AMS Books Online

Provides downloadable books on a range of mathematical topics.

http://www.ams.org/online_bks/online_subject.html#MP

Basic Concepts of Mathematics

This text by Elias Zakon helps the student complete the transition from purely manipulative to rigorous mathematics. Chapters cover Set Theory, the Real Numbers, and n-dimensional Geometry.

http://www.trillia.com/zakon1.html

Chebyshev and Fourier Spectral Methods

A book by John P. Boyd (2nd edition) available from Dover.

http://www-personal.engin.umich.edu/~jpboyd/BOOK_Spectral2000.html

Dynamics and Chaos

Class notes by Evans M. Harrell II for an introductory course on dynamical systems and chaos, taken by mathematicians, engineers, and physicists. This text concentrates on models rather than proofs in order to bring out the concepts of dynamics and chaos. Theorems are carefully stated, though only occasionally proved.

http://www.mathphysics.com/dynam/

Finite Applied Associative Algebra (semigroups) & Digital Networks

A compendium of papers by Nico F. Benschop on abstract algebra, number theory, computer science and physics.

http://home.claranet.nl/users/benschop/

Fractals in the Plane - Ergodic Theory Methods

A book by F. Przytycki and M. Urbanski in Postscript.

http://www.math.unt.edu/~urbanski/book1.html

Fundamentals of Model Theory

Introductory textbook by William Weiss and Cherie D'Mello. PostScript, DVI, GIF.

http://at.yorku.ca/i/a/a/i/10.htm

Generatingfunctionology

By Herbert S. Wilf. Published by Academic Press. PDF.

http://www.math.upenn.edu/~wilf/DownldGF.html

Geometric Constraint Solving

An electronic primer by William Bouma, Xiangping Chen, Ioannis Fudos, Christoph Hoffmann, and Pamela J. Vermeer.

http://www.cs.purdue.edu/homes/cmh/electrobook/intro.html

Harmonic Analysis and Partial Differential Equations

A book by Dahlberg and Kenig in postscript (bitmapped fonts). The page also contains another book by Dahlberg: "Icke Linjära Evolutionsekvationer" (Swedish).

http://www.math.chalmers.se/Math/Research/GeometryAnalysis/Lecturenotes/

Integral and Differential Equations

Class notes by Jim Herod at Georgia Tech.

http://www.math.gatech.edu/~herod/4348/4348.html

Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem

Monograph by Peter B. Gilkey published by Publish or Perish and CRC Press. Whole book or chapters in DVI and Postscript.

http://www.emis.de/monographs/gilkey/

Lecture notes by László Lovász

Discrete mathematics topics in Postscript. Includes "Discrete Mathematics", "Semidefinite optimization", "Topological methods in combinatorics", and "Complexity of algorithms".

http://www.cs.elte.hu/~lovasz/notes.html

Linear Methods of Applied Mathematics

Textbook suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations by Evans M. Harrell II and James V. Herod. HTML, RTF and PDF with Maple and Mathematica worksheets.

http://www.mathphysics.com/pde/

Linear Programming: Foundations and Extensions

Book by Robert J. Vanderbei in PDF.

http://www.princeton.edu/~rvdb/LPbook/

Linearization via the Lie Derivative

By Carmen Chicone and Richard Swanson. LaTeX, DVI, PostScript and PDF.

http://ejde.math.txstate.edu/Monographs/02/abstr.html

Mathematical Methods of Engineering Analysis

Book by Erhan Çinlar and Robert J. Vanderbei. Topics covered: functions on metric spaces, differential and integral equations, convex analysis, and measure and integration.

http://www.princeton.edu/~rvdb/506book/book.pdf

Mathematical Principles of Natural Philosophy

Principia by Isaac Newton (1687) translated by Andrew Motte (1729) in HTML (incomplete).

http://members.tripod.com/~gravitee/

Matrix Analysis and Applied Linear Algebra

By Carl D. Meyer. Full text in PDF with errata, updates and solutions.

http://www.matrixanalysis.com/

Multigrid Methods

"An Introduction to Multigrid Methods" by Pieter Wesseling.

http://www.mgnet.org/mgnet-books-wesseling.html

Multiplier Ideals for Algebraic Geometers

Draft of a part of a book in preparation on positivity in algebraic geometry by Robert Lazarsfeld. DVI and PostScript.

http://www.math.lsa.umich.edu/~rlaz/

Natural Operations in Differential Geometry

By Ivan Kolar, Jan Slovak and Peter W. Michor, originally published by Springer-Verlag in 1993. DVI, PostScript and PDF.

http://www.emis.de/monographs/KSM/

Numerical Grid Generation

A book by Thompson, Warsi, and Mastin, previously published by Elsevier, in HTML.

http://www.erc.msstate.edu/publications/gridbook/

Numerical Recipes Books On-Line

The complete Numerical Recipes books in C, Fortran 77, and Fortran 90 On-Line, in both PostScript and Adobe Acrobat formats.

http://www.nr.com/oldverswitcher.html

Numerics - Interactive

In this book by Thomas Risse, basic numerical algorithms are presented and implemented in order to determine the precision of computation, to solve systems of linear equations, to evaluate elementary functions, to find zeros, to integrate and to solve ordinary differential equations numerically. The performance of different algorithms can be compared.

http://www.weblearn.hs-bremen.de/risse/MAI/docs/numerics.pdf

Physics, Invariant Theory, Modular Forms, and Algebraic Geometry

Several lecture note sets by Igor Dolgachev in various formats, including DVI and PostScript.

http://www.math.lsa.umich.edu/~idolga/lecturenotes.html

Plane Geometry

Shalosh B. Ekhad XIV. A fully illustrated and completely self-contained Elementary Geometry textbook (ca. 2050), downloaded from the future by Doron Zeilberger. Entirely written in Maple.

http://www.math.rutgers.edu/~zeilberg/GT.html

Semi-Simple Lie Algebras and their Representations

Book for particle physicists by Robert N. Cahn. Published by Benjamin-Cummings in 1984. Chapters in PostScript.

http://phyweb.lbl.gov/~rncahn/www/liealgebras/texall.pdf

Several Complex Variables

Several sets of lecture notes by Jean-Pierre Demailly, some in French, including "Potential theory in several complex variables", and "Multiplier ideal sheaves and analytic methods in algebraic geometry" in DVI or PostScript.

http://www-fourier.ujf-grenoble.fr/~demailly/lectures.html

Sheaf Cohomology

Mathematical notes on sheaves and other topics by P. Morandi.

http://sierra.nmsu.edu/morandi/notes/mathematicalnotes.html

Spinors, Spectral Geometry, and Riemannian Submersions

Monograph by Peter B. Gilkey, John V. Leahy and Jeonghyeong Park published by Seoul National University in 1998. DVI and PostScript.

http://www.emis.de/monographs/GLP/

Tensor Calculus and Continuum Mechanics

Textbook by John H. Heinbockel. Whole book or chapters in PostScript and PDF.

http://www.math.odu.edu/~jhh/counter2.html

The FEMCI Book

Finite Element Modeling Continuous Improvement. A web text by Ryan Simmons.

http://femci.gsfc.nasa.gov/femcibook.html