/) 86 | * [Calculus.org](http://calculus.org/) 87 | * [Ximera](https://ximera.osu.edu/) : free interactive mathematics textbooks (Ohio State University) 88 | * [Almost Fun](https://www.almostfun.org/lessons/) 89 | * [Oxford Mathematics](https://www.youtube.com/c/OxfordMathematics) 90 | * [Math Academy](https://mathacademy.com/) 91 | 92 | ## Learn to Learn 93 | 94 | * [Understanding Mathematics](https://github.com/nelson-brochado/understanding-math) 95 | 96 | ## Youtube Series 97 | 98 | * [Brandon Foltz](https://www.youtube.com/@BrandonFoltz) 99 | * [StatQuest](https://www.youtube.com/channel/UCtYLUTtgS3k1Fg4y5tAhLbw) 100 | * [3Blue1Brown](https://www.youtube.com/@3blue1brown) 101 | * [NPTEL](https://www.youtube.com/@iit) 102 | * [PatrickJMT](https://www.youtube.com/@patrickjmt) 103 | * [Professor Leonard](https://www.youtube.com/@ProfessorLeonard) 104 | * [Precalculus - College Algebra/Trigonometry](https://www.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP) 105 | * [Calculus 1](https://www.youtube.com/playlist?list=PLF797E961509B4EB5) 106 | * [Calculus 2](https://www.youtube.com/playlist?list=PLDesaqWTN6EQ2J4vgsN1HyBeRADEh4Cw-) 107 | * [Calculus 3](https://www.youtube.com/playlist?list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7) 108 | * [Differential Equations](https://www.youtube.com/playlist?list=PLDesaqWTN6ESPaHy2QUKVaXNZuQNxkYQ_) 109 | * [To The Point Math](https://www.youtube.com/playlist?list=PLDesaqWTN6ETc1ZwHWijCBcZ2gOvS2tTN) 110 | * [Crash Course](https://www.youtube.com/@crashcourse) 111 | * [Harvard](https://www.youtube.com/@harvard) 112 | * [MIT OpenCourseWare](https://www.youtube.com/@mitocw) 113 | * [Mathologer](https://www.youtube.com/@Mathologer) 114 | * [The Math District](https://www.youtube.com/@TheMathDistrict) 115 | * [Mathematical Monk](https://www.youtube.com/@mathematicalmonk) 116 | * [The Math Sorcerer](https://www.youtube.com/@TheMathSorcerer) 117 | 118 | ## Tools 119 | 120 | * [Symbolab](https://www.symbolab.com/) 121 | * [Desmos](https://www.desmos.com/calculator) 122 | * [Math Words](http://www.mathwords.com/) 123 | * [Wolfram Alpha](http://www.wolframalpha.com/) 124 | * [Maxima](https://maxima.sourceforge.io/) 125 | * [Sympy](https://www.sympy.org/) 126 | * [Sagemath](http://www.sagemath.org/) 127 | * [Unit Converter](https://unitconverters.net) 128 | * [GeoGebra](https://www.geogebra.org/?lang=en) 129 | * [Macaulay2](http://www2.macaulay2.com/Macaulay2/) 130 | * [Singular](https://www.singular.uni-kl.de/) 131 | * [GNU Octave](https://www.gnu.org/software/octave/) 132 | * [Magma](http://magma.maths.usyd.edu.au/magma/) 133 | * [Maple](https://www.maplesoft.com/products/Maple/) 134 | * [Matlab](https://www.mathworks.com/products/matlab.html) 135 | * [Wolfram Mathematica](https://www.wolfram.com/mathematica/) 136 | * [Free Math](https://freemathapp.org) 137 | * [xhub](https://chrome.google.com/webstore/detail/xhub/anidddebgkllnnnnjfkmjcaallemhjee) 138 | * [CopyPasteMathjax](https://www.copypastemathjax.com/) 139 | * [Finance calculators](https://www.financecharts.com/pages/5724-retirement-calculators-and-stock-market-tips) 140 | * [Mathcheap](https://mathcheap.xyz) 141 | * [Midpoint Calculator](https://midpointcalculator.co) 142 | * [Quartiles Calculator](https://quartilecalculator.net) 143 | * [Corca Editor](https://corca.io/) 144 | 145 | ## Questions and Answers 146 | 147 | * [Mathematics Stack Exchange](http://math.stackexchange.com/) 148 | * [MathOverflow](http://mathoverflow.net/) - for professional mathematicians 149 | 150 | ## Encyclopedia 151 | 152 | * [Encyclopedia of Mathematics](https://www.encyclopediaofmath.org) 153 | * [Planetmath](http://planetmath.org/) 154 | * [ProofWiki](https://proofwiki.org/wiki/Main_Page) 155 | * [Wolfram Mathworld](http://mathworld.wolfram.com/) 156 | * [The On-Line Encyclopedia of Integer Sequences](https://oeis.org) - Great compendium of many different integer sequences. Founded 1964 by N. J. A. Sloane. 157 | * 💲 [The Princeton Companion to Mathematics](https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics) - Timothy Gowers (Professor, Fields medallist), June Barrow-Green (Professor), and Imre Leader (Professor). 158 | * 💲 [Encyclopedia of Distances (4th Edition)](https://link.springer.com/book/10.1007/978-3-662-52844-0) - Michel Marie Deza, Elena Deza. 159 | 160 | ## Books 161 | 162 | * [Calculus: Basic Concepts for High Schools](https://archive.org/details/TarasovCalculus) - L.V. Tarasov 163 | * [Basics of Algebra, Topology, and Differential Calculus](http://www.cis.upenn.edu/~jean/math-basics.pdf) - Jean Gallier (University of Pennsylvania) 164 | * [Multivariable Calculus](http://people.math.gatech.edu/%7Ecain/notes/calculus.html) - G. Cain, J. Herod (Georgia Tech) 165 | * [Wikibooks](https://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf) 166 | * [Online Mathematics Textbooks](https://people.math.gatech.edu/~cain/textbooks/onlinebooks.html) 167 | * [Beginning and Intermediate Algebra](http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf) 168 | * [Free Mathematics Books](https://github.com/EbookFoundation/free-programming-books/blob/master/books/free-programming-books-subjects.md#mathematics) 169 | * [Trigonometry](http://www.mecmath.net/trig/trigbook.pdf) 170 | 171 | ## Magazines 172 | 173 | * [Quanta Magazine](https://www.quantamagazine.org/mathematics/) - Features latest research breakthroughs in an accessible style for non-experts. 174 | * [Bulletin of the American Mathematical Society](https://www.ams.org/journals/bull/all_issues.html) - Expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. 175 | * [Notices of the American Mathematical Society](http://www.ams.org/cgi-bin/notices/amsnotices.pl?article_id=fullissue&article_type=gallery&gallery_type=fullissue) - Publicizes activities of the Society and features surveys, reports, news, announcements, and opinions on industry trends, academia, and research. 176 | * [European Mathematical Society Magazine](https://euromathsoc.org/magazine) - The Magazine features announcements about meetings and conferences, articles outlining current trends in scientific development, reports on member societies, and many other informational items. 177 | * [Mathematics Today by Institute of Mathematics and its Applications](https://ima.org.uk/publications/mathematics-today/) - News, opinions, and articles related to mathematics, so the reader stays updated. 178 | * [Crux Mathematicorum by Canadian Mathematical Society](https://cms.math.ca/publications/crux/) - source of unique and challenging mathematical problems designed for the secondary and undergraduate levels. It includes an Olympiad Corner which is helpful for math competitions. 179 | 180 | ## Blogs 181 | 182 | * [BetterExplained](https://betterexplained.com/) - Maintained by Kalid Azad 183 | * [ILoveMaths](http://ilovemaths.com/) - For grades 6 thru 12 in K-12 system 184 | * [3blue1brown](https://www.3blue1brown.com/) - Animated Maths 185 | * [Mathsisfun](https://www.mathsisfun.com) simple text lightweight site for students up to highschool 186 | * [MathematicsIsAScience](https://calculus123.com/wiki/Peter_Saveliev) - Peter Saveliev (Professor of mathematics at Marshall University, Huntington WV, USA) 187 | 188 | ## Meetings and Conferences 189 | 190 | * [MathsJam](https://mathsjam.com/) - monthly local recreational maths/puzzle meetups and an annual gathering in Staffordshire, England 191 | * [Talking Maths in Public](https://talkingmathsinpublic.uk/) - a conference for maths communicators, running every two years, usually in the UK 192 | * [Bridges](https://www.bridgesmathart.org/) - an annual conference on mathematical connections in art, music, architecture, and culture. The 2025 meeting is in Eindhoven, Netherlands. 193 | 194 | ## Misc 195 | * [Areas of mathematics on Wikipedia](https://en.wikipedia.org/wiki/Areas_of_mathematics) 196 | * [Paul's Online Math Notes](http://tutorial.math.lamar.edu/) - Paul Dawkins (Lamar University) 197 | * [List of electronic textbooks](http://faculty.atu.edu/mfinan/nnotes.html) - Marcel B. Finan (Arkansas Tech University) 198 | * [Topology Atlas](http://at.yorku.ca/topology/) 199 | * [Recreations in Math](http://djm.cc/library/Recreations_in_Mathematics_Licks_edited.pdf) - H. E. Licks (1917) 200 | * [Magic Squares and Cubes](http://djm.cc/library/Magic_Squares_Cubes_Andrews_edited.pdf) - W. S. Andrews (1917) 201 | * [Convex Optimization](https://web.stanford.edu/~boyd/cvxbook/) - Stephen Boyd and Lieven Vandenberghe 202 | * [Fabrice Baudoin's Notes](https://fabricebaudoin.wordpress.com/) - Both research and lecture notes on many topics, Including Diffusions on foliated manifold, Stochastic Calculus, Global analysis in Dirichlet spaces, and more. 203 | 204 | # Branches of Mathematics 205 | 206 | **Content Format** \ 207 | 📖 Books \ 208 | 🎥 Videos \ 209 | 📝 Lecture notes, slides, articles, papers 210 | 211 | ## Foundations of Mathematics 212 | ### Transition To Pure Rigour Math 213 | * 📝 [Basic Concepts of Mathematics](http://www.trillia.com/zakon1.html) - Elias Zakon 214 | * 📝 [Book of Proof](https://richardhammack.github.io/BookOfProof/) - Richard Hammak (Virginia Commonwealth University) 215 | * 📖 [How to Prove It: A Structured Approach (3rd Edition)](https://ia800501.us.archive.org/7/items/how-to-prove-it-a-structured-approach-daniel-j.-velleman/How%20to%20Prove%20It%20A%20Structured%20Approach%20%28Daniel%20J.%20Velleman%29.pdf) - Daniel J. Velleman (Professor). 216 | 217 | ### Set Theory 218 | 219 | * 📝 [Sets, Relations, Functions](http://www.cosc.brocku.ca/~duentsch/papers/methprimer1.html) - Ivo Düntsch, Günther Gediga 220 | * 📝 [An Introduction to Set Theory](http://www.math.toronto.edu/weiss/set_theory.pdf) - William A. R. Weiss 221 | * 📝 [Set Theory and Foundations of Mathematics](http://www.settheory.net/) - Sylvain Poirier 222 | * 📝 [Set Theory on the Stanford Encyclopedia of Philosophy](http://plato.stanford.edu/entries/set-theory/) 223 | 224 | ### Logic 225 | 226 | * 📝 [Introduction to Logic](https://pdfs.semanticscholar.org/6967/f52773d9c2ccfc94658657a5761e0f00e95a.pdf) - Michael Genesereth, Eric Kao (Stanford University) 227 | * 📝 [An Introduction to Formal Logic](https://www.fecundity.com/codex/forallx.pdf) - P.D. Magnus (University at Albany) 228 | * 📝 [A Problem Course in Mathematical Logic](http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf) - Stefan Bilaniuk (Trent University) 229 | * 📝 [Computability - An introduction to recursive function theory](http://poincare.matf.bg.ac.rs/~zarkom/Book_Math__Cutland_Computability.pdf) - Nigel Cutland (University of Hull) 230 | * 📝 [Language, Proof, and Logic](http://homepages.uc.edu/~martinj/Symbolic_Logic/341%20Syllabus,%20Textbook,%20Handouts,%20Notes/LPL%20textbook.pdf) - Jon Barwise, John Etchemendy 231 | * 📝 [Mathematical Logic](http://www.mathematik.uni-muenchen.de/~schwicht/lectures/logic/ws03/ml.pdf) - Helmut Schwichtenberg 232 | * 📝 [Mathematical Logic](http://www.personal.psu.edu/t20/notes/logic.pdf) - Stephen G. Simpson (Pennsylvania State University) 233 | * 📝 [Formal Logic](http://maude.sip.ucm.es/~miguelpt/papers/flogic.pdf) - Miguel Palomino 234 | * 📝 [Predictive Arithmetic](https://web.math.princeton.edu/~nelson/books/pa.pdf) - Edward Nelson 235 | * 📝 [Proofs and Concepts: the fundamentals of abstract mathematics](http://people.uleth.ca/~dave.morris/books/proofs+concepts.html) - Joy Morris, Dave Morris 236 | * 📝 [Mathematical Reasoning: Writing and Proof](https://www.tedsundstrom.com/mathreasoning) - Ted Sundstrom 237 | * 📝 [Logic and Proof](http://leanprover.github.io/logic_and_proof/) - Jeremy Avigad, Robert Y. Lewis, and Floris van Doorn 238 | * 📝 [QED - an interactive textbook](https://teorth.github.io/QED) - Terence Tao 239 | * 📝 [Open Logic Textbook](http://builds.openlogicproject.org/) - collaborative effort, main contributors listed [here](https://openlogicproject.org/people/) 240 | 241 | ### Category Theory 242 | 243 | * 📝 [Introduction to Category Theory and Categorical Logic](http://www.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf) - Thomas Streicher 244 | * 📝 [An Introduction to Category Theory](http://www.cs.man.ac.uk/~hsimmons/zCATS.pdf) - Harold Simmons 245 | * 📝 [Category Theory](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.211.4754&rep=rep1&type=pdf) - Steve Awodey (Carnegie Mellon University) 246 | * 📝 [Category Theory](http://www.mathematik.uni-muenchen.de/~pareigis/Vorlesungen/04SS/Cats1.pdf) - B. Pareigis 247 | * 📝 [Category Theory for Computing Science](https://web.archive.org/web/20181221233252/http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf) - Michael Barr, Charles Wells 248 | * 📝 [Toposes, Triples and Theories](http://www.tac.mta.ca/tac/reprints/articles/12/tr12.pdf) - Michael Barr, Charles Wells 249 | * 📝 [Abelian Categories](http://www.tac.mta.ca/tac/reprints/articles/3/tr3abs.html) - Peter Freyd 250 | * 📝 [Categories and Groupoids](http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html) - P. J. Higgins 251 | * 📝 [Basic Concepts of Enriched Category Theory](http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html) - G. M. Kelley 252 | * 📝 [Abstract and Concrete Categories: The Joy of Cats](http://www.tac.mta.ca/tac/reprints/articles/17/tr17abs.html) - Jiri Adamek, Horst Herrlich, George Strecker 253 | * 📝 [Seven Sketches in Compositionality: An Invitation to Applied Category Theory](http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf) - Brendan Fong and David I. Spivak (MIT) 254 | * 📝 [Category Theory in Context](http://www.math.jhu.edu/~eriehl/context/) - Emily Riehl (John Hopkins University) 255 | 256 | ### Type Theory 257 | * 📝 [Proofs and Types](http://www.paultaylor.eu/stable/prot.pdf) - Jean-Yves Girard 258 | * 📝 [Intuitionistic Type Theory](https://archive-pml.github.io/martin-lof/pdfs/Bibliopolis-Book-retypeset-1984.pdf) - Per Martin-Lof 259 | * 📝 [Type Theory and Functional Programming](https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/) - Simon Thompson 260 | * 📝 [Programming in Martin-Lof’s Type Theory](http://www.cse.chalmers.se/research/group/logic/book/book.pdf) - Bengt Nordstrom, Kent Petersson, Jan M. Smith 261 | 262 | ### Homotopy Type Theory 263 | 264 | * 📝 [Homotopy Type Theory](https://hottheory.files.wordpress.com/2013/03/hott-online-611-ga1a258c.pdf) 265 | 266 | ### Surreal Numbers 267 | 268 | * 📝 [Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness](http://www.math.harvard.edu/~knill/teaching/mathe320_2015_fall/blog15/surreal1.pdf) - D. E. Knuth 269 | * 📝 [Surreal Numbers and Games](http://web.mit.edu/sp.268/www/2010/surreal.pdf) 270 | * 📝 [Conway names, the simplicity hierarchy and the surreal number tree](http://www.ohio.edu/people/ehrlich/ConwayNames.pdf) - Philip Ehrlich 271 | 272 | 273 | ## Number Theory 274 | 275 | * 📝 [Elementary Number Theory: Primes, Congruences, and Secrets](http://wstein.org/ent/ent.pdf) - William Stein 276 | * 📝 [Elementary Number Theory](http://math.utoledo.edu/~codenth/Spring_13/3200/ENT-books/Elementary_Number_Theory-Clark.pdf) - W. Edwin Clark (University of South Florida) 277 | * 📝 [A Course on Number Theory](http://www.maths.qmul.ac.uk/~pjc/notes/nt.pdf) - Peter J. Cameron 278 | * 📝 [A Computational Introduction to Number Theory and Algebra](http://shoup.net/ntb/ntb-v2.pdf) - Victor Shoup 279 | * 📝 [Number Theory: A Contemporary Introduction](http://alpha.math.uga.edu/~pete/4400FULL.pdf) - Pete L. Clark 280 | * 📝 [An Introduction to the Theory of Numbers](http://www.trillia.com/moser-number.html) - Leo Moser 281 | * 📝 [Yet Another Introductory Number Theory Textbook](https://www.poritz.net/jonathan/share/yaintt/) - Jonathan A. Poritz 282 | 283 | ### Algebraic Number Theory 284 | 285 | * 📝 [Introduction to Algebraic Number Theory](http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf) 286 | * 📝 [Introduction to Algebraic Number Theory](http://www1.spms.ntu.edu.sg/~frederique/ANT10.pdf) - F. Oggier 287 | * 📝 [Algebraic Number Theory](http://www.jmilne.org/math/CourseNotes/ANT.pdf) - J.S. Milne 288 | * 📝 [Algebraic Number Theory Course Notes](http://people.math.gatech.edu/~mbaker/pdf/ANTBook.pdf) - Matthew Baker (Georgia Tech) 289 | * 📝 [A Course In Algebraic Number Theory](http://www.math.uiuc.edu/~r-ash/ANT.html) - Robert Ash 290 | 291 | ### Analytic Number Theory 292 | 293 | * 📝 [Introduction to Analytic Number Theory](http://www.math.uiuc.edu/~hildebr/ant/main.pdf) - A.J. Hildebrand (University of Illinois) 294 | * 📝 [Elements of Analytic Number Theory](http://math.nsc.ru/~vdovin/lectures/numth_eng.pdf) - P. S. Kolesnikov, E. P. Vdovin (Novosibirsk) 295 | * 📝 [Analytic Number Theory](http://www.mathematik.uni-muenchen.de/~forster/v/ann/annth_all.pdf) - Otto Forster (LMU Munich) 296 | * 📝 [Analytic Number Theory - Lecture Notes based on Davenport’s book](http://www2.math.uu.se/~astrombe/analtalt08/www_notes.pdf) - Andreas Strömbergsson 297 | 298 | 299 | ## Algebra 300 | 301 | * 📝 [A Course in Universal Algebra](http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html) - S. Burris, H.P. Sankappanavar 302 | * 📝 [A Course in Commutative Algebra](https://faculty.math.illinois.edu/~r-ash/ComAlg.html) - Robert Ash 303 | * 📝 [First Course in Algebra](http://djm.cc/library/First_Algebra_Hawkes_Luby_Touton_edited.pdf) - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1910) 304 | * 📝 [Second Course in Algebra](http://djm.cc/library/Second_Algebra_Hawkes_Luby_Touton_edited.pdf) - Herbert E. Hawkes, William A. Luby, Frank C. Touton (1911) 305 | * 📝 [Algebra: An Elementary Text-Book, Part I](http://djm.cc/library/Algebra_Elementary_Text-Book_Part_I_Chrystal_edited.pdf) - G. Chrystal (1904) 306 | * 📝 [Algebra: An Elementary Text-Book, Part II](http://djm.cc/library/Algebra_Elementary_Text-Book_Part_II_Chrystal_edited02.pdf) - G. Chrystal (1900) 307 | * 📝 [Understanding Algebra](https://jamesbrennan.org/algebra) - James W. Brennan 308 | 309 | ### Abstract Algebra 310 | 311 | * 📝 [Introduction to Abstract Algebra](https://zodml.org/sites/default/files/Introduction_to_Abstract_Algebra_0.pdf) - D. S. Malik, John N. Mordeson, M.K. Sen (Creighton University) 312 | * 📝 [Introduction to Modern Algebra](http://aleph0.clarku.edu/~djoyce/ma225/algebra.pdf) - David Joyce (Clark University) 313 | * 📝 [Algebraic Methods](http://www1.spms.ntu.edu.sg/~frederique/AA11.pdf) - F. Oggier 314 | * 📝 [Abstract Algebra : Theory and Applications](http://abstract.ups.edu/download/aata-20150812.pdf) - Thomas W. Judson, Robert A. Beezer (Austin State University) 315 | * 📝 [An Undergraduate Course in Abstract Algebra](http://www.maths.usyd.edu.au/u/bobh/UoS/rfwhole.pdf) - Robert Howlett 316 | * 📝 [Elements of Abstract and Linear Algebra](http://www.math.miami.edu/~ec/book) - E.H. Connell (University of Miami) 317 | * 📝 [Abstract Algebra: The Basic Graduate Year](http://www.math.uiuc.edu/~r-ash/Algebra.html) - Robert Ash 318 | * 📝 [Abstract Algebra: Harvard Extension (Archived)](https://web.archive.org/web/20150528171650/extension.harvard.edu/open-learning-initiative/abstract-algebra) - Benedict Gross 319 | * 📝 [Abstract Algebra: Harvard Extension Videos](https://www.youtube.com/playlist?list=PLA58AC5CABC1321A3) - Benedict Gross 320 | 321 | ### Group Theory 322 | 323 | * 📝 [Notes on Group Theory](https://www2.bc.edu/mark-reeder/Groups.pdf) - Mark Reeder 324 | * 📝 [Group Theory](http://www.jmilne.org/math/CourseNotes/GT.pdf) - J.S. Milne 325 | * 📝 [Notes on Finite Group Theory](http://www.maths.qmul.ac.uk/~pjc/notes/gt.pdf) - Peter J. Cameron 326 | * 📝 [Group Theory](http://www.cns.gatech.edu/GroupTheory/index.html) - Pedrag Civitanovic 327 | 328 | ### Linear Algebra 329 | 330 | * 📝 [Fundamentals of Linear Algebra](http://www.math.ubc.ca/~carrell/NB.pdf) - James B. Carrell 331 | * 📝 [Linear Algebra and Matrices](https://web.archive.org/web/20140824074655/http://mathstat.helsinki.fi/~fluch/linear_algebra_1-sp07/la1.pdf) - Martin Fluch 332 | * 📝 [Vector Space Theory](http://www.maths.usyd.edu.au/u/bobh/UoS/MATH2902/vswhole.pdf) - Robert Howlett 333 | * 📝 [Linear Algebra](http://joshua.smcvt.edu/linearalgebra) - Jim Hefferon 334 | * 📝 [MIT OpenCourseWare Lectures on Linear Algebra (18.06) as Jupyter Notebooks](https://github.com/juanklopper/MIT_OCW_Linear_Algebra_18_06) - Juan Klopper 335 | * 📝 [Elementary Linear Algebra](http://www.numbertheory.org/book/) - Keith Matthews 336 | * 📝 [A First Courses in Linear Algebra](http://linear.ups.edu/) - Rob Breezer 337 | * 📝 [Linear Algebra](https://www.math.ucdavis.edu/~linear/) - David Cherney, Tom Denton, Andrew Waldron 338 | * 📝 [Introduction to vectors and tensors, Vol 1: linear and multilinear algebra](http://oaktrust.library.tamu.edu/handle/1969.1/2502) - Ray M Bowen, C. C. Wang 339 | * 📝 [Introduction to vectors and tensors, Vol 2: vector and tensor analysis](http://oaktrust.library.tamu.edu/handle/1969.1/3609) - Ray M Bowen, C. C. Wang 340 | * 📝 [Introduction to Applied Linear Algebra](https://web.stanford.edu/~boyd/vmls/vmls.pdf) - Stephen Boyd (Stanford University), Lieven Vandenberghe (UCLA) 341 | * 📝 [Linear Algebra Done Wrong](https://www.math.brown.edu/~treil/papers/LADW/LADW_2017-09-04.pdf) - Sergei Treil 342 | * 📝 [Immersive Linear Algebra](http://immersivemath.com/ila/index.html) - J. Ström, K. Åström, and T. Akenine-Möller 343 | * 📝 [Interactive Linear Algebra](https://textbooks.math.gatech.edu/ila/) - Dan Margalit and Joseph Rabinoff 344 | * 📝 [Linear Algebra, Infinite Dimensions, and Maple](https://people.math.gatech.edu/~herod/Hspace/Hspace.html) - James Herod 345 | * 📖 [Linear Algebra Done Right](https://linear.axler.net/) - Sheldon Axler 346 | 347 | ### Ring Theory 348 | 349 | * 📝 [Foundations of Module and Ring Theory](http://www.math.uni-duesseldorf.de/~wisbauer/book.pdf) - Robert Wisbauer (University of Düsseldorf) 350 | 351 | ### Galois Theory 352 | 353 | * 📝 [An Introduction to Galois Theory](http://www.maths.gla.ac.uk/~ajb/dvi-ps/Galois.pdf) - Andrew Baker (University of Glasgow) 354 | * 📝 [Fields and Galois Theory](http://www.jmilne.org/math/CourseNotes/FT.pdf) - J.S. Milne 355 | * 📝 [Galois theory](http://homepages.warwick.ac.uk/~masda/MA3D5/Galois.pdf) - Miles Reid 356 | * 📝 [Galois Theory](https://eclass.uoa.gr/modules/document/file.php/MATH594/Stewart%20Galois%204th%20edition.pdf) - Ian Stewart 357 | * 📝 [Galois Theory](https://arxiv.org/pdf/2408.07499) — Tom Leinster (University of Edinburgh) 358 | 359 | ### Lie Algebras 360 | 361 | * 📝 [Lie Algebras](http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf) - Shlomo Sternberg 362 | 363 | ## Combinatorics 364 | 365 | * 📝 [Basic Combinatorics](http://www.math.utk.edu/~wagner/papers/comb.pdf) - Carl G. Wagner (University of Tennessee) 366 | * 📝 [Applied Combinatorics](http://people.math.gatech.edu/~trotter/book.pdf) - Mitchel T. Keller, William T. Trotter 367 | * 📝 [Notes on Combinatorics](http://www.maths.qmul.ac.uk/~pjc/notes/comb.pdf) - Peter J. Cameron 368 | * 📝 [Analytic Combinatorics](http://algo.inria.fr/flajolet/Publications/book.pdf) - Philippe Flajolet, Robert Sedgewick 369 | * 📝 [generatingfunctionology](http://www.math.upenn.edu/~wilf/DownldGF.html) - Herbert Wilf 370 | 371 | ### Graph Theory 372 | 373 | * 📝 [Graph Theory: Lecture Notes](http://www.personal.psu.edu/cxg286/Math485.pdf) - Christopher Griffin 374 | * 📝 [Graph Theory](http://www.cs.unibo.it/babaoglu/courses/cas00-01/tutorials/GraphTheory.pdf) - Reinhard Diestel 375 | 376 | 377 | ## Geometry and Topology 378 | 379 | * 📝 [Fundamentals of Geometry](http://polly.phys.msu.ru/~belyaev/geometry.pdf) - Oleg A. Belyaev 380 | * 📝 [A=B](https://www.math.upenn.edu/~wilf/AeqB.html) - M. Petkovsek, H. Wilf, D. Zeilberger 381 | * 📝 [Elements](http://aleph0.clarku.edu/~djoyce/java/elements/toc.html) - Euclid 382 | * 📝 [Euclid's Elements Redux](http://starrhorse.com/euclid/) - Daniel Callahan 383 | * 📝 [Mathematical Illustrations](http://www.math.ubc.ca/~cass/graphics/manual/) - Bill Casselman 384 | * 📝 [Byrne's Euclid](https://www.c82.net/euclid/) - Oliver Byrne 385 | * 📝 [Plane Geometry](http://djm.cc/library/Plane_Geometry_Wentworth_Smith_edited.pdf) - George Wentworth and David Eugene Smith (1913) 386 | * 📝 [Planes and Spherical Trigonometry](http://djm.cc/library/Plane_Spherical_Trigonometry_Wentworth_Smith_edited_2.pdf) - George Wentworth and David Eugene Smith (1915) 387 | * 📝 [Coordinate Geometry](http://djm.cc/library/Coordinate_Geometry_Fine_Thompson_edited03.pdf) - Henry Buchard Fine and Henry Dallas Thompson (1911) 388 | * 📝 [Analytic Geometry](http://djm.cc/library/Analytic_Geometry_Siceloff_Wentworth_Smith_edited.pdf) - Lewis Parker Siceloff, George Wentworth, David Eugene Smith (1922) 389 | 390 | ### Differential Geometry 391 | 392 | * 📝 [Introduction to Differential Geometry](https://people.math.ethz.ch/~salamon/PREPRINTS/diffgeo.pdf) - Joel W. Robbin, Dietmar A. Salamon 393 | * 📝 [Notes on Differential Geometry and Lie Groups](https://www.cis.upenn.edu/~jean/gbooks/manif.html) - Jean Gallier (University of Pennsylvania) 394 | * 📝 [Topics in Differential Geometry](http://www.mat.univie.ac.at/~michor/dgbook.pdf) - Peter W. Michor 395 | * 📝 [Lectures on Differential Geometry](http://mysite.science.uottawa.ca/rossmann/Differential%20Geometry%20book_files/Diffgeo.pdf) - Wulf Rossmann 396 | * 📝 [An Introduction to Riemannian Geometry](http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf) - Sigmundur Gudmundsson (Lund University) 397 | * 📝 [The Geometry and Topology of Three-Manifolds](http://msri.org/publications/books/gt3m/) - W. Thurston 398 | * 📝 [Semi-Riemann Geometry and General Relativity](http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf) - Shlomo Sternberg 399 | * 📝 [Discrete Differential Geometry](http://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf) - Keenan Crane 400 | 401 | ### Algebraic Geometry 402 | 403 | * 📝 [A Brief Introduction to Algebraic Geometry](https://ksda.ccny.cuny.edu/PostedPapers/rickksda1107.pdf) - R.C. Churchill 404 | * 📝 [Introduction to Algebraic Geometry](http://www.math.lsa.umich.edu/~idolga/631.pdf) - Igor V. Dolgachev 405 | * 📝 [Foundations of Algebraic Geometry](http://math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf) - Ravi Vakil 406 | * 📝 [Algebraic Geometry](http://www.cis.upenn.edu/~jean/algeoms.pdf) - Jean Gallier, Stephen S. Shatz (University of Pennsylvania) 407 | * 📝 [Algebraic Geometry](http://www.jmilne.org/math/CourseNotes/AG.pdf) - J.S. Milne 408 | * 📝 [Algebraic Geometry](http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/main.pdf) - Andreas Gathmann (University of Kaiserslautern) 409 | * 📝 [The Stacks Project](https://stacks.math.columbia.edu/) - Maintained by Aise Johan de Jong (Columbia) 410 | 411 | ### Algebraic Statistics 412 | * 📝 [Lectures on Algebraic Statistics](https://math.berkeley.edu/~bernd/owl.pdf) - Mathias Drton, Bernd Sturmfels, Seth Sullivant 413 | * 📝 [An Introduction to Algebraic Statistics](https://www3.diism.unisi.it/~chiantini/did/00Book.pdf) - Cristiano Bocci, Luca Chiantini and Anthony V. Geramita 414 | * 📝 [Algebraic Statistics](https://tore.tuhh.de/dspace-cris-server/api/core/bitstreams/a0c378d5-ce8e-442a-8891-9e7f763b4279/content) - Karl-Heinz Zimmermann 415 | * 📝 [Algebraic Statistics for Computational Biology](http://yaroslavvb.com/papers/pachter-algebraic.pdf) - Pachter, and Sturmfels. 416 | 417 | ### Topology 418 | 419 | * 📝 [Elementary Applied Topology](https://www.math.upenn.edu/~ghrist/notes.html) - Robert Ghrist (UPenn) 420 | * 📝 [Introduction to Topology](http://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf) 421 | * 📝 [Introduction to Topology](http://www.math.bme.hu/~kalex/Teaching/Spring10/Topology/TopNotes_Spring10.pdf) - Alex Küronya 422 | * 📝 [Introductory Topology](http://www.math.clemson.edu/~jimlb/Teaching/2009-10/Math986/Topology.pdf) - Jim L. Brown 423 | * 📝 [General Topology](http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/Topo.pdf) - Pierre Schapira (Paris VI University) 424 | * 📝 [Elementary Topology Problem Textbook](http://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf) 425 | * 📝 [General Topology](http://www.math.ku.dk/~moller/e03/3gt/notes/gtnotes.pdf) - Jesper M. Møller 426 | * 📝 [Topology Topics](http://mathonline.wikidot.com/topology) 427 | 428 | ### Algebraic Topology 429 | 430 | * 📝 [Algebraic Topology](http://www.math.cornell.edu/~hatcher/AT/AT.pdf) - Allen Hatcher 431 | * 📝 [A Concise Course in Algebraic Topology](http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf) - J. P. May 432 | * 📝 [Introduction to Algebraic Topology](http://www.math.muni.cz/~cadek/at/at.pdf) - Martin Cadek 433 | * 📝 [Algebra and Topology](http://webusers.imj-prg.fr/~pierre.schapira/lectnotes/AlTo.pdf) - Pierre Schapira (Paris VI University) 434 | * 📝 [Lecture Notes in Algebraic Topology](http://www.indiana.edu/~jfdavis/teaching/m623/book.pdf) - James F. Davis, Paul Kirk (Indiana University) 435 | * 📝 [Algebraic Topology](https://www.ma.utexas.edu/ibl1/courses/resources/12_15_07_grad_alg_top_mooremethod.pdf) - Michael Starbird 436 | * 📝 [Lecture Notes on Algebraic Topology](http://www.math.nus.edu.sg/~matwujie/ma5209.pdf) - Jie Wu 437 | 438 | 439 | ## Analysis 440 | 441 | ### Real Analysis 442 | 443 | * 📝 [MIT OpenCourseWare Lectures on Calculus](https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/) - G. Strang 444 | * 📝 [Elementary Calculus: An Approach Using Infinitesimals](http://www.math.wisc.edu/~keisler/calc.html) - Professor H. Jerome Keisler 445 | * 📝 [An Introduction to Real Analysis](https://www.math.ucdavis.edu/~hunter/intro_analysis_pdf/intro_analysis.pdf) - John K. Hunter (University of California at Davis) 446 | * 📝 [Introduction to Real Analysis](http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF) - William F. Trench (Trinity University, Texas) 447 | * 📝 [Basic Analysis: Introduction to Real Analysis](http://www.jirka.org/ra/realanal.pdf) - Jiří Lebl 448 | * 📝 [Elementary Real Analysis](http://prac.im.pwr.wroc.pl/~kwasnicki/pl/stuff/tbb-hyper.pdf) - Thomson, Bruckner 449 | * 📝 [Lecture Notes in Real Analysis](http://ms.mcmaster.ca/~sawyer/Publications/Real_Analysis.pdf) - Eric T. Sawyer (McMaster University) 450 | * 📝 [Real Analysis](http://math.harvard.edu/~ctm/papers/home/text/class/harvard/212a/course/course.pdf) - C. McMullen 451 | * 📝 [Real Analysis for Graduate Students](http://bass.math.uconn.edu/3rd.pdf) - Richard F. Bass 452 | * 📝 [Modern Real Analysis](http://www.math.purdue.edu/~torres/pubs/Modern-real-analysis.pdf) - William P. Ziemer (Indiana University) 453 | * 📝 [Mathematical Analysis Vol I](http://www.trillia.com/zakon-analysisI.html) - Elias Zakon 454 | * 📝 [Mathematical Analysis Vol II](http://www.trillia.com/zakon-analysisII.html) - Elias Zakon 455 | * 📝 [Advanced Calculus](http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf) - Lynn Loomis, Schlomo Sternberg 456 | * 📝 [ Analysis of Functions of a Single Variable](http://spot.colorado.edu/~baggett/analysis.html) - Lawerence Baggett 457 | * 📝 [The Calculus of Functions of Several Variables](http://www.synechism.org/wp/the-calculus-of-functions-of-several-variables/) - Dan Sloughter 458 | * 📝 [A ProblemText in Advanced Calculus](http://web.pdx.edu/~erdman/PTAC/problemtext_pdf.pdf) - John M. Erdman 459 | * 📝 [Calculus and Linear Algebra. Vol. 1](http://hdl.handle.net/2027/spo.5597602.0001.001) - Wilfred Kaplan, Donald J. Lewis 460 | * 📝 [Calculus and Linear Algebra. Vol. 2](https://quod.lib.umich.edu/s/spobooks/5597602.0002.001) - Wilfred Kaplan, Donald J. Lewis 461 | * 📝 [Introduction to Calculus I and II](http://www.math.odu.edu/~jhh/counter10.html) - J.H. Heinbockel 462 | * 📝 [Active Calculus](http://faculty.gvsu.edu/boelkinm/Home/Active_Calculus.html) - Matt Boelkins 463 | * 📝 [Supplements to the Exercises in Chapters 1-7 of Walter Rudin's "Principles of Mathematical Analysis"](https://math.berkeley.edu/~gbergman/ug.hndts/#Rudin) - George M. Bergman 464 | * 📝 [Calculus Made Easy](http://calculusmadeeasy.org/) - Silvanus P. Thompson (1910) 465 | * 📝 [Elements of Differential and Integral Calculus](http://djm.cc/library/Elements_Differential_Integral_Calculus_Granville_edited_2.pdf) - William Anthony Granville (1911) 466 | * 📝 [Precalculus](https://stitz-zeager.com/szprecalculus07042013.pdf) - Carl Stitz, Jeff Zeager 467 | 468 | ### Harmonic Analysis 469 | 470 | * 📝 [Harmonic Analysis Lecture Notes](http://www.math.uiuc.edu/~laugesen/545/545Lectures.pdf) - Richard S. Laugesen (University of Illinois at Urbana–Champaign) 471 | * 📝 [Harmonic Analysis](http://www.math.uchicago.edu/~schlag/harmonicnotes.pdf) - W. Schlag 472 | * 📝 [Lecture Notes: Fourier Transform and its Applications](https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf) - Brad Osgood 473 | * 📝 [Fourier Analysis](http://www.reed.edu/physics/courses/Physics331.f08/pdf/Fourier.pdf) - Lucas Illing 474 | * 📝 [Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications](https://ccrma.stanford.edu/~jos/mdft) - Julius O. Smith III (Stanford University) 475 | 476 | ### Complex Analysis 477 | 478 | * 📝 [Introduction to Complex Analysis](https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/complex.pdf) - Michael Taylor 479 | * 📝 [An Introduction to Complex Analysis and Geometry](http://www.math.uiuc.edu/~jpda/jpd-complex-geometry-book-5-refs-bip.pdf) - John P. D'Angelo (University of Illinois) 480 | * 📝 [A First Course in Complex Analysis](http://math.sfsu.edu/beck/papers/complex.pdf) - Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka 481 | * 📝 [A Guide to Complex Variables](http://www.math.wustl.edu/~sk/books/guide.pdf) - Steven G. Krantz 482 | * 📝 [Complex Analysis](http://www.maths.manchester.ac.uk/~cwalkden/complex-analysis/complex_analysis.pdf) - Charles Walkden 483 | * 📝 [Complex Analysis](http://www.math.ku.dk/noter/filer/koman-12.pdf) - Christian Berg 484 | * 📝 [Complex Variables](http://people.math.sc.edu/girardi/m7034/book/AshComplexVariablesWithHyperlinks.pdf) - R. B. Ash, W.P. Novinger 485 | * 📝 [Complex Analysis](http://www.maths.lth.se/matematiklu/personal/olofsson/CompHT06.pdf) - Christer Bennewitz 486 | * 📝 [Complex Analysis](https://web.archive.org/web/20150620124453/https://www.math.washington.edu/~marshall/math_536/Notes.pdf) - Donald E. Marshall 487 | * 📝 [A Concise Course in Complex Analysis and Riemann Surfaces](https://gauss.math.yale.edu/~ws442/complex.pdf) - Wilhelm Schlag 488 | * 📝 [Complex Analysis](http://people.math.gatech.edu/%7Ecain/winter99/complex.html) - G. Cain (Georgia Tech) 489 | * 📝 [Complex Analysis](https://complex-analysis.com/) - Juan Carlos Ponce Campuzano 490 | 491 | ### Functional Analysis 492 | 493 | * 📝 [An Introduction to Functional Analysis](https://www.math.uwaterloo.ca/~lwmarcou/notes/pmath453.pdf) - Laurent W. Marcoux (University of Waterloo) 494 | * 📝 [Functional Analysis: Lecture Notes](http://users.math.msu.edu/users/jeffrey/920/920notes.pdf) - Jeff Schenker (Michigan State University) 495 | * 📝 [Functional Analysis Lecture Notes](https://archive.org/details/TB_Ward___Functional_analysis_lecture_notes) - T.B. Ward (University of East Anglia) 496 | * 📝 [Functional Analysis](http://www.maths.lancs.ac.uk/~belton/www/notes/fa_notes.pdf) - Alexander C. R. Belton 497 | * 📝 [Topics in Real and Functional Analysis](https://www.mat.univie.ac.at/~gerald/ftp/book-fa/fa.pdf) - Gerald Teschl 498 | * 📝 [Functional Analysis](http://www2.math.ou.edu/~cremling/teaching/lecturenotes/fa-new/LN-I.pdf) - Christian Remling 499 | * 📝 [Theory of Functions of a Real Variable](http://www.math.harvard.edu/~shlomo/docs/Real_Variables.pdf) - Shlomo Sternberg 500 | * 📝 [Functional Analysis](http://spot.colorado.edu/~baggett/functional.html) - Lawerence Baggett 501 | 502 | ### Measure Theory 503 | 504 | * 📝 [An Introduction to Measure Theory](https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf) - Terence Tao (UCLA) 505 | * 📝 [Lecture Notes on Measure Theory and Functional Analysis](http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf) - P. Cannarsa, T. D’Aprile 506 | * 📝 [Lecture Notes in Measure Theory](http://www.math.chalmers.se/~borell/MeasureTheory.pdf) - Christer Borell 507 | * 📝 [A Crash Course on the Lebesgue Integral and Measure Theory](http://www.gold-saucer.org/math/lebesgue/lebesgue.pdf) - Steve Cheng 508 | * 📝 [Measure Theory](https://www.math.ucdavis.edu/~hunter/measure_theory/measure_notes.pdf) - John K. Hunter (University of California at Davis) 509 | * 📝 [Measure and Integration](https://people.math.ethz.ch/~salamon/PREPRINTS/measure.pdf) - Dietmar A. Salamon (ETH Zürich) 510 | * 📝 [Lecture notes: Measure Theory](http://www.math.ucsd.edu/~bdriver/240-00-01/Lecture_Notes/measurep.pdf) - Bruce K. Driver 511 | 512 | ### Ordinary Differential Equations 513 | 514 | * 📝 [Difference Equations To Differential Equations](http://www.synechism.org/wp/difference-equations-to-differential-equations/) - Dan Sloughter 515 | * 📝 [Ordinary Differential Equation](https://www.math.uni-bielefeld.de/~grigor/odelec2008.pdf) - Alexander Grigorian (University of Bielefeld) 516 | * 📝 [Ordinary Differential Equations: Lecture Notes](http://www.cs.bgu.ac.il/~leonid/ode_bio_files/Ionascu_LectNotes.pdf) - Eugen J. Ionascu 517 | * 📝 [Ordinary Differential Equations](http://www.math.lmu.de/~philip/publications/lectureNotes/ODE.pdf) - Peter Philip 518 | * 📝 [Ordinary Differential Equations](http://users.math.msu.edu/users/gnagy/teaching/ode.pdf) - Gabriel Nagy 519 | * 📝 [Ordinary Differential Equations and Dynamical Systems](http://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf) - Gerald Teschl 520 | * 📝 [Notes on Differential Equations](http://leipper.org/manuals/zip-fill/dn-difeq-notes.pdf) - Bob Terrell 521 | * 📝 [Elementary Differential Equations](http://digitalcommons.trinity.edu/mono/8/) - William F. Trench 522 | * 📝 [Elementary Differential Equations With Boundary Value Problems](http://digitalcommons.trinity.edu/mono/9/) - William F. Trench 523 | * 📝 [Notes on Diffy Qs: Differential Equations for Engineers](http://www.jirka.org/diffyqs/) - Jiří Lebl 524 | * 📝 [Differential Equations](http://djm.cc/library/Differential_Equations_Phillips_edited.pdf) - H. B. Phillips (1922) 525 | 526 | ### Partial Differential Equations 527 | 528 | * 📝 [Notes on Partial Differential Equations](https://www.math.ucdavis.edu/~hunter/pdes/pde_notes.pdf) - John K. Hunter (University of California at Davis) 529 | * 📝 [Partial Differential Equations: Lecture Notes](http://www.math.uni-leipzig.de/~miersemann/pdebook.pdf) - Erich Miersemann (Leipzig University) 530 | * 📝 [Linear Methods of Applied Mathematics](http://www.mathphysics.com/pde/) - E. Harrell, J. Herod (Georgia Tech) 531 | 532 | 533 | ## Probability and Statistics 534 | 535 | ### Probability Theory 536 | 537 | * 📝 [Introduction to Probability](https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf) - Charles M. Grinstead, J. Laurie Snell 538 | * 📝 [Introduction to Probability](http://vfu.bg/en/e-Learning/Math--Bertsekas_Tsitsiklis_Introduction_to_probability.pdf) - Dimitri P. Bertsekas, John N. Tsitsiklis (MIT) 539 | * 📝 [A Short Introduction to Probability](http://www.maths.uq.edu.au/~kroese/asitp.pdf) - Dirk P. Kroese (University of Queensland) 540 | * 📝 [Probability: Theory and Examples](https://www.math.duke.edu/~rtd/PTE/PTE4_1.pdf) - Rick Durrett 541 | * 📝 [Probability and Statistics Cookbook](https://github.com/mavam/stat-cookbook/releases/download/0.2.3/stat-cookbook.pdf) - Matthias Vallentin (UC Berkeley) 542 | * 📝 [The Only Probability Cheatsheet You'll Ever Need](http://www.wzchen.com/probability-cheatsheet/) - William Chen 543 | * 📝 [An Introduction to Probability and Random Processes](http://www.ellerman.org/Davids-Stuff/Maths/Rota-Baclawski-Prob-Theory-79.pdf) - Gian-Carlo Rota, Kenneth Baclawski 544 | * 📝 [Foundations of Constructive Probability Theory](https://arxiv.org/pdf/1906.01803.pdf) - Yuen-Kwok Chan 545 | 546 | ### Statistics 547 | 548 | * 📝 [Lecture Notes on Statistical Theory](http://homepages.math.uic.edu/~rgmartin/Teaching/Stat411/Notes/411notes.pdf) - Ryan Martin (University of Illinois) 549 | * 📝 [Introduction to Statistics and Data Analysis for Physicists](http://www-library.desy.de/preparch/books/vstatmp_engl.pdf) - Gerhard Bohm, Günter Zech 550 | * 📝 [Probability and Mathematical Statistics](http://www.iiserpune.ac.in/~ayan/MTH201/Sahoo_textbook.pdf) - Prasanna Sahoo (University of Louisville) 551 | * 📝 [Lectures on Statistics](http://math.arizona.edu/~faris/stat.pdf) - William G. Faris 552 | * 📝 [Statistical Theory](http://pages.pomona.edu/~ajr04747/Fall2009/Math152/Notes/Math152NotesFall09.pdf) - Adolfo J. Rumbos 553 | * 📝 [Theory of Statistics](http://mason.gmu.edu/~jgentle/books/MathStat.pdf) - James E. Gentle (George Mason University) 554 | * 📝 [Theory of Statistics](http://math.arizona.edu/~jwatkins/notests.pdf) - Joseph C. Watkins (University of Arizona) 555 | * 📝 [Glossary of Data Modeling](https://web.archive.org/web/20130523134625/http://www.aiaccess.net/e_gm.htm) - AI Access 556 | * 📝 [Statistics Papers](http://www.ats.ucla.edu/stat/papers/) - List of statistics papers curated by the Institute for Digital Research and Education (IDRE) at UCLA on methods such as bootstrap and factor invariance. 557 | * 📝 [NIST Handbook of Statistical Methods](http://itl.nist.gov/div898/handbook/index.htm) - Resource on practical statistics directed towards scientists and engineers. 558 | * 📝 [Concepts and Applications of Inferential Statistics](http://vassarstats.net/textbook/) - Richard Lowry 559 | * 📝 [Rough set data analysis: A road to non-invasive knowledge discovery](http://www.cosc.brocku.ca/~duentsch/papers/methprimer2.html) - Ivo Düntsch, Günther Gediga 560 | * 📝 [Statistical Thinking for the 21st Century](https://statsthinking21.org/) - Russell A. Poldrack 561 | * 📝 [Odds and Ends: Introducing Probability & Decision with a Visual Emphasis](https://jonathanweisberg.org/vip/) - Jonathan Weisberg 562 | * 📝 [Seeing Theory](https://seeing-theory.brown.edu/) - Daniel Kunin, Jingru Guo, Tyler Dae Devlin, and Daniel Xiang 563 | * 📝 [Statistics Done Wrong](https://www.statisticsdonewrong.com/) - Alex Reinhart 564 | * 📝 [All of Statistics: A Concise Course in Statistical Inference](https://link.springer.com/book/10.1007/978-0-387-21736-9) - Larry Wasserman 565 | 566 | ### Statistical Learning 567 | 568 | * 📝 [An Introduction to Statistical Learning with Applications in R](http://www-bcf.usc.edu/~gareth/ISL/ISLR%20First%20Printing.pdf) - Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani 569 | * 📝 [The Elements of Statistical Learning](http://web.stanford.edu/~hastie/Papers/ESLII.pdf) - Trevor Hastie, Robert Tibshirani, Jerome Friedman 570 | * 📝 [Statistical Learning Theory](https://web.stanford.edu/class/cs229t/notes.pdf) - Percy Liang 571 | * 📝 [Reinforcement Learning: An Introduction](https://webdocs.cs.ualberta.ca/~sutton/book/bookdraft2016sep.pdf) - Richard S. Sutton, Andrew G. Barto 572 | 573 | ### Stochastic processes 574 | 575 | * 📝 [Lectures on Stochastic Processes](http://www.math.tifr.res.in/~publ/ln/tifr24.pdf) - K. Ito (Tata Institute of Fundamental Research, Bombay) 576 | * 📝 [Probability and Stochastic Processes with Applications](http://www.math.harvard.edu/~knill/teaching/math144_1994/probability.pdf) - Oliver Knill (Harvard University) 577 | * 📝 [Stochastic Processes](http://statweb.stanford.edu/~adembo/math-136/nnotes.pdf) - Amir Dembo (Stanford University) 578 | * 📝 [Lecture Notes on Stochastic Processes](http://www.mi.fu-berlin.de/wiki/pub/CompMolBio/MarkovKetten15/stochastic_processes_2011.pdf) - Frank Noé, Bettina Keller and Jan-Hendrik Prinz (Freie Universität Berlin) 579 | * 📝 [Introduction to Stochastic Processes - Lecture Notes](https://www.ma.utexas.edu/users/gordanz/notes/introduction_to_stochastic_processes.pdf) - Gordan Žitković (University of Texas) 580 | * 📝 [Applied Stochastic Processes in science and engineering](https://www.math.uwaterloo.ca/~mscott/Little_Notes.pdf) - Matt Scott (University of Waterloo) 581 | * 📝 [An Introduction to Stochastic Processes in Continuous Time](http://www.math.leidenuniv.nl/~spieksma/colleges/sp-master/sp-hvz1.pdf) - Flora Spieksma (Leiden University) 582 | * 📝 [Markov Chains and Mixing Times](http://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf) - David A. Levin, Yuval Peres, Elizabeth L. Wilmer 583 | * 📝 [Convergence of Stochastic Processes](http://www.stat.yale.edu/~pollard/Books/1984book/pollard1984.pdf) - David Pollard 584 | 585 | 586 | ## Numerical Analysis 587 | 588 | * 📝 [Introduction to Numerical Analysis](http://www.math.umd.edu/~dlevy/resources/notes.pdf) - Doron Levy (University of Maryland) 589 | * 📝 [A Concise Introduction to Numerical Analysis](http://www.ima.umn.edu/~arnold/597.00-01/nabook.pdf) - Douglas N. Arnold (University of Minnesota) 590 | * 📝 [Numerical Analysis](http://people.cs.uchicago.edu/~ridg/newna/nalrs.pdf) - L. Ridgway Scott 591 | * 📝 [Lectures In Basic Computational Numerical Analysis](https://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1000&context=math_textbooks) - J. M. McDonough (University of Kentucky) 592 | * 📝 [Advanced Numerical Methods and Their Applications to Industrial Problems: Adaptive Finite Element Methods](https://user.math.uni-bremen.de/schmi/SS04/YSU_Notes.pdf) - Alfred Schmidt, Arsen Narimanyan 593 | * 📝 [Numerical Analysis for Engineers](https://ece.uwaterloo.ca/~dwharder/nm/) - Douglas Wilhelm Harder 594 | * 📝🎥 [Advanced Linear Algebra: Foundations to Frontiers](https://www.cs.utexas.edu/users/flame/laff/alaff/frontmatter.html) - Robert van de Geijn, Margaret Myers (University of Texas at Austin) 595 | 596 | ## Signal processing 597 | 598 | * 📝 [Introduction to Signal Processing](http://www.ece.rutgers.edu/~orfanidi/intro2sp/orfanidis-i2sp.pdf) - Sophocles J. Orfanidis (Rutgers University) 599 | * 📝 [Foundations of Signal Processing](http://www.fourierandwavelets.org/FSP_v1.1_2014.pdf) - Martin Vetterli, Jelena Kovacevic, Vivek K Goyal 600 | * 📝 [An Introduction to Statistical Signal Processing](https://ee.stanford.edu/~gray/sp.pdf) - Robert M. Gray, Lee D. Davisson 601 | * 📝 [Think DSP](https://greenteapress.com/wp/think-dsp/) - Allen B. Downey 602 | * 📝 [Linear algebra, signal processing, and wavelets. A unified approach.](https://www.uio.no/studier/emner/matnat/math/MAT-INF2360/v15/kompendium/applinalgpython.pdf) - Øyvind Ryan (University of Oslo) 603 | 604 | 605 | ## Mathematics for Computer Science 606 | 607 | * 📝 [Mathematics for Computer Science](https://people.csail.mit.edu/meyer/mcs.pdf) - Eric Lehman, F. Thomson Leighton, Albert R. Meyer 608 | * 📝 [Algorithms and Complexity](http://www.math.upenn.edu/%7Ewilf/AlgComp3.html) - H. Wilf 609 | * 📝 [Lecture Notes on Optimization](http://people.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf) - Pravin Varaiya 610 | * 📝 [Information Theory, Inference, and Learning Algorithms](http://www.inference.org.uk/mackay/itila/book.html) - David J. C. MacKay 611 | * 📝 [The Chaos Textbook: Mathematics in the age of the computer](https://hypertextbook.com/chaos/) - Glenn Elert 612 | 613 | ## Mathematical Biology 614 | 615 | * 📝 [Mathematical Biology](http://www.math.ust.hk/~machas/mathematical-biology.pdf) - Jeffrey Chasnov 616 | 617 | ## Mathematical Physics 618 | 619 | * 📝 [Introduction to Continuum Mechanics](http://oaktrust.library.tamu.edu/handle/1969.1/2501) - Ray. M. Bowen 620 | * 📝 [Mathematical Tools for Physics](http://www.physics.miami.edu/nearing/mathmethods/) - James Nearing 621 | * 📝 [Mechanism of the Heavens (1831)](http://www.malaspina.com/etext/heavens.htm) - Mary Somerville 622 | 623 | # Students Lecture Notes 624 | * [Evan Chen](https://web.evanchen.cc/coursework.html) - MIT. 2012 ~ 2018. Covers Combinatorics, Number Theory, Honors Algebra, Set Theory, Real Analysis, Graph Theory, and more. 625 | * [Dexter Chua](https://dec41.user.srcf.net/notes/) - Harvard. 2013 ~ 2018. Covers Analysis, Probability, Linear Algebra, Complex Analysis, Numerical Analysis, Statistics, Optimization, Algebraic Topology, Quantum Field Theory, and more. 626 | 627 | # Related Awesome Lists 628 | * [Theoretical Computer Science](https://github.com/mostafatouny/awesome-theoretical-computer-science) 629 | 630 | # License 631 | 632 | [![CC0](http://i.creativecommons.org/p/zero/1.0/88x31.png)](http://creativecommons.org/publicdomain/zero/1.0/) 633 | 634 | To the extent possible under law, [Cyrille Rossant](http://cyrille.rossant.net) has waived all copyright and related or neighboring rights to this work. 635 | -------------------------------------------------------------------------------- /build_toc.py: -------------------------------------------------------------------------------- 1 | """Generate the table of contents and insert it at the top of README.md.""" 2 | 3 | 4 | import re 5 | 6 | 7 | _HEADER_REGEX = r'([#]+) ([^\n]+)' 8 | _PUNCTUATION_REGEX = r'[^\w\- ]' 9 | _HEADER_TEMPLATE = '{indent}* [{name}](#{anchor})' 10 | _START_TOC = '' 11 | _END_TOC = '' 12 | 13 | 14 | def _anchor(name): 15 | anchor = name.lower().replace(' ', '-') 16 | anchor = re.sub(_PUNCTUATION_REGEX, '', anchor) 17 | return anchor 18 | 19 | 20 | def _parse_header(header): 21 | r = re.match(_HEADER_REGEX, header) 22 | if r: 23 | level = len(r.group(1)) 24 | name = r.group(2) 25 | return level, _anchor(name), name 26 | 27 | 28 | def _iter_headers(md): 29 | headers = (line for line in md.splitlines() 30 | if line.startswith('#')) 31 | for header in headers: 32 | yield header 33 | 34 | 35 | def _get_header_item(header): 36 | level, anchor, name = _parse_header(header) 37 | indent = ' ' * max(0, level - 1) 38 | return _HEADER_TEMPLATE.format(**locals()) 39 | 40 | 41 | def _gen_items(md): 42 | for header in _iter_headers(md): 43 | item = _get_header_item(header) 44 | yield item 45 | 46 | 47 | def _read_md(filename): 48 | with open(filename, 'r') as f: 49 | return f.read() 50 | 51 | 52 | def gen_toc(filename): 53 | md = _read_md(filename) 54 | i = md.index(_START_TOC) + len(_START_TOC) + 2 55 | j = md.index(_END_TOC) 56 | with open(filename, 'w') as f: 57 | f.write(md[:i]) 58 | for item in _gen_items(md): 59 | if 'Awesome Math' in item: 60 | continue 61 | f.write(item + '\n') 62 | f.write('\n' + md[j:]) 63 | 64 | 65 | if __name__ == '__main__': 66 | filename = 'README.md' 67 | gen_toc(filename) 68 | -------------------------------------------------------------------------------- /contributing.md: -------------------------------------------------------------------------------- 1 | # Contribution Guidelines 2 | 3 | Please ensure your pull request adheres to the following guidelines: 4 | 5 | - Search previous suggestions before making a new one, as yours may be a duplicate. 6 | - Make an individual pull request for each suggestion. 7 | - Use the following format: `[Item Name](link) - Author (University)` 8 | - New categories or improvements to the existing categorization are welcome. 9 | - Check your spelling and grammar. 10 | - The pull request and commit should have a useful title. 11 | 12 | Thank you for your suggestions! 13 | --------------------------------------------------------------------------------