| Linear Methods of Applied Mathematics - This is a WWW textbook written by Evans M. Harrell II and James V. Herod, both of Georgia Tech. It is suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations. Students are expected to have completed two years of calculus and an introduction to ordinary differential equations and vector spaces. Topics include Fourier series, Green's functions, and PDEs.
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| Allen Hatcher's Homepage - Contains textbooks in Algebraic Topology, K-Theory, and 3-Manifolds.
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| Generatingfunctionology - By Herbert S. Wilf. Published by Academic Press. PDF.
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| Euclid's Elements - Edited by D.E. Joyce. HTML text with Java applets.
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| Fundamentals of Model Theory - Introductory textbook by William Weiss and Cherie D'Mello. PostScript, DVI, GIF.
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| Introduction to Probability - An online textbook in PDF format, by Charles M. Grinstead and J. Laurie Snell
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| A=B - Combinatorics text by Marko Petkovsek, Herbert Wilf and Doron Zeilberger. Published by A. K. Peters. PDF.
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| Abstract Algebra - Three books by Robert B. Ash (chapters in PDF): Abstract Algebra: The Basic Graduate Year, A Course In Algebraic Number Theory, and A Course In Commutative Algebra.
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| 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.
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| Mixed Motives - Monograph by Marc Levine published by AMS in 1998. Whole book or chapters in PDF.
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| Tensor Calculus and Continuum Mechanics - A free downloadable textbook on introductory tensor analysis and continuum mechanics, in PDF format, from Professor John J. Heinbockel at Old Dominion University.
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| 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.
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| Elements of Abstract and Linear Algebra - Foundational textbook on abstract algebra with emphasis on linear algebra by Edwin H. Connell. Whole book or chapters in DVI, PostScript, and PDF.
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| Complex Analysis - Textbook for an introductory course in complex analysis by George Cain. Chapters in PDF.
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| Universal Algebra - "A Course in Universal Algebra" by Stanley Burris and H. P. Sankappanavar. PostScript and PDF.
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| C*-Algebras - "An Introduction to C*-Algebras" by Pierre de la Harpe and Vaughan Jones. The site is in French, but the book is in English. Chapters in PostScript.
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| Index Theory, Geometric Scattering, and Differential analysis on manifolds with corners - Several books by Richard Melrose et al. in PostScript.
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| Linear Algebra - Textbook by Jim Hefferon covering the material of any undergraduate first linear algebra course. Book or chapters in PDF.
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| Abstract Algebra - Lecture notes by David Wilkins at Trinity College, Dublin.
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| Templates for the Solution of Linear Systems - Book on iterative methods by Richard Barrett et al. in HTML and Postscript.
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| Semi-Simple Lie Algebras and their Representations - Book for particle physicists by Robert N. Cahn. Published by Benjamin-Cummings in 1984. Chapters in PostScript.
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| Abstract Algebra II - A companion volume to "Abstract Algebra" by John A. Beachy and Bill Blair published by Waveland Press in 1995. Chapters in PostScript.
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| Linearization via the Lie Derivative - By Carmen Chicone and Richard Swanson. LaTeX, DVI, PostScript and PDF.
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| Multivariable Calculus - Textbook by George Cain and James Herod. Chapters in PDF.
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| Finite Rank Torsion Free Modules Over Dedekind Domains - Monograph in commutative ring theory by Lee Lady. DVI and PDF.
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| Topology Course Lecture Notes - By Aisling McCluskey and Brian McMaster. HTML with symbol fonts, DVI and PostScript.
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| Trigonometry - "Dave's Short Trig Course" by D. E. Joyce. HTML with Java.
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| Analysis WebNotes - John Lindsay Orr, University of Nebraska--Lincoln.
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| Advanced Calculus and Analysis - Lecture notes from the University of Aberdeen for a first course in Analysis.
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| Interactive Real Analysis - An interactive textbook using Java.
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| Complex and Functional Analysis - Course notes and old exams in PDF, PS, DVI, and TeX for a first course in Complex and Functional Analysis.
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| Category Theory - "A Gentle Introduction to Category Theory - the calculational approach" by Maarten M. Fokkinga in PostScript.
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| 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.
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| Dynamical Systems - 1927 classic by George D. Birkhoff published by AMS. Scanned chapters in PDF.
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| Complex analytic and algebraic geometry - Book by Jean-Pierre Demailly in PostScript.
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| Physics, Invariant Theory, Modular Forms, and Algebraic Geometry - Several lecture note sets by Igor Dolgachev in various formats, including DVI and PostScript.
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| Differential Geometry - Notes by Balázs Csikós. Chapters in PostScript.
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| Functional Analysis and Semi-Groups - Book by Einar Hille and Ralph S. Phillips published by AMS in 1957. Scanned chapters in PDF.
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| Global Analysis - "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.
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| Complex Dynamics in Higher Dimensions - CBMS lecture notes by John Erik Fornæss at the bottom of page with other papers by the author and Nessim Sibony. PostScript.
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| 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.
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| Algebraic Topology by Solomon Lefschetz - Published by the AMS, available for free download as PDF files.
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| Travelling Wave Solutions of Parabolic Systems - Translation of a monograph by Aizik Volpert, Vitaly Volpert, and Vladimir Volpert published by AMS in 1994. Whole book or chapters in PDF.
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| Differential Geometry - Several books by Peter W. Michor et al. including "Foundations of Differential Geometry", "Natural operations in differential geometry" (corrected version), "Transformation Groups", and "Gauge theory for fiber bundles" plus papers by the author in postscript.
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| Computational Geometry and Computational Optimization - Lecture notes by Jianer Chen in PostScript.
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| Differential Topology - Course notes by Matthew G. Brin in PostScript including "Introduction to Differential Topology", "Introduction to Seifert fibered 3-manifolds", "Groups acting on 1-dimensional spaces", and "Presentations, conjugacy, roots and centralizers in groups of piecewise linear homeomorphisms of the real line".
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| History of Calculus - Guide To History of Calculus. Topic essays and biographies keyed to the chapters and content of the 10th edition of Thomas's Calculus.
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| Linear Programming: Foundations and Extensions - Book by Robert J. Vanderbei in PDF.
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| Mathematical Methods of Engineering Analysis - Book by Erhan Çinlar and Robert J. Vanderbei in PDF. Topics covered: functions on metric spaces, differential and integral equations, convex analysis, and measure and integration.
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| Numerical Analysis - "Introduction to Numerical Analysis Using Maple" by Barry G. Adams in HTML.
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| Dynamical Systems and Fractals - Lecture Notes by David J. Wright in HTML.
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| Mathematical Modeling in a Real and Complex World - Online guide book by Frank Wattenberg in HTML.
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| Geometric Constraint Solving - An electronic primer by William Bouma, Xiangping Chen, Ioannis Fudos, Christoph Hoffmann, and Pamela J. Vermeer.
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| Fundamental Problems in Algorithmic Algebra - Book by Chee Yap published by Oxford University Press in 1999.
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| Abstract Algebra - "Intro to Abstract Algebra" by Paul Garrett in PostScript and PDF.
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| The FEMCI Book - Finite Element Modeling Continuous Improvement. A web text by Ryan Simmons.
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| Algebraic K-theory - "An introduction to algebraic K-theory" by Charles Weibel. Chapters in DVI.
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| Complex Analysis - Course notes by Harold V. McIntosh in HTML.
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| Dynamics in One Complex Variable: Introductory Lectures - Lecture notes by John Milnor in TeX and PostScript.
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| Linear Algebra and Applications - Textbook by Thomas Shores. GIFs of pages.
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| Mathematical Principles of Natural Philosophy - Principia by Isaac Newton (1687) translated by Andrew Motte (1729) in HTML (incomplete).
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| The Limits of Mathematics - An online course on information theory and the limits of formal reasoning by G.J. Chaitin.
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| Hilbert Space Methods for Partial Differential Equations - A group of free papers on partial differential equations.
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| 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.
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| Introduction to Differential Geometry and General Relativity - A course from the Department of Mathematics at Hofstra University on differential geometry and general relativity.
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| Algebraic Combinatorics via Finite Group Actions - A hypertext by A. Betten, H. Fripertinger and A. Kerber.
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| 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.
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| Numerics - interactive - In this PDF 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.
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| Geometric Asymptotics - This book by Guillemin and Sternberg includes the method of stationary phase, geometrical optics, quantization.
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| Differential Algebra - Scans of Ritt's 1950 classic in PDF.
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| Applied Cryptography - 1996 CRC Handbook of Applied Cryptography by Menezes, van Oorschot and Vanstone in PDF.
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| Graph Theory - Hyperlinked PDF version of a book by Reinhard Diestel.
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| Linear Algebra, Infinite Dimensions, and Maple - A textbook by James Herod.
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| 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.
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| Finite Simple Groups - "The classification of the finite simple groups" by D. Gorenstein, R. Lyons, and R. Solomon in PDF.
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| Monotone Operators in Banach Space and Nonlinear Partial Differential Equations - A monograph by Ralph Showalter in PDF.
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| Matrices - The 1934 classic "Lectures on Matrices" by Wedderburn in scanned PDF.
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| Stochastic Calculus Notes - These notes by Alan Bain provide a complete elementary introduction to stochastic integration with respect to continuous semimartingales.
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| Grothendieck's Séminaire de Géometrie Algébrique - Scanned from the original typescript into JPEG format.
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| Linear Algebra - "Elementary Linear Algebra" by Keith Matthews. Lecture notes and solutions from 1991 in PDF or PostScript.
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| Numerical Grid Generation - A book by Thompson, Warsi, and Mastin, previously published by Elsevier, in HTML.
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| Wavelets - An Introduction to Wavelets by Amara Graps in HTML, PDF or Postscript.
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| Course Notes by Jim Milne - Algebraic number theory, Class field theory, Algebraic Geometry, Elliptic Curves, Modular functions and forms, Abelian varieties, Etale Cohomology. TeX, DVI, PS and PDF.
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| Toposes, Triples and Theories - A book by Michael Barr and Charles Wells originally published by Springer Verlag.
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| Dynamical Systems and Ergodic Theory - "Lectures on Dynamical Systems and Ergodic Theory" by Mark Pollicott and Michiko Yuri. Published by Cambridge University Press in 1998 (London Mathematical Society Students Texts, No. 40).
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| Optimization - "Lecture Notes on Optimization" by Pravin Varaiya. This book is an introduction to mathematical programming, optimal control, and dynamic programming.
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| Multigrid Methods - "An Introduction to Multigrid Methods" by Pieter Wesseling.
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| Calculus - "The Calculus Bible" by G. S. Gill.
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| 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.
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| Course Notes - Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
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| Differential Geometry - Lecture notes for a course at the Weizmann Institute of Science by Sergei Yakovenko. Chapters in DVI.
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| Entropy of Compact Group Automorphisms - Lecture notes based on a course at Ohio State in 1994 by Thomas Ward in DVI and PostScript.
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| Complex-Analytic Geometry of Complex Parallelizable Manifolds - Monograph by Jörg Winkelmann. Chapters in DVI.
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| Finite Applied Associative Algebra (semigroups) & Digital Networks - A compendium of papers by Nico F. Benschop on abstract algebra, number theory, computer science and physics.
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| Differential Geometry - Lecture notes for an honors course at the University of Adelaide by Michael Murray in HTML with GIFs.
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| Matrix Analysis and Applied Linear Algebra - By Carl D. Meyer. Full text in PDF with errata, updates and solutions.
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| Complex Analysis - Course notes and quizzes by Paul Scott in HTML.
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| Complex Numbers - Dave's Short Course on Complex Numbers (David Joyce).
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| Discrete Mathematics - Lecture notes by László Lovász in Postscript. Includes "Discrete Mathematics", "Semidefinite optimization", "Topological methods in combinatorics", and "Complexity of algorithms".
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| Textbook in Problems on Elementary Topology - The core of the book is the material included usually into the Topology part of the two year geometry course in the Mathematical Department of St. Petersburg University. This lecture course was composed by Vladimir Abramovich Rokhlin in the sixties and has almost not changed since then.
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| Splines and Wavelets - A monograph by Karl Scherer in German (DVI and Postscript).
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| Riemannian Geometry - "An Introduction to Riemannian Geometry" by S. Gudmundsson in postscript (1996).
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| 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).
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| Topology Without Tears - A course in topology by Sidney A. Morris in HTML with embedded GIFs. Must purchase to view.
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| Potential Theory - Two texts by V.I. Fabrikant: Applications of Potential Theory in Mechanics, Selection of New Results (1989); Mixed Boundary Value Problems of Potential Theory and their Applications in Engineering (1991). Text in PDF with figures separately in JPG.
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| Fractals in the Plane - Ergodic Theory Methods - A book by F. Przytycki and M. Urbanski in Postscript.
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| Complex analysis and dynamics - Various lecture notes C. McMullen
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| Abstract Algebra with GAP - A laboratory manual by J. G. Rainbolt and J. A. Gallian.
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| Abstract Algebra - A book draft: "Applied Abstract Algebra" by D. Joyner, R. Kreminski, J. Turisco in HTML.
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| Abstract Algebra Notes - A collection of short notes by Bruce Ikenaga in PostScript.
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| Calculus Using Infinitesimals - Elementary Calculus: An Approach - a book by H. Jerome Keisler originally published by Prindle, Weber & Schmidt (2nd ed: 1986)
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| Flatland - A romance of many dimensions. With Illustrations by the Author, A SQUARE (Edwin A. Abbott 1838-1926). HTML.
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| Geometry and the Imagination - An online course by John Conway, Peter Doyle, Jane Gilman and Bill Thurston in HTML and PostScript.
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| Sheaf Cohomology - Mathematical notes on sheaves and other topics by P. Morandi.
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| Description Logics Handbook - A course on Description Logics (the Semantic Web underlying formalism) by E. Franconi (modules in pdf)
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| Number Theory - "An Introduction to the Theory of Numbers" by Leo Moser is a textbook covering following topics: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. The textbook can be downloaded in several formats in pdf. Licensing terms for various uses are described on the web page.
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| Manifolds, Tensors, Analysis, and Applications - Book by R. Abraham, J. E. Marsden, and T. Ratiu originally published by Addison-Wesley in 1983. Chapters in PDF.
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| Wavelet Tutorial - Guide to wavelet analysis by Robi Polikar.
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| Meta Math! The Quest for Omega - A mathematical and philosophical book by Gregory Chaitin on logic, information theory, complexity, etc. (available in html or pdf).
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| Mathematical Analysis I - This text by Elias Zakon covers the basic topics of undergraduate real analysis including: metric spaces, function limits and continuity, sequences and series of functions, power series, and differentiation and integration.
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| Mathematical Illustrations - A manual of geometry and PostScript by Bill Casselman, including code samples and packages.
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| Chebyshev and Fourier Spectral Methods - A book by John P. Boyd (2nd edition) available from Dover.
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| Differentiable manifolds - Lecture notes by Mariusz Wodzicki in postscript or pdf.
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| Partial Differential Equations - Maple lessons for an undergraduate course in Differential Equations by Jim Herod.
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| Functional Analysis - Lecture notes by Paul Garrett.
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| Mechanism of the Heavens - A book on celestial mechanics by Mary Somerville (1831).
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| Algorithms and Complexity - By Herbert S. Wilf. In print 1986-1994. Single PDF file.
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| Finite Element Method/Boundary Element Method - Notes by Peter Hunter and Andrew Pullan in pdf.
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| Group Characters, Symmetric Functions, and the Hecke Algebra - A book by David M. Goldschmidt based on lecture notes of a course given at Berkeley in 1989.
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| Linear Algebra Notes and Exercises - A collection of mini-lessons in pdf format designed for self-instruction over the web by Jonathan Spingarn.
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| Distributions, Fourier Transforms and Microlocal Analysis - A short course by Yuri Safarov
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| Fourier Analysis - Lecture notes by Yuri Safarov.
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| Real Analysis - Lecture notes by Yuri Safarov.
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| Inverse Problems - Lecture notes by Sze Tan.
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| Topology - Lecture notes by David R. Wilkins at Trinity College, Dublin.
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| Differential Geometry and Physics - Lecture notes by Gabriel Lugo.
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| Complex algebraic varieties and their cohomology - A book of notes by Donu Arapura.
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| Differential forms - An introduction to differential forms and other notes by Donu Arapura.
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| Chaos - Introduction To Chaos by Michael Cross. An online course at Caltech.
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| Ordinary Differential Equations - Course notes by Klaus Schmitt at the University of Utah.
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| Ordinary Differential Equations - Informal postscript notes for a course by Sheldon Newhouse at Michigan State.
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| Partial Differential Equations - "PDE Primer" by Ralph Showalter at Oregon State.
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| Partial Differential Equations - Lecture notes on Analysis and PDEs by Bruce Driver at UCSD.
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| Differential Equations - Postscript notes on various topics in differential equations by Bruce Ikenaga.
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| Integral And Differential Equations - Class notes by Jim Herod at Georgia Tech.
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| 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.
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| Matroid Decomposition - Monograph by Klaus Truemper published by Academic Press in 1992. Chapters in PostScript.
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| 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.
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| 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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| 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.
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| A Problem Course in Mathematical Logic; by Stefan Bilaniuk - Volume I: Propositional and First-Order Logic. Volume II: Computability and Incompleteness.
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| Differential geometry - A textbook by Ruslan Sharipov (English and Russian versions).
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| Tensor analysis - A quick introduction to tensor analysis by Ruslan Sharipov (English and Russian versions).
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| Linear algebra and multidimensional geometry - A textbook by Ruslan Sharipov (English and Russian versions).
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