├── LICENSE └── README.md /LICENSE: -------------------------------------------------------------------------------- 1 | This is free and unencumbered software released into the public domain. 2 | 3 | Anyone is free to copy, modify, publish, use, compile, sell, or 4 | distribute this software, either in source code form or as a compiled 5 | binary, for any purpose, commercial or non-commercial, and by any 6 | means. 7 | 8 | In jurisdictions that recognize copyright laws, the author or authors 9 | of this software dedicate any and all copyright interest in the 10 | software to the public domain. We make this dedication for the benefit 11 | of the public at large and to the detriment of our heirs and 12 | successors. We intend this dedication to be an overt act of 13 | relinquishment in perpetuity of all present and future rights to this 14 | software under copyright law. 15 | 16 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 17 | EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF 18 | MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 19 | IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR 20 | OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 21 | ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 22 | OTHER DEALINGS IN THE SOFTWARE. 23 | 24 | For more information, please refer to 25 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | ## Online Mathematics Textbooks 2 | 3 | > *editor's note* this list was [originally authored](http://people.math.gatech.edu/~cain/textbooks/onlinebooks.html) by George Cain of Georgia Tech and is offered here on github so it might be preserved/maintained after his passing in 2015. 4 | 5 | (If GA Tech prefers that their page be preserved and the canonical reference I can take this repo down). 6 | 7 | The writing of textbooks and making them freely available on the web is an idea whose time has arrived. Most college mathematics textbooks attempt to be all things to all people and, as a result, are much too big and expensive. This perhaps made some sense when these books were rather expensive to produce and distribute--but this time has passed. 8 | 9 | 1. Professor [Jim Herod](http://www.math.gatech.edu/~herod) and I have written [_Multivariable Calculus_](../notes/calculus.html) ,a book which we and a few others have used here at Georgia Tech for two years. We have also proposed that this be the first calculus course in the curriculum here, but that is another story.... 10 | 11 | 2. Although it is still in print, [_Calculus_](http://ocw.mit.edu/ans7870/textbooks/Strang/strangtext.htm),by [Gilbert Strang](http://www-math.mit.edu/~gs/) is made available through [MIT's OpenCourseWare](http://ocw.mit.edu/index.html) electronic publishing initiative. 12 | 13 | 3. Here is one that has also been used here at Georgia Tech. [_Linear Methods of Applied Mathematics_](http://www.mathphysics.com/pde/), by [Evans Harrell](http://www.math.gatech.edu/~harrell) and [James Herod](http://www.math.gatech.edu/~herod). 14 | 15 | 4. Yet another one produced at Georgia Tech is [_Linear Algebra, Infinite Dimensions, and Maple_](http://www.math.gatech.edu/~herod/Hspace/Hspace.html), by [James Herod](http://www.math.gatech.edu/~herod). 16 | 17 | 5. George Cain has also written a modest book, [_Complex Analysis_](../winter99/complex.html), which he has used in his introductory undergraduate complex analysis course at GA Tech. 18 | 19 | 6. [_Complex Variables_](http://www.math.uiuc.edu/~r-ash/CV.html) , by [Robert Ash](http://www.math.uiuc.edu/~r-ash) and [W. P. Novinger](http://www.math.fsu.edu/People/faculty.php?id=448). This is a substantial revision of the first edition of Professor Ash's complex variables text originally published in 1971. 20 | 7. Professor [E.H. Connell](http://www.math.miami.edu/~ec) of the University of Miami has made available on the web his book [_Elements of Abstract and Linear Algebra_](http://www.math.miami.edu/~ec/book). You should read his insightful comments about textbooks. 21 | 22 | 8. An introductory algebraic topology book, [_Algebraic Topology I_](http://www.math.cornell.edu/~hatcher/), by [Professor Allen Hatcher](http://www.math.cornell.edu/~hatcher/), of Cornell University, is available, and Professor Hatcher promises the second volume, Algebraic Topology II, will be ready soon. 23 | 24 | 9. [_The Geometry and Topology of Three-Manifolds_](http://msri.org/publications/books/gt3m/), by William Thurston. This is an electronic edition of the 1980 lecture notes distributed by Princeton University. 25 | 26 | 10. [Professor Jim Hefferon](http://joshua.smcvt.edu/math/hefferon.html) of Saint Michaels's College has made available his undergraduate textbook [_Linear Algebra_](http://joshua.smcvt.edu/linalg.html). 27 | 28 | 11. Another elementary linear algebra textbook is [_Elementary Linear Algebra_](http://www.numbertheory.org/book/), by [Keith Matthews](http://www.numbertheory.org/keith.html). 29 | 30 | 12. [_Introduction to Probability_](http://www.dartmouth.edu/~chance/teaching_aids/books_atricles/probability_book/book.html), by Charles Grinstead & J. Laurie Snell. 31 | 32 | 13. [_An Introduction to Probability and Random Processes_](http://www.ellerman.org/Davids-Stuff/Maths/Rota-Baclawski-Prob-Theory-79.pdf), by Gian-Carlo Rota and [Kenneth Baclawski](http://www.ccs.neu.edu/home/kenb/). This is the 1979 manuscript of the work Professor Rota had been working on for some time. It is made available through the efforts of [David Ellerman.](http://www.ellerman.org/Davids-Stuff/AboutDavidEllerman.htm) 33 | 34 | 14. [Professor Herbert Wilf](http://www.cis.upenn.edu/~wilf) has made available his book [_generatingfunctionology_](http://www.math.upenn.edu/~wilf/DownldGF.html). 35 | 36 | 15. Another one by [Professor Wilf](http://www.cis.upenn.edu/~wilf) is [_Algorithms and Complexity_](http://www.cis.upenn.edu/%7Ewilf/AlgComp3.html). 37 | 38 | 16. [_A = B_](http://www.cis.upenn.edu/~wilf/AeqB.html), by Marko Petkovsek, [Herbert Wilf](http://www.cis.upenn.edu/~wilf), and [Doron Zeilberger](http://www.math.rutgers.edu/~zeilberg/). 39 | 40 | 17. Furnished by [David Joyce](http://aleph0.clarku.edu/~djoyce/home.html) is a version of perhaps the greatest textbook of them all, [_Euclid's Elements_](http://aleph0.clarku.edu/~djoyce/java/elements/toc.html). 41 | 42 | 18. Daniel Callahan has also provided what he calls a "an open textbook based on Euclid's Elements", [_Euclid's 'Elements' Redux_](http://starrhorse.com/euclid/). 43 | 44 | 19. Originally published by [Springer-Verlag](http://www.springer.de), the book [_A Course in Universal Algebra_](http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html), by [Stanley Burris](http://www.math.uwaterloo.ca/~snburris/), and H. P. Sankappanavar, is available online. 45 | 46 | 20. [Professor Robert Ash](http://www.math.uiuc.edu/~r-ash/) has written and made available [_Abstract Algebra:The Basic Graduate Year_](http://www.math.uiuc.edu/~r-ash/Algebra.html). 47 | 48 | 21. Another one by [Professor Ash](http://www.math.uiuc.edu/~r-ash/) is [_A Course In Algebraic Number Theory_](http://www.math.uiuc.edu/~r-ash/ANT.html). 49 | 50 | 22. [Professor Ash](http://www.math.uiuc.edu/~r-ash/) has also completed and made available [_A Course in Commutative Algebra_](http://www.math.uiuc.edu/~r-ash/). 51 | 52 | 23. Originally published by Prindle, Weber & Schmidt but currently out of print, [_Elementary Calculus: An Approach Using Infinitesimals_](http://www.math.wisc.edu/~keisler/calc.html), by [Professor H. Jerome Keisler](http://www.math.wisc.edu/~keisler), is now freely available online. 53 | 54 | 24. [_Graph Theory_](http://diestel-graph-theory.com/index.html), by [Reinhard Diestel](http://diestel-graph-theory.com/index.html). 55 | 56 | 25. Available for self-study from [The Trillia Group](http://www.trillia.com) is [_Basic Concepts of Mathematics_](http://www.trillia.com/zakon1.html), by Elias Zakon. 57 | 58 | 26. Another one from [The Trillia Group](http://www.trillia.com) is [_An Introduction to the Theory of Numbers_](http://www.trillia.com/moser-number.html) by Leo Moser. 59 | 60 | 27. Also from [The Trillia Group](http://www.trillia.com) are [_Mathematical Analysis I_](http://www.trillia.com/zakon-analysisI.html), and [_Mathematical Analysis II_](http://www.trillia.com/zakon-analysisII.html), by Elias Zakon. 61 | 62 | 28. Thanks to Malaspina Great Books, [_Mechanism of the Heavens_ (1831)](http://www.malaspina.com/etext/heavens.htm), by Mary Somerville, is available online. This second edition was prepared by Russell McNeil. 63 | 64 | 29. [_Lecture Notes on Optimization_](http://robotics.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf), by [Pravin Varaiya](http://robotics.eecs.berkeley.edu/~varaiya/). This is a re-issue of a book out of print since 1975\. It is an introduction to mathematical programming, optimal control, and dynamic programming. 65 | 66 | 30. Published by Cambridge Press, but still freely available is [_Mathematical Ilustrations_](http://www.math.ubc.ca/~cass/graphics/manual/), by [Bill Casselman](http://www.math.ubc.ca/~cass/). 67 | 68 | 31. [_A Problem Course in Mathematical Logic_](http://euclid.trentu.ca/math/sb/pcml/pcml.html), by [Stefan Bilaniuk](http://euclid.trentu.ca/math/sb/stefan.html) . 69 | 70 | 32. [_Concepts and Applications of Inferential Statistics_](http://vassarstats.net/textbook/), by Richard Lowry. 71 | 72 | 33. Published by Cambridge University Press, [_A Computational Introduction to Number Theory and Algebra_](http://shoup.net/ntb/), by [Victor Shoup](http://shoup.net/) is nevertheless freely available on-line. 73 | 74 | 35. Yet another one out of print, but now freely available is [_Convergence of Stochastic Processes_](http://www.stat.yale.edu/~pollard/), by [David Pollard](http://www.stat.yale.edu/~pollard/). 75 | 76 | 36. Designed for undergraduate physics students is [_Mathematical Tools for Physics_](http://www.physics.miami.edu/nearing/mathmethods/), by James Nearing. 77 | 78 | 37. [_A First Course in Linear Algebra_](http://linear.ups.edu/), by [Rob Beezer](http://buzzard.ups.edu/). 79 | 80 | 38. [_Group Theory_](http://www.cns.gatech.edu/GroupTheory/index.html), by [Pedrag Civitanovic](http://www.cns.gatech.edu/%7Epredrag/). 81 | 82 | 39. [Shlomo Sternberg](http://www.math.harvard.edu/people/SternbergShlomo.html) has written [_Theory of Functions of a Real Variable_](http://www.math.harvard.edu/~shlomo/docs/Real_Variables.pdf). 83 | 84 | 40. [_Lie Algebras_](http://www.math.harvard.edu/~shlomo/docs/lie_algebras.pdf) is another one by [Professor Sternberg](http://www.math.harvard.edu/people/SternbergShlomo.html) 85 | 86 | 42. Yet another one by [Professor Sternberg](http://www.math.harvard.edu/people/SternbergShlomo.html) is [_Semi-Riemann Geometry and General Relativity_](http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf) 87 | 88 | 43. [_Advanced Calculus_](http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf), by Lynn Loomis and Schlomo Sternberg 89 | 90 | 44. [_Difference Equations to Differential Equations_](http://synechism.org/drupal/de2de/), by [Dan Sloughter](http://math.furman.edu/~dcs/). 91 | 92 | 45. [_The Calculus of Functions of Several Variables_](http://synechism.org/drupal/cfsv/) is another one by [Professor Sloughter](http://math.furman.edu/~dcs/). 93 | 94 | 46. [_Notes on Differential Equations_](http://www.math.cornell.edu/~bterrell/dn.pdf), by [Bob Terrell](http://www.math.cornell.edu/~bterrell/). 95 | 96 | 47. [_Sets, Relations, Functions_](http://www.cosc.brocku.ca/~duentsch/papers/methprimer1.html), by [Ivo Düntsch](http://www.cosc.brocku.ca/~duentsch/) and Günther Gediga. 97 | 98 | 48. Another one by [Düntsch](http://www.cosc.brocku.ca/~duentsch/) and Gediga is [_Rough Set Data Analysis_](http://www.cosc.brocku.ca/~duentsch/papers/methprimer2.html). 99 | 100 | 49. [_Predicative Arithmetic_](http://www.math.princeton.edu/~nelson/books/pa.pdf), by [Edward Nelson](http://www.math.princeton.edu/~nelson/index.html). 101 | 102 | 50. [_Toposes, Triples and Theories_](http://www.tac.mta.ca/tac/reprints/articles/12/tr12.pdf), by Michael Barr and [Charles Wells](http://www.cwru.edu/artsci/math/wells/home.html). This was orinally published by Springer-Verlag, 1985 103 | 104 | 51. Also by Barr and Wells is [_Category Theory for Computing Science_](http://www.tac.mta.ca/tac/reprints/articles/22/tr22.pdf). 105 | 106 | 52. [_Information Theory, Inference, and Learning Algorithms_](http://www.inference.phy.cam.ac.uk/mackay/itila/book.html), by [David J. C. MacKay](http://www.inference.phy.cam.ac.uk/mackay/) is published by Cambridge University Press, but is, nevertheless, freely available online. 107 | 108 | 53. [_Numerical Methods and Analysis for Engineers_](http://www.ece.uwaterloo.ca/~ece204/TheBook/), by [Douglas Wilhelm Harder](https://ece.uwaterloo.ca/~dwharder/). 109 | 110 | 54. [_Analysis of Functions of a Single Variable_](http://spot.colorado.edu/~baggett/analysis.html), by [Lawerence Baggett](http://spot.colorado.edu/~baggett/), was originally written to be used for a one semester senior course, but the author suggests that it is more appropriate for first year graduate students. 111 | 112 | 55. Another one by Baggett ia [_Functional Analysis_](http://spot.colorado.edu/~baggett/functional.html). 113 | 114 | 56. [_Convex Optimization_](http://www.stanford.edu/~boyd/cvxbook/), by [Stephen Boyd](http://www.stanford.edu/~boyd/), and [Lieven Vandenberghe](http://www.ee.ucla.edu/~vandenbe/) is freely available thanks to [Cambridge University Press](http://www.cambridge.org/us/catalogue/catalogue.asp?isbn=0521833787). 115 | 116 | 57. [_Introduction to Statistical Signal Processing_](http://ee.stanford.edu/~gray/sp.html), by [R. M. Gray](http://ee.stanford.edu/~gray/) and L. D. Davisson is, according to Professor Gray, a "...much revised version of the earlier text _Random Processes: An Introduction for Engineers_, Prentice-Hall, 1986, which is long out of print." The current book is published by [Cambridge University Press](http://www.cambridge.org/aus/catalogue/catalogue.asp?isbn=9780521838603). 117 | 118 | 58. [_Abelian Categories_](http://www.tac.mta.ca/tac/reprints/articles/3/tr3abs.html), by Peter Freyd. This was published originally by Harper & Row. 119 | 120 | 59. Published by Van Nostrand in 1971 and now available is [_Categories and Groupoids_](http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html), by P. J. Higgins. 121 | 122 | 60. [_Basic Concepts of Enriched Category Theory_](http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html), by G. M. Kelley, was published by Cambridge University Press. 123 | 124 | 61. [_Abstract and Concrete Categories:The Joy of Cats_](http://www.tac.mta.ca/tac/reprints/articles/17/tr17abs.html), by [Jiri Adamek](http://www.tu-braunschweig.de/iti/mitarbeiter/adamek), [Horst Herrlich](http://www.informatik.uni-bremen.de/~herrlich/), and [George Strecker](http://www.math.ksu.edu/~strecker/). 125 | 126 | 62. [_A Problem Text in Advanced Calculus_](http://web.pdx.edu/~erdman/PTAC/problemtext_pdf.pdf), by [John Erdman](http://web.pdx.edu/~erdman//). 127 | 128 | 63. [_Abstract Algebra:Theory and Applications_](http://abstract.ups.edu/), by [Tom Judson](http://faculty.sfasu.edu/judsontw/). 129 | 130 | 64. Originally published by Pearson in 2003, [_Introduction to Real Analysis_](http://digitalcommons.trinity.edu/mono/7/), by [William F. Trench](http://ramanujan.math.trinity.edu/wtrench/index.shtml) is now freely available. 131 | 132 | 65. Another by [Professor Trench](http://ramanujan.math.trinity.edu/wtrench/index.shtml) is [_Elementary Differential Equations_](http://digitalcommons.trinity.edu/mono/8/) , originally published by Brooks/Cole Thompson Learning in 2000\. 133 | 134 | 66. [_Elementary Differential Equations With BoundaryValue Problems_](http://digitalcommons.trinity.edu/mono/9/), also by [Professor Trench](http://ramanujan.math.trinity.edu/wtrench/index.shtml), and also originally published by Brooks/Cole Thomson Learning in 2000\. 135 | 136 | 67. [_Notes on Diffy Qs: Differential Equations for Engineers_](http://www.jirka.org/diffyqs/), by [Jiří Lebl](http://www.jirka.org/) . 137 | 138 | 68. According to the authors, [_Proofs and Concepts: the fundamentals of abstract mathematics_](http://people.uleth.ca/~dave.morris/books/proofs+concepts.html), by [Dave Morris](http://people.uleth.ca/~dave.morris/), and [Joy Morris](http://www.cs.uleth.ca/~morris/), provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. 139 | 140 | 69. [_Mathematical Biology_](http://www.math.ust.hk/~machas/mathematical-biology.pdf), by [Jeffrey Chasnov](http://www.math.ust.hk/~machas). 141 | 142 | 70. Originally published in 1970, [_Calculus and Linear Algebra. Vol. 1_](http://hdl.handle.net/2027/spo.5597602.0001.001) and also [_Calculus and Linear Algebra. Vol. 2_](http://hdl.handle.net/2027/spo.5597602.0002.001), by Wilfred Kaplan and Donald J. Lewis, are available thanks to the Scholarly Publishing Office of the University Library at University of Michigan. 143 | 144 | 71. [_Introduction to Calculus I and II_](http://www.math.odu.edu/~jhh/counter10.html), by J.H. Heinbockel. 145 | 146 | 72. [_Active Calculus_](http://faculty.gvsu.edu/boelkinm/Home/Open_Calculus.html), by [Matt Boelkins.](http://faculty.gvsu.edu/boelkinm/Home/MB.html) 147 | 148 | 74. [_Analytic Combinatorics_](http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html), by [Philippe Flajolet](http://algo.inria.fr/flajolet/) and [Robert Sedgewick.](http://www.cs.princeton.edu/~rs/) 149 | 150 | 75. [_Mathematical Reasoning: Writing and Proof_](https://sites.google.com/site/mathematicalreasoning3ed/), by [Ted Sundstrom](https://sites.google.com/site/tedsundstrom/). Earlier editions of this one were published by Pearson Education, Inc., but this most recent edition is now freely available. 151 | 152 | 76. [_Linear Algebra_](https://www.math.ucdavis.edu/~linear/), by [David Cherney](https://www.math.ucdavis.edu/~cherney/), [Tom Denton](https://www.math.ucdavis.edu/~sdenton/), and [Andrew Waldron](https://www.math.ucdavis.edu/~wally/) 153 | 154 | 77. [_Yet Another Introductory Number Theory Textbook_](http://www.poritz.net/jonathan/share/yaintt/), by [Jonathan Poritz](http://www.poritz.net/jonathan/). 155 | 156 | 78. [_Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra_ and _Vol. 2, Vector and Tensor Analysis_](http://rbowen.tamu.edu/), by Ray M. Bowen and C.-C. Wang are revisons of works originally published by Plenum Press. They are available from Dover Press, but made freely available here. 157 | 158 | 79. [_Introduction to Continuum Mechanics_](http://rbowen.tamu.edu/), by Ray. M. Bowen, also originally published by Plenum Press and now available from Dover and made freely available here. 159 | 160 | 80. Not simply an online textbook, but certainly in the same spirit is the [Topology Webcourse](http://at.yorku.ca/course/index.htm) project undertaken by [Topology Atlas](http://at.yorku.ca/topology/). 161 | --------------------------------------------------------------------------------