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 in its
present unorganized form.

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....

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

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

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

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

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.

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.

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.

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

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

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

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

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.

Professor Herbert Wilf (and
the publisher, A. K. Peters) has made
available his book generatingfunctionology.

Another one by Professor Wilf
is Algorithms and
Complexity.

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..

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

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

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

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

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

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

Understanding
Calculus, by Faraz Hussain.

Calculus
Without Limits, by John C. Sparks.

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.

Graph
Theory, by Reinhard Diestel.

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

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

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

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

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.

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

A Problem
Course in Mathematical Logic, by Stefan Bilaniuk .

Concepts and
Applications of Inferential Statistics, by Richard Lowry.

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.

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

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

Designed for undergraduate physics students is Mathematical Tools
for Physics, by James Nearing.

Elementary Number
Theory, by William Stein.

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

A First Course in Linear
Algebra, by Rob Beezer.

Group
Theory, by Pedrag
Civitanovic.

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

Lie
Algebras is another one by Professor
Sternberg

Yet another one by Professor
Sternberg is Semi-Riemann
Geometry and General Relativity

Advanced
Calculus, by Lynn Loomis and Schlomo Sternberg

Difference Equations to
Differential Equations, by Dan
Sloughter.

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

Notes on
Differential Equation, by Bob Terrell.

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

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

Predicative
Arithmetic, by Edward Nelson.

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

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

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

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

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.

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

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

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.

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

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

Introduction to
Statistical Signal Processing, by R. M. 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.

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

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

Abelian
Categories, by Peter Freyd. This was published originally by Harper
& Row.

Published by Van Nostrand in 1971 and now available is Categories
and Groupoids, by P. J. Higgins.

Basic
Concepts of Enriched Category Theory, by G. M. Kelley, was published
by Cambridge University Press.

Abstract
and Concrete Categories:The Joy of Cats, by Jiri Adamek, Horst Herrlich, and
George Strecker.

A
Problem Text in Advanced Calculus, by John Erdman.

Abstract Algebra:Theory and
Applications, by Tom
Judson.

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

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

George Cain
School of Mathematics
Georgia Institute of Technology
[email-masked]

23 February 2009