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AMS Books Online
- Provides downloadable books on a range of mathematical topics.
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.
Chebyshev and Fourier Spectral Methods
- A book by John P. Boyd (2nd edition) available from Dover.
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.
Dynamics in One Complex Variable: Introductory Lectures
- Lecture notes by John Milnor in TeX and PostScript.
The FEMCI Book
- Finite Element Modeling Continuous Improvement. A web text by Ryan Simmons.
Finite Applied Associative Algebra (semigroups) & Digital Networks
- A compendium of papers by Nico F. Benschop on abstract algebra, number theory, computer science and physics.
Finite Rank Torsion Free Modules Over Dedekind Domains
- Monograph in commutative ring theory by Lee Lady. DVI and PDF.
Fractals in the Plane - Ergodic Theory Methods
- A book by F. Przytycki and M. Urbanski in Postscript.
Fundamentals of Model Theory
- Introductory textbook by William Weiss and Cherie D'Mello. PostScript, DVI, GIF.
- By Herbert S. Wilf. Published by Academic Press. PDF.
Geometric Constraint Solving
- An electronic primer by William Bouma, Xiangping Chen, Ioannis Fudos, Christoph Hoffmann, and Pamela J. Vermeer.
- "The Convenient Setting of Global Analysis" - foundations of differential calculus in infinite dimensions with applications to differential geometry and global analysis by Andreas Kriegl and Peter W. Michor published by AMS in 1997. Whole book or chapters in crosslinked PDF.
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).
Homeomorphisms in Analysis
- A survey by C. Goffman, T. Nishiura, D. Waterman in PDF. In particular, the effects of homeomorphic changes of domain on the analyticity of a function are studied.
Integral and Differential Equations
- Class notes by Jim Herod at Georgia Tech.
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.
Lecture notes by László Lovász
- Discrete mathematics topics in Postscript. Includes "Discrete Mathematics", "Semidefinite optimization", "Topological methods in combinatorics", and "Complexity of algorithms".
Lecture Notes on Optimization
- By Pravin Varaiya. This book is an introduction to mathematical programming, optimal control, and dynamic programming. [PDF]
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.
Linear Programming: Foundations and Extensions
- Book by Robert J. Vanderbei in PDF.
Linearization via the Lie Derivative
- By Carmen Chicone and Richard Swanson. LaTeX, DVI, PostScript and PDF.
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. [PDF]
Mathematical Principles of Natural Philosophy
- Principia by Isaac Newton (1687) translated by Andrew Motte (1729) in HTML (incomplete).
Matrix Analysis and Applied Linear Algebra
- By Carl D. Meyer. Full text in PDF with errata, updates and solutions.
Monotone Operators in Banach Space and Nonlinear Partial Differential Equations
- A monograph by Ralph Showalter in PDF.
- "An Introduction to Multigrid Methods" by Pieter Wesseling.
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.
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.
Numerical Grid Generation
- A book by Thompson, Warsi, and Mastin, previously published by Elsevier, in HTML.
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.
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. [PDF]
Physics, Invariant Theory, Modular Forms, and Algebraic Geometry
- Several lecture note sets by Igor Dolgachev in various formats, including DVI and PostScript.
- 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.
Practical Foundations of Mathematics
- An account of the foundations of mathematics (algebra) and theoretical computer science, from a modern constructive viewpoint by Paul Taylor. Published by Cambridge University Press. HTML approximation.
Semi-Simple Lie Algebras and their Representations
- Book for particle physicists by Robert N. Cahn. Published by Benjamin-Cummings in 1984. Chapters in PostScript. [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.
- Mathematical notes on sheaves and other topics by P. Morandi.
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.
Splines and Wavelets
- A monograph by Karl Scherer in German (DVI and Postscript).
- A fairly complete elementary introduction to the basics of stochastic integration with respect to continuous semimartingales by Alan Bain. All the theory usually needed for basic mathematical finance. Sixty pages in DVI, postscript, and PDF.
Tensor Calculus and Continuum Mechanics
- Textbook by John H. Heinbockel. Whole book or chapters in PostScript and PDF.
Theory of Symmetry and Ornament
- Monograph by Slavik V. Jablan published by the Serbian Academy of Science and Arts in 1995. HTML
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