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.
- 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
Evans Harrell and
- Yet another one produced at Georgia Tech is
Linear Algebra, Infinite Dimensions, and Maple, by
- 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
- 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
- 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
- Professor Herbert Wilf
(and the publisher,
A. K. Peters) has made available his book
- Another one by
is Algorithms and
- A = B,
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..
- Furnished by David Joyce
is a version of perhaps the greatest textbook of them all,
- Daniel Callahan has also
provided what he calls a "an open textbook based on Euclid's Elements",
Euclid's 'Elements' Redux.
- Originally published by Springer-Verlag,
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.
- Understanding Calculus, by Faraz Hussain.
- 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
- 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.
- Also from The Trillia Group are
Mathematical Analysis I, and
Mathematical Analysis II,
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
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
- Published by Cambridge Press, but still freely available is
by Bill Casselman.
A Problem Course in Mathematical Logic, by
Stefan Bilaniuk .
Concepts and Applications of Inferential Statistics,
by Richard Lowry.
- Published by Cambridge University Press,
A Computational Introduction to Number Theory and Algebra, by
Victor Shoup is nevertheless 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
- Designed for undergraduate physics students is
Mathematical Tools for Physics, by James Nearing.
Elementary Number Theory, by
- A First Course in Linear Algebra, by Rob Beezer.
Group Theory, by
- Shlomo Sternberg has written
Theory of Functions of a Real Variable.
- Lie Algebras is another one by
- 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 Equations, 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
- 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
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,
Douglas Wilhelm Harder.
Analysis of Functions of a Single Variable,
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
- 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
Horst Herrlich, and
A Problem Text in Advanced Calculus, by
- Abstract Algebra:Theory and Applications, by Tom Judson.
- Originally published by Pearson in 2003,
Introduction to Real Analysis, by
William F. Trench is now freely available.
- Notes on Diffy Qs: Differential Equations for Engineers, by
Jiří Lebl .
- According to the authors, Proofs
Concepts: the fundamentals of abstract mathematics, by
Dave Morris, and
provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics.
- Mathematical Biology, by Jeffrey Chasnov.
- Originally published in 1970,
Calculus and Linear Algebra. Vol. 1 and also
Calculus and Linear Algebra. Vol. 2, by
Wilfred Kaplan and Donald J. Lewis, are available thanks to
the Scholarly Publishing Office of the University Library at University of Michigan.
- Lectures on Probability, Statistics and Econometrics, by
- Introduction to Calculus I and II, by
- Active Calculus, by
by Philippe Flajolet and
- Mathematical Reasoning: Writing and
Proof, by Ted Sundstrom.
Earlier editions of this one were published by Pearson Education, Inc., but this most recent edition is
now freely available.
- Not simply an online textbook, but certainly in the same spirit
is the Topology Webcourse
project undertaken by
- This is, I suppose, not a textbook, but nevertheless an interesting reference:
The Matrix Cookbook, by
Kaare Brandt Petersen, and
Michael Syskind Pedersen.
School of Mathematics
Georgia Institute of Technology
10 May 2013