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Online Mathematics Textbooks

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.

A few years ago when I first posted a list of mathematics textbooks freely available on line, there existed only a handful of such books. Now there are many. The list here has grown and grown and is perhaps in serious need of some kind of organization into topics. There are also now many other sites at which there are links to on-line mathematics books and lecture notes. This site is far from comprehensive and I have considered abandoning it. Many people, however, still seem to find it useful, and so I shall continue to maintain it for a while.

  1. Professor Jim Herod and I have written Multivariable Calculus ,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....

  2. Although it is still in print, Calculus,by Gilbert Strang is made available through MIT's OpenCourseWare electronic publishing initiative.

  3. Here is one that has also been used here at Georgia Tech. Linear Methods of Applied Mathematics, by Evans Harrell and James Herod.

  4. Yet another one produced at Georgia Tech is Linear Algebra, Infinite Dimensions, and Maple, by James Herod.

  5. One more recent one by Professor Herod is Partial Differential Equations.

  6. I have also written a modest book, Complex Analysis, which I have used in our introductory undergraduate complex analysis course here.

  7. Complex Variables , by Robert Ash and W. P. Novinger. This is a substantial revision of the first edition of Professor Ash's complex variables text originally published in 1971.

  8. Professor E.H. Connell of the University of Miami has made available on the web his book Elements of Abstract and Linear Algebra. You should read his insightful comments about textbooks.

  9. An introductory algebraic topology book, Algebraic Topology I, by Professor Allen Hatcher, of Cornell University, is available, and Professor Hatcher promises the second volume, Algebraic Topology II, will be ready soon.

  10. The Geometry and Topology of Three-Manifolds, by William Thurston. This is an electronic edition of the 1980 lecture notes distributed by Princeton University.

  11. Professor Jim Hefferon of Saint Michaels's College has made available his undergraduate textbook Linear Algebra.

  12. Another elementary linear algebra textbook is Elementary Linear Algebra, by Keith Matthews.

  13. Introduction to Probability, by Charles Grinstead & J. Laurie Snell.

  14. An Introduction to Probability and Random Processes, by Gian-Carlo Rota and Kenneth Baclawski. 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.

  15. Professor Herbert Wilf (and the publisher, Academic Press) has made available his book generatingfunctionology.

  16. Another one by Professor Wilf is Algorithms and Complexity.

  17. A = B, by Marko Petkovsek, Herbert Wilf, and Doron Zeilberger. This one is also available in print and is available online with the blessing of the publisher, A. K. Peters, Ltd..

  18. Perhaps the greatest textbook of them all is Euclid's Elements.

  19. Originally published by Springer-Verlag, the book A Course in Universal Algebra, by Stanley Burris, and H. P. Sankappanavar, is available online.

  20. Professor Robert Ash has written and made available Abstract Algebra:The Basic Graduate Year.

  21. Another one by Professor Ash is A Course In Algebraic Number Theory.

  22. Professor Ash has also completed and made available A Course in Commutative Algebra.

  23. The Calculus Bible is an elementary calculus textbook from Professor G. S. Gill of the Brigham Young University Mathematics Department.

  24. Calculus Without Limits, by John C. Sparks.

  25. Originally published by Prindle, Weber & Schmidt but currently out of print, Elementary Calculus: An Approach Using Infinitesimals, by Professor H. Jerome Keisler, is now freely available online.

  26. Handbook of Applied Cryptography, by Alfred J. Menezes , Paul C. van Oorschot, and Scott A. Vanstone, is freely available thanks to the publisher, CRC Press.

  27. Graph Theory, by Reinhard Diestel.

  28. Available for self-study from The Trillia Group is Basic Concepts of Mathematics, by Elias Zakon.

  29. Another one from The Trillia Group is An Introduction to the Theory of Numbers by Leo Moser.

  30. Yet another from The Trillia Group is Mathematical Analysis I, by Elias Zakon.

  31. Thanks to Malaspina Great Books, Mechanism of the Heavens (1831), by Mary Somerville, is available online. This second edition was prepared by Russell McNeil.

  32. Lecture Notes on Optimization, by Pravin 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.

  33. A Manual of Mathematical Ilustration, by Bill Casselman, shows, at several levels of sophistication, how to use PostScript for producing mathematical graphics.

  34. Chebyshev and Fourier Spectral Methods (2nd. Edition), by John P. Boyd. This is the free online version of the Dover 2001 edition.

  35. A Problem Course in Mathematical Logic, by Stefan Bilaniuk .

  36. Concepts and Applications of Inferential Statistics, by Richard Lowry.

  37. To be published soon by Cambridge University Press, A Computational Introduction to Number Theory and Algebra, by Victor Shoup will nevertheless remain freely available on-line.
  38. Out of print for sometime, but freely available is Graph Theory with Applications, by J. A. Bondy and U. S. R. Murty.
  39. Yet another one out of print, but now freely available is Convergence of Stochastic Processes, by David Pollard.
  40. Designed for undergraduate physics students is Mathematical Tools for Physics, by James Nearing.

  41. Elementary Number Theory, by William Stein.

  42. A Modern Course on Curves and Surfaces, by Richard Palais.

  43. A First Course in Linear Algebra, by Rob Beezer.

  44. Group Theory, by Pedrag Civitanovic.

  45. Shlomo Sternberg has written Theory of Functions of a Real Variable.

  46. Lie Algebras is another one by Professor Sternberg

  47. Yet another one by Professor Sternbergis Semi-Riemann Geometry and General Relativity

  48. Advanced Calculus, by Lynn Loomis and Schlomo Sternberg

  49. Originally published by Springer-Verlag and now out of print, Non-Uniform Randon Variate Generation, by Luc Devroye is now, thanks to the author, freely available.

  50. Difference Equations to Differential Equations, by Dan Sloughter.

  51. The Calculus of Functions of Several Variables is another one by Professor Sloughter.

  52. Notes on Differential Equation, by Bob Terrell.

  53. Sets, Relations, Functions, by Ivo Düntsch and Günther Gediga.

  54. Another one by Düntsch and Gediga is Rough Set Data Analysis.

  55. Predicative Arithmetic, by Edward Nelson.

  56. Toposes, Triples and Theories, by Michaele Barr and Charles Wells.

  57. Information Theory, Inference, and Learning Algorithms, by David J. C. MacKay is published by Cambridge University Press, but is, nevertheless, freely available online.

  58. Linear Partial Differential Equations and Fourier Theory , by Marcus Pivato.

  59. Another one by Professor Pivato is Voting, Arbitration, and Fair Division: The Mathematics of Social Choice.

  60. Introduction to Vectors and Tensors, Volume 1, Linear and Multilinear Algebra, and Introduction to Vectors and Tensors, Volume 2, Vector and Tensor Analysis by Ray M. Bowen and C.-C.Wang, are revised versions of books originally published by Plenum Press in 1976.
  61. Another one by Professor Bowen and originally published by Plenum Press is Introduction to Continuum Mechanics for Engineers.
  62. Numerical Methods and Analysis for Engineers, by Douglas Wilhelm Harder.

  63. Analysis of Functions of a Single Variable, by Lawerence 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.

  64. Not simply an online textbook, but certainly in the same spirit is the Topology Webcourse project undertaken by Topology Atlas.

  65. Not really a textbook either, Constants, by Steven Finch, is, nevertheless, a nice collection of essays. The title pretty much describes the subject.

George Cain
School of Mathematics
Georgia Institute of Technology

26 October 2006