Science: Math: Publications: Online_Texts
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- A=B - Combinatorics text by Marko Petkovsek, Herbert Wilf and Doron Zeilberger. Published by A. K. Peters. PDF.
- Abstract Algebra - Course notes by J.S. Milne. Topics covered are group, fields and Galois, algebraic number, class field theories. Other areas discussed are modular functions and forms, elliptic curves, algebraic geometry, Etale Cohomology, and Abelian varieties. In HTML, PDF, PostScript and DVI formats.
- Abstract Algebra - Lecture notes by David Wilkins at Trinity College, Dublin.
- Abstract Algebra - "Intro to Abstract Algebra" by Paul Garrett in PostScript and PDF.
- 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.
- Abstract Algebra - A book draft: "Applied Abstract Algebra" by D. Joyner, R. Kreminski, J. Turisco in HTML.
- 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.
- Abstract Algebra Notes - A collection of short notes by Bruce Ikenaga in PostScript.
- Abstract Algebra with GAP - A laboratory manual by J. G. Rainbolt and J. A. Gallian.
- Advanced Calculus and Analysis - Lecture notes by Ian Craw from a course at the Univ. of Aberdeen. HTML with GIFs.
- Algebra notes - Roy Smith's course notes in linear algebra, elementary abstract algebra, basic graduate algebra, and a survey of the Riemann-Roch theorem from Riemann to Hirzebruch. [PDF]
- Algebraic Combinatorics via Finite Group Actions - HTML book by A. Betten, H. Fripertinger, and A. Kerber.
- Algebraic Geometry - Various lecture notes by J.S. Milne.
- Algebraic Geometry - A. Grothendieck's "Séminaire de Géometrie Algébrique" produced by F. Calegari, J. Borger and W. Stein. JPEG scans of typewritten material.
- Algebraic K-theory - "An introduction to algebraic K-theory" by Charles Weibel. Chapters in DVI.
- Algebraic Topology - Basic core material along with a number of optional topics of a relatively elementary nature by Allen Hatcher. PDF and Postscript.
- Algebraic Topology - 1942 classic by Solomon Lefschetz published by AMS. Chapters in scanned PDF.
- Algorithms and Complexity - By Herbert S. Wilf. In print 1986-1994. Single PDF file.
- Analysis WebNotes - Online course by John Lindsay Orr. Chapters also available in LaTeX.
- Analytic Differential Equations - Lectures on Analytic Differential Equations by Sergei Yakovenko at the Weizmann Institute. [PDF]
- 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.
- Calculus - "The Calculus Bible" by G. S. Gill.
- Calculus - "Advanced Calculus" by Shlomo Sternberg covers analysis on linear spaces and manifolds extending through introductory differential geometry.
- Calculus - Textbook by Gilbert Strang in pdf.
- Calculus Using Infinitesimals - Elementary Calculus: An Approach - a book by H. Jerome Keisler originally published by Prindle, Weber & Schmidt (2nd ed: 1986)
- 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.
- Category Theory - "A Gentle Introduction to Category Theory - the calculational approach" by Maarten M. Fokkinga in PostScript.
- Chaos - Introduction To Chaos by Michael Cross. An online course at Caltech.
- Chebyshev and Fourier Spectral Methods - A book by John P. Boyd (2nd edition) available from Dover.
- Complex algebraic varieties and their cohomology - A book of notes by Donu Arapura.
- Complex Analysis - "A First Course in Complex Analysis" by Matthias Beck, Gerald Marchesi, and Dennis Pixton is a set of lecture notes for a one-semester undergraduate course, relying on as few concepts from real analysis as possible. Numerous exercises are included.
- Complex Analysis - Textbook for an introductory course in complex analysis by George Cain. Chapters in PDF.
- Complex Analysis - Course notes by Harold V. McIntosh in HTML.
- Complex analysis and dynamics - Various lecture notes C. McMullen
- Complex analytic and algebraic geometry - Book by Jean-Pierre Demailly in PostScript.
- Complex and Functional Analysis - Lecture notes by Douglas N. Arnold for a course at Penn State. Two parts in TeX, DVI, PostScript and PDF.
- 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.
- Complex Numbers - Dave's Short Course on Complex Numbers (David Joyce).
- Complex-Analytic Geometry of Complex Parallelizable Manifolds - Monograph by Jörg Winkelmann.
- Computational Geometry and Computational Optimization - Lecture notes by Jianer Chen in PostScript.
- Description Logics Handbook - A course on Description Logics (the Semantic Web underlying formalism) by E. Franconi (modules in pdf)
- Differentiable manifolds - Lecture notes by Mariusz Wodzicki in postscript or pdf.
- Differential Algebra - Scans of Ritt's 1950 classic in PDF.
- Differential Equations - Postscript notes on various topics in differential equations by Bruce Ikenaga.
- Differential forms - An introduction to differential forms and other notes by Donu Arapura.
- Differential Geometry - Notes by Balázs Csikós. Chapters in PostScript.
- Differential Geometry - Lecture notes for a course at the Weizmann Institute of Science by Sergei Yakovenko. Chapters in DVI.
- 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.
- Differential Geometry - Lecture notes for an honors course at the University of Adelaide by Michael Murray in HTML with GIFs.
- Differential geometry - A textbook by Ruslan Sharipov (English and Russian versions).
- Differential Geometry and General Relativity - An introduction to differential geometry and general relativity by Stefan Waner at Hofstra. This is an upper level undergraduate mathematics course which assumes a knowledge of calculus and some linear algebra.
- Differential Geometry and Physics - Lecture notes by Gabriel Lugo.
- 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".
- Discrete Mathematics - Lecture notes by László Lovász in Postscript. Includes "Discrete Mathematics", "Semidefinite optimization", "Topological methods in combinatorics", and "Complexity of algorithms".
- Distributions, Fourier Transforms and Microlocal Analysis - A short course by Yuri Safarov
- Dynamical Systems - 1927 classic by George D. Birkhoff published by AMS. Scanned chapters in PDF.
- Dynamical Systems and Fractals - Lecture Notes by David J. Wright in 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.
- Dynamics in One Complex Variable: Introductory Lectures - Lecture notes by John Milnor in TeX and PostScript.
- 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.
- Entropy of Compact Group Automorphisms - Lecture notes based on a course at Ohio State in 1994 by Thomas Ward in DVI and PostScript.
- Euclid's Elements - Edited by D.E. Joyce. HTML text with Java applets.
- 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 Fields - An Introduction to Finite Fields by Bill Cherowitzo (html).
- Finite Rank Torsion Free Modules Over Dedekind Domains - Monograph in commutative ring theory by Lee Lady. DVI and PDF.
- Finite Simple Groups - "The classification of the finite simple groups" by D. Gorenstein, R. Lyons, and R. Solomon in PDF.
- Flatland - A romance of many dimensions. With Illustrations by the Author, A SQUARE (Edwin A. Abbott 1838-1926). HTML.
- Fourier Analysis - Lecture notes by Yuri Safarov.
- Fractals in the Plane - Ergodic Theory Methods - A book by F. Przytycki and M. Urbanski in Postscript.
- Functional Analysis - Lecture notes by Paul Garrett.
- Functional Analysis and Semi-Groups - Book by Einar Hille and Ralph S. Phillips published by AMS in 1957. Scanned chapters in PDF.
- Fundamental Problems in Algorithmic Algebra - Book by Chee Yap published by Oxford University Press in 1999.
- Fundamentals of Model Theory - Introductory textbook by William Weiss and Cherie D'Mello. PostScript, DVI, GIF.
- Generatingfunctionology - By Herbert S. Wilf. Published by Academic Press. PDF.
- Geometric Asymptotics - This book by Guillemin and Sternberg includes the method of stationary phase, geometrical optics, quantization.
- Geometric Constraint Solving - An electronic primer by William Bouma, Xiangping Chen, Ioannis Fudos, Christoph Hoffmann, and Pamela J. Vermeer.
- Geometry and the Imagination - An online course by John Conway, Peter Doyle, Jane Gilman and Bill Thurston in HTML and PostScript.
- 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.
- Graph Theory - Hyperlinked PDF version of a book by Reinhard Diestel.
- 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.
- Group theory - A self-contained course using formalized mathematics for interactive online education.
- 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).
- Hilbert Space Methods for Partial Differential Equations - Textbook for beginning graduate students of mathematics, engineering, and the physical sciences by Ralph Showalter. Chapters in PostScript and PDF.
- History of mathematics - Notes by Donald Lancon, Jr. Contains a brief history of calculus and other interesting stuff.
- 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.
- Index Theory, Geometric Scattering, and Differential analysis on manifolds with corners - Several books by Richard Melrose et al. in PostScript.
- 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.
- Inverse Problems - Lecture notes by Sze Tan.
- Lie superalgebras - Irving Kaplansky's material on Lie superalgebras.
- The Limits of Mathematics - An online course on information theory and the limits of formal reasoning by G.J. Chaitin.
- Linear Algebra - "Elementary Linear Algebra" by Keith Matthews. Lecture notes and solutions from 1991 in PDF or PostScript.
- Linear Algebra - Textbook by Jim Hefferon covering the material of any undergraduate first linear algebra course. Book or chapters in PDF.
- Linear Algebra and Applications - Textbook by Thomas Shores. GIFs of pages.
- Linear algebra and multidimensional geometry - A textbook by Ruslan Sharipov (English and Russian versions).
- Linear Algebra, Infinite Dimensions, and Maple - A textbook by James Herod.
- 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 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.
- 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.
- Math Wizard - E-book gives some ideas on alternative approaches to teaching and learning math. Page includes table of contents. Requires a purchase.
- 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.
- Mathematical Illustrations - A manual of geometry and PostScript by Bill Casselman, including code samples and packages.
- Mathematical Logic - "A Problem Course in Mathematical Logic" by Stefan Bilaniuk in LaTeX, PostScript or PDF.
- 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.
- Mathematical Modeling in a Real and Complex World - Online guide book by Frank Wattenberg in HTML.
- Mathematical Principles of Natural Philosophy - Principia by Isaac Newton (1687) translated by Andrew Motte (1729) in HTML (incomplete).
- Matrices - The 1934 classic "Lectures on Matrices" by Wedderburn in scanned PDF.
- Matrix Analysis and Applied Linear Algebra - By Carl D. Meyer. Full text in PDF with errata, updates and solutions.
- Matroid Decomposition - Monograph by Klaus Truemper published by Academic Press in 1992. Chapters in PostScript.
- Measure Theory - A book by D.H. Fremlin. Plain tex sources.
- Mechanism of the Heavens - A book on celestial mechanics by Mary Somerville (1831).
- 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).
- Mixed Motives - Monograph by Marc Levine published by AMS in 1998. Whole book or chapters in PDF.
- Monotone Operators in Banach Space and Nonlinear Partial Differential Equations - A monograph by Ralph Showalter in PDF.
- Multigrid Methods - "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.
- Multivariable Calculus - Textbook by George Cain and James Herod. Chapters in PDF.
- 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.
- 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.
- 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 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.
- Open Math Text Lecture Notes - Lecture notes on various topics (English and Spanish) in Word and PDF format.
- Optimization - "Lecture Notes on Optimization" by Pravin Varaiya. This book is an introduction to mathematical programming, optimal control, and dynamic programming.
- Ordinary Differential Equations - Course notes by Klaus Schmitt at the University of Utah.
- Partial Differential Equations - Lecture notes on Analysis and PDEs by Bruce Driver at UCSD.
- Partial Differential Equations - "PDE Primer" by Ralph Showalter at Oregon State.
- Partial Differential Equations - Maple lessons for an undergraduate course in Differential Equations by Jim Herod.
- Physics, Invariant Theory, Modular Forms, and Algebraic Geometry - Several lecture note sets by Igor Dolgachev in various formats, including DVI and PostScript.
- 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.
- 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.
- 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.
- Probability - "Introduction to Probability" by Charles M. Grinstead and J. Laurie Snell in PDF. Published by the AMS. The site also contains additional teaching resources.
- Probability guide for non-mathematicians - Probability theory basics, applications (including to gambling), interpretations, books, free texts.
- Real Analysis - Lecture notes by Yuri Safarov.
- Riemannian Geometry - "An Introduction to Riemannian Geometry" by S. Gudmundsson in postscript (1996).
- Semi-Simple Lie Algebras and their Representations - Book for particle physicists by Robert N. Cahn. Published by Benjamin-Cummings in 1984. Chapters in PostScript.
- 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.
- Sheaf Cohomology - 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).
- 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.
- Templates for the Solution of Linear Systems - Book on iterative methods by Richard Barrett et al. in HTML and Postscript.
- Tensor analysis - A quick introduction to tensor analysis by Ruslan Sharipov (English and Russian versions).
- 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
- Topology - Lecture notes by David R. Wilkins at Trinity College, Dublin.
- Topology - "Textbook in Problems on Elementary Topology" by Viro, Ivanov, Kharlamov and Netsvetaev - draft version in postscript. The page also includes several papers on real algebraic geometry.
- Topology Course Lecture Notes - By Aisling McCluskey and Brian McMaster. HTML with symbol fonts, DVI and PostScript.
- Topology Without Tears - A course in topology by Sidney A. Morris in HTML with embedded GIFs. Must purchase to view.
- Toposes, Triples and Theories - A book by Michael Barr and Charles Wells originally published by Springer Verlag.
- 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.
- Trigonometry - "Dave's Short Trig Course" by D. E. Joyce. HTML with Java.
- Universal Algebra - "A Course in Universal Algebra" by Stanley Burris and H. P. Sankappanavar. PostScript and PDF.
- 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. [PDF]
- Wavelet Tutorial - Guide to wavelet analysis by Robi Polikar.
- Wavelets - An Introduction to Wavelets by Amara Graps in HTML, PDF or Postscript.
- Why study calculus? - A brief look at some of the history of mathematics by Eric Schechter.
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