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AMS Books Online
Provides downloadable books on a range of mathematical topics.
http://www.ams.org/online_bks/online_subject.html#MP
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Analysis
Lecture notes by Yuri Safarov.
http://www.mth.kcl.ac.uk/courses/cm221.html
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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.
http://www.trillia.com/zakon1.html
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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
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Complex Analysis
Lecture notes by Yuri Safarov.
http://www.mth.kcl.ac.uk/courses/cm322.html
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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.
http://www.mathphysics.com/dynam/
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Dynamics in One Complex Variable: Introductory Lectures
Lecture notes by John Milnor in TeX and PostScript.
http://www.math.sunysb.edu/cgi-bin/preprint.pl?ims90-5
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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.
http://www.uea.ac.uk/~h720/lecturenotes/
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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.
http://home.claranet.nl/users/benschop/
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Finite Rank Torsion Free Modules Over Dedekind Domains
Monograph in commutative ring theory by Lee Lady. DVI and PDF.
http://www.math.hawaii.edu/~lee/book/
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Finite Simple Groups
"The classification of the finite simple groups" by D. Gorenstein, R. Lyons, and R. Solomon in PDF.
http://www.ams.org/online_bks/surv40-1/
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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
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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
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Generatingfunctionology
By Herbert S. Wilf. Published by Academic Press. PDF.
http://www.math.upenn.edu/~wilf/DownldGF.html
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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
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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.
http://www.ams.org/online_bks/surv53/
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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.
http://www.ams.org/online_bks/ulect4/
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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).
http://www.math.chalmers.se/Math/Research/GeometryAnalysis/Lecturenotes/
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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.
http://www.ams.org/online_bks/surv54/
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Index Theory, Geometric Scattering, and Differential Analysis on Manifolds with Corners
Several books by Richard Melrose et al. in PostScript.
http://www-math.mit.edu/~rbm/book.html
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Integral and Differential Equations
Class notes by Jim Herod at Georgia Tech.
http://www.math.gatech.edu/~herod/4348/4348.html
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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.
http://www.emis.de/monographs/gilkey/
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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
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Lecture Notes on Optimization
By Pravin Varaiya. This book is an introduction to mathematical programming, optimal control, and dynamic programming.
http://paleale.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf
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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/
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Linear Partial Differential Equations and Fourier Theory
Complete textbook by Marcus Pivato on the solutions of linear partial differential equations, with emphasis on eigenfunction methods (and hence, Fourier analysis). Lots of pictures.
http://xaravve.trentu.ca/pde.pdf
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Linear Programming: Foundations and Extensions
Book by Robert J. Vanderbei in PDF.
http://www.princeton.edu/~rvdb/LPbook/
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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
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Math Wizard
E-book gives some ideas on alternative approaches to teaching and learning math. Page includes table of contents. Requires a purchase.
http://home.earthlink.net/~susankennison/mathwizard/
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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
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Mathematical Modeling in a Real and Complex World
Online guide book by Frank Wattenberg in HTML.
http://www.math.montana.edu/frankw/ccp/modeling/topic.htm
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Mathematical Principles of Natural Philosophy
Principia by Isaac Newton (1687) translated by Andrew Motte (1729) in HTML (incomplete).
http://members.tripod.com/~gravitee/
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Matrix Analysis and Applied Linear Algebra
By Carl D. Meyer. Full text in PDF with errata, updates and solutions.
http://www.matrixanalysis.com/
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Mechanism of the Heavens
A book on celestial mechanics by Mary Somerville (1831).
http://www.malaspina.com/etext/heavens.htm
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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).
http://www.umcs.maine.edu/~chaitin/omega.html
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Monotone Operators in Banach Space and Nonlinear Partial Differential Equations
A monograph by Ralph Showalter in PDF.
http://www.ams.org/online_bks/surv49/
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Multigrid Methods
"An Introduction to Multigrid Methods" by Pieter Wesseling.
http://www.mgnet.org/mgnet-books-wesseling.html
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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.
http://www.math.lsa.umich.edu/~rlaz/
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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.
http://www.emis.de/monographs/KSM/
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Numerical Grid Generation
A book by Thompson, Warsi, and Mastin, previously published by Elsevier, in HTML.
http://www.erc.msstate.edu/publications/gridbook/
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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.
http://www.nr.com/nronline_switcher.html
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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
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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.
http://www.math.lsa.umich.edu/~idolga/lecturenotes.html
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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.
http://www.math.rutgers.edu/~zeilberg/GT.html
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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.
http://www.cs.man.ac.uk/~pt/Practical_Foundations/index.html
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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.
http://phyweb.lbl.gov/~rncahn/www/liealgebras/texall.pdf
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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.
http://www-fourier.ujf-grenoble.fr/~demailly/lectures.html
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Sheaf Cohomology
Mathematical notes on sheaves and other topics by P. Morandi.
http://sierra.nmsu.edu/morandi/notes/mathematicalnotes.html
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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.
http://www.emis.de/monographs/GLP/
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Splines and Wavelets
A monograph by Karl Scherer in German (DVI and Postscript).
http://www.iam.uni-bonn.de/~scherer/wavelets.html
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Stochastic Calculus
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.
http://www.chiark.greenend.org.uk/~alanb/
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Templates for the Solution of Linear Systems
Book on iterative methods by Richard Barrett et al. in HTML and Postscript.
http://netlib2.cs.utk.edu/linalg/html_templates/Templates.html
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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
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The FEMCI Book
Finite Element Modeling Continuous Improvement. A web text by Ryan Simmons.
http://femci.gsfc.nasa.gov/femcibook.html
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The Limits of Mathematics
An online course on information theory and the limits of formal reasoning by G.J. Chaitin.
http://www.umcs.maine.edu/~chaitin/lm.html
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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
http://www.emis.de/monographs/jablan/
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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.
http://www.ams.org/online_bks/mmono140/
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Voting, Arbitration & Fair Division: Mathematics of Social Choice
An introduction to `social choice theory', which uses mathematics to study the strengths/weaknesses of voting systems, arbitration schemes, and other methods of group decision making. Lots of pictures, requires only basic linear algebra. Author: Marcus Pivato.
http://xaravve.trentu.ca/pivato/Teaching/voting.pdf
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