From: Subject: Online texts Date: Thu, 5 Mar 2009 08:00:53 -0600 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_004E_01C99D68.81BB38A0" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3350 This is a multi-part message in MIME format. ------=_NextPart_000_004E_01C99D68.81BB38A0 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.math.gatech.edu/~cain/textbooks/onlinebooks.html =EF=BB=BF Online texts

Online Mathematics Textbooks

The writing of textbooks and making them freely available on the web is = an idea=20 whose time has arrived. Most college mathematics textbooks attempt to be = all=20 things to all people and, as a result, are much too big and expensive. = This=20 perhaps made some sense when these books were rather expensive to = produce and=20 distribute--but this time has passed.=20

A few years ago when I first posted a list of mathematics textbooks = freely=20 available on line, there existed only a handful of such books. Now there = are=20 many. The list here has grown and grown and is perhaps in serious need = of some=20 kind of organization into topics. There are also now many other sites at = which=20 there are links to on-line mathematics books and lecture notes. This = site is far=20 from comprehensive and I have considered abandoning it. Many people, = however,=20 still seem to find it useful, and so I shall continue to maintain it in = its=20 present unorganized form.=20

  1. Professor Jim = Herod and I=20 have written Multivar= iable=20 Calculus ,a book which we and a few others have used here at = Georgia=20 Tech for two years. We have also proposed that this be the first = calculus=20 course in the curriculum here, but that is another story....

  2. Although it is still in print, Ca= lculus,by=20 Gilbert Strang is made = available=20 through MIT's = OpenCourseWare=20 electronic publishing initiative.

  3. Here is one that has also been used here at Georgia Tech. Linear Methods of Applied=20 Mathematics, by Evans=20 Harrell and James = Herod.

  4. Yet another one produced at Georgia Tech is Linear = Algebra,=20 Infinite Dimensions, and Maple, by James Herod.

  5. I have also written a modest book, Comple= x=20 Analysis, which I have used in our introductory undergraduate = complex=20 analysis course here.

  6. Complex = Variables ,=20 by Robert Ash and W. P. = Novinger.=20 This is a substantial revision of the first edition of Professor Ash's = complex=20 variables text originally published in 1971.

  7. Professor E.H. = Connell of the=20 University of Miami has made available on the web his book Elements of Abstract = and Linear=20 Algebra. You should read his insightful comments about = textbooks.=20

  8. An introductory algebraic topology book, Algebraic Topology = I,=20 by Professor Allen=20 Hatcher, of Cornell University, is available, and Professor = Hatcher=20 promises the second volume, Algebraic Topology II, will be ready soon. =

  9. The = Geometry and=20 Topology of Three-Manifolds, by William Thurston. This is an=20 electronic edition of the 1980 lecture notes distributed by Princeton=20 University.

  10. Professor = Jim=20 Hefferon of Saint Michaels's College has made available his = undergraduate=20 textbook Linear=20 Algebra.

  11. Another elementary linear algebra textbook is Elementary Linear = Algebra,=20 by Keith Matthews.

  12. Introduction=20 to Probability, by Charles Grinstead & J. Laurie Snell.

  13. An=20 Introduction to Probability and Random Processes, by = Gian-Carlo Rota=20 and Kenneth = Baclawski. This is=20 the 1979 manuscript of the work Professor Rota had been working on for = some=20 time. It is made available through the efforts of Davi= d=20 Ellerman.=20

  14. Professor Herbert = Wilf (and=20 the publisher, A. K. Peters) = has made=20 available his book generatingfunct= ionology.

  15. Another one by Professor Wilf=20 is Algorithms and=20 Complexity.

  16. A =3D = B, by=20 Marko Petkovsek, Herbert = Wilf,=20 and Doron = Zeilberger. This=20 one is also available in print and is available online with the = blessing of=20 the publisher, A. K. Peters, = Ltd..

  17. Perhaps the greatest textbook of them all is Eucli= d's=20 Elements.

  18. Originally published by Springer-Verlag, the book A = Course in=20 Universal Algebra, by Stanley Burris, = and H. P.=20 Sankappanavar, is available online.

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

  20. Another one by Professor=20 Ash is A Course In = Algebraic=20 Number Theory.

  21. Professor Ash has = also=20 completed and made available A=20 Course in Commutative Algebra.=20

  22. The = Calculus=20 Bible is an elementary calculus textbook from Professor G. S. = Gill of=20 the Brigham Young University = Mathematics=20 Department.

  23. Understanding = Calculus, by Faraz Hussain.=20

  24. Calculus=20 Without Limits, by John C. Sparks.

  25. Originally published by Prindle, Weber & Schmidt but currently = out of=20 print, Elementary=20 Calculus: An Approach Using Infinitesimals, by Professor H. Jerome = Keisler, is=20 now freely available online.

  26. Graph=20 Theory, by Reinhard = Diestel.

  27. Available for self-study from The=20 Trillia Group is Basic=20 Concepts of Mathematics, by Elias Zakon.

  28. Another one from The Trillia = Group=20 is An = Introduction to=20 the Theory of Numbers by Leo Moser.=20

  29. Yet another from The Trillia = Group=20 is Mathematical=20 Analysis I, by Elias Zakon.=20

  30. Thanks to Malaspina Great Books, Mechanism of = the=20 Heavens (1831), by Mary Somerville, is available online. This = second=20 edition was prepared by Russell McNeil.

  31. Lecture=20 Notes on Optimization, by Pravin = Varaiya. This is=20 a re-issue of a book out of print since 1975. It is an introduction to = mathematical programming, optimal control, and dynamic programming.

  32. A=20 Manual of Mathematical Ilustration, by Bill = Casselman, shows,=20 at several levels of sophistication, how to use PostScript for = producing=20 mathematical graphics.

  33. A = Problem=20 Course in Mathematical Logic, by Stefan = Bilaniuk .

  34. Concepts and=20 Applications of Inferential Statistics, by Richard Lowry.=20

  35. To be published soon by Cambridge University Press, A Computational Introduction to = Number Theory=20 and Algebra, by Victor Shoup = will=20 nevertheless remain freely available on-line.

  36. Out of print for sometime, but freely available is = Graph=20 Theory with Applications, by J. A. = Bondy=20 and U. S. R. Murty.

  37. Yet another one out of print, but now freely available is Convergence of = Stochastic Processes, by David Pollard.=20

  38. Designed for undergraduate physics students is Mathematica= l Tools=20 for Physics, by James Nearing.

  39. Elementary Number=20 Theory, by William = Stein.

  40. A=20 Modern Course on Curves and Surfaces, by Richard Palais.

  41. A First Course in Linear=20 Algebra, by Rob = Beezer.

  42. Group=20 Theory, by Pedrag=20 Civitanovic.

  43. Shlomo=20 Sternberg has written T= heory=20 of Functions of a Real Variable.

  44. Lie= =20 Algebras is another one by Professo= r=20 Sternberg

  45. Yet another one by Professo= r=20 Sternberg is Semi-Riemann=20 Geometry and General Relativity

  46. <= I>Advanced=20 Calculus, by Lynn Loomis and Schlomo Sternberg

  47. Difference = Equations to=20 Differential Equations, by Dan=20 Sloughter.

  48. The Calculus of = Functions=20 of Several Variables is another one by Professor Sloughter.

  49. Notes = on=20 Differential Equation, by Bob Terrell.

  50. S= ets,=20 Relations, Functions, by Ivo D=C3=BCntsch and = G=C3=BCnther=20 Gediga.=20

  51. Another one by D=C3=BCntsch=20 and Gediga is R= ough=20 Set Data Analysis.

  52. Predicativ= e=20 Arithmetic, by Edward = Nelson.

  53. Toposes,=20 Triples and Theories, by Michael Barr and Charles = Wells. This=20 was orinally published by Springer-Verlag, 1985

  54. Inf= ormation=20 Theory, Inference, and Learning Algorithms, by David J. C. = MacKay is=20 published by Cambridge University Press, but is, nevertheless, freely=20 available online.

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

  56. Another one by Professor = Pivato is Voting,=20 Arbitration, and Fair Division: The Mathematics of Social = Choice.

  57. Introduction = to Vectors and Tensors, Volume 1, Linear and Multilinear = Algebra, and=20 Introduction = to=20 Vectors and Tensors, Volume 2, Vector and Tensor Analysis by = Ray M. = Bowen and=20 C.-C.Wang, are revised versions of books originally published by = Plenum Press=20 in 1976.=20

  58. Another one by Professor = Bowen and=20 originally published by Plenum Press is Introduction = to=20 Continuum Mechanics for Engineers.=20

  59. Numerical=20 Methods and Analysis for Engineers, by Douglas Wilhelm = Harder.

  60. Ana= lysis=20 of Functions of a Single Variable, by Lawerence Baggett, was = originally written to be used for a one semester senior course, but = the author=20 suggests that it is more appropriate for first year graduate students.

  61. Convex=20 Optimization, by Stephen=20 Boyd, and Lieven=20 Vandenberghe is freely available thanks to Cambridge=20 University Press.

  62. Mathematics=20 Under the Microscope, by Alexandre = Borovik, is,=20 according to the author, an attempt "to start a dialogue between=20 mathematicians and cognitive scientists."=20

  63. Introduction = to=20 Statistical Signal Processing, by R. M. Gray and L. D. = Davisson is,=20 according to Professor Gray, a "...much revised version of the earlier = text=20 Random Processes: An Introduction for Engineers, Prentice-Hall, = 1986,=20 which is long out of print." The current book is published by Cambridge=20 University Press.=20

  64. Originally published by Prentice-Hall, and now out of print, Real=20 Analysis, by Andrew Bruckner, Judith Bruckner, and Brian = Thomson, is,=20 thanks to the authors, now freely available online.

  65. Also by Bruckner, Bruckner, and Thomson, and originally published = by=20 Prentice-Hall, Elementary = Real=20 Analysis is also now available.

  66. Abe= lian=20 Categories, by Peter Freyd. This was published originally by = Harper=20 & Row.=20

  67. Published by Van Nostrand in 1971 and now available is Cat= egories=20 and Groupoids, by P. J. Higgins.

  68. B= asic=20 Concepts of Enriched Category Theory, by G. M. Kelley, was = published=20 by Cambridge University Press.

  69. A= bstract=20 and Concrete Categories:The Joy of Cats, by Jiri = Adamek, Horst = Herrlich, and=20 George Strecker.

  70. A=20 Problem Text in Advanced Calculus, by John Erdman.

  71. Abstract Algebra:Theory = and=20 Applications, by Tom=20 Judson.

  72. Not simply an online textbook, but certainly in the same spirit is = the Topology Webcourse = project=20 undertaken by Topology = Atlas.

  73. This is, I suppose, not a textbook, but nevertheless an = interesting=20 reference: The Matrix=20 Cookbook, by Kaare Brandt = Petersen,=20 and Michael Syskind Pedersen.=20

George = Cain
School of Mathematics
Georgia Institute of = Technology
cain@math.gatech.edu
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