Online Texts (173)
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 Lie superalgebras   - Irving Kaplansky's material on Lie superalgebras. - http://justpasha.org/math/links/subj/lie/kaplansky/    History of mathematics - Notes by Donald Lancon, Jr. Contains a brief history of calculus and other interesting stuff. - http://www.obkb.com/dcljr/mathemat.html Why study calculus? - A brief look at some of the history of mathematics by Eric Schechter. - http://www.math.vanderbilt.edu/~schectex/courses/whystudy.html Graph Theory - Hyperlinked PDF version of a book by Reinhard Diestel. - http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/ 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. - http://www.math.uga.edu/%7eroy/ Probability guide for non-mathematicians - Probability theory basics, applications (including to gambling), interpretations, books, free texts. - http://probability.infarom.ro/ 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 includ - http://math.sfsu.edu/beck/complex.html Linear Algebra and Applications - Textbook by Thomas Shores. GIFs of pages. - http://www.math.unl.edu/~tshores1/linalgtext.html 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/ The FEMCI Book - Finite Element Modeling Continuous Improvement. A web text by Ryan Simmons. - http://femci.gsfc.nasa.gov/femcibook.html 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 Pi - http://xaravve.trentu.ca/pivato/Teaching/voting.pdf 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 Calculus - Textbook by Gilbert Strang in pdf. - http://ocw.mit.edu/ans7870/textbooks/Strang/strangtext.htm Measure Theory - A book by D.H. Fremlin. Plain tex sources. - http://www.essex.ac.uk/maths/staff/fremlin/mt.htm Complex-Analytic Geometry of Complex Parallelizable Manifolds - Monograph by Jörg Winkelmann. - http://www.iecn.u-nancy.fr/~winkelma/mirror/unibas/cplx/papers/gca.html 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. - http://www.princeton.edu/~rvdb/506book/book.pdf 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.mth.uea.ac.uk/~h720/lecturenotes/ Abstract Algebra Notes - A collection of short notes by Bruce Ikenaga in PostScript. - http://www.millersville.edu/~bikenaga/absalg/absanote.html Open Math Text Lecture Notes - Lecture notes on various topics (English and Spanish) in Word and PDF format. - http://openmathtext.org/downloads.html 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/ 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. - http://ejde.math.txstate.edu/Monographs/01/abstr.html 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 Finite Fields - An Introduction to Finite Fields by Bill Cherowitzo (html). - http://www-math.cudenver.edu/~wcherowi/courses/finflds.html Differential Geometry - Lecture notes for an honors course at the University of Adelaide by Michael Murray in HTML with GIFs. - http://internal.maths.adelaide.edu.au/people/mmurray/dg_hons/dg_hons.html 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/ Mathematical Logic - "A Problem Course in Mathematical Logic" by Stefan Bilaniuk in LaTeX, PostScript or PDF. - http://euclid.trentu.ca/math/sb/pcml/ 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/ 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/ 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/ Matroid Decomposition - Monograph by Klaus Truemper published by Academic Press in 1992. Chapters in PostScript. - http://www.emis.de/monographs/md/ 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/ Integral And Differential Equations - Class notes by Jim Herod at Georgia Tech. - http://www.math.gatech.edu/~herod/4348/4348.html Differential Equations - Postscript notes on various topics in differential equations by Bruce Ikenaga. - http://marauder.millersville.edu/~bikenaga/diffeq/deqnote.html Analytic Differential Equations - Lectures on Analytic Differential Equations by Sergei Yakovenko at the Weizmann Institute. - http://www.wisdom.weizmann.ac.il/~yakov/thebook.pdf Partial Differential Equations - Lecture notes on Analysis and PDEs by Bruce Driver at UCSD. - http://math.ucsd.edu/~driver/231-02-03/lecture_notes.htm Ordinary Differential Equations - Course notes by Klaus Schmitt at the University of Utah. - http://www.math.utah.edu/~schmitt/math6410.html Chaos - Introduction To Chaos by Michael Cross. An online course at Caltech. - http://www.cmp.caltech.edu/~mcc/Chaos_Course/Outline.html Differential forms - An introduction to differential forms and other notes by Donu Arapura. - http://www.math.purdue.edu/~dvb/ Complex algebraic varieties and their cohomology - A book of notes by Donu Arapura. - http://www.math.purdue.edu/~dvb/book.html Differential Geometry and Physics - Lecture notes by Gabriel Lugo. - http://people.uncw.edu/lugo/COURSES/DiffGeom/dg1.htm Topology - Lecture notes by David R. Wilkins at Trinity College, Dublin. - http://www.maths.tcd.ie/~dwilkins/Courses/212/ Distributions, Fourier Transforms and Microlocal Analysis - A short course by Yuri Safarov - http://www.mth.kcl.ac.uk/~ysafarov/Lectures/ 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/ Algorithms and Complexity - By Herbert S. Wilf. In print 1986-1994. Single PDF file. - http://www.cis.upenn.edu/~wilf/AlgComp3.html Mechanism of the Heavens - A book on celestial mechanics by Mary Somerville (1831). - http://www.malaspina.com/etext/heavens.htm Differentiable manifolds - Lecture notes by Mariusz Wodzicki in postscript or pdf. - http://math.berkeley.edu/~wodzicki/214/ Mathematical Illustrations - A manual of geometry and PostScript by Bill Casselman, including code samples and packages. - http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/ 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. - http://www.trillia.com/zakon-analysisI.html 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 Wavelet Tutorial - Guide to wavelet analysis by Robi Polikar. - http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html 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 Num - http://www.trillia.com/moser-number.html Description Logics Handbook - A course on Description Logics (the Semantic Web underlying formalism) by E. Franconi (modules in pdf) - http://www.inf.unibz.it/~franconi/dl/course/ Sheaf Cohomology - Mathematical notes on sheaves and other topics by P. Morandi. - http://sierra.nmsu.edu/morandi/notes/mathematicalnotes.html Geometry and the Imagination - An online course by John Conway, Peter Doyle, Jane Gilman and Bill Thurston in HTML and PostScript. - http://www.geom.uiuc.edu/docs/education/institute91/ Flatland - A romance of many dimensions. With Illustrations by the Author, A SQUARE (Edwin A. Abbott 1838-1926). HTML. - http://www.geom.uiuc.edu/~banchoff/Flatland/ Calculus Using Infinitesimals - Elementary Calculus: An Approach - a book by H. Jerome Keisler originally published by Prindle, Weber & Schmidt (2nd ed: 1986) - http://www.math.wisc.edu/~keisler/calc.html Abstract Algebra - A book draft: "Applied Abstract Algebra" by D. Joyner, R. Kreminski, J. Turisco in HTML. - http://web.usna.navy.mil/~wdj/book/ Abstract Algebra with GAP - A laboratory manual by J. G. Rainbolt and J. A. Gallian. - http://euler.slu.edu/Dept/Faculty/rainbolt/manual.html Complex analysis and dynamics - Various lecture notes C. McMullen - http://math.harvard.edu/~ctm/past.html 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 Topology Without Tears - A course in topology by Sidney A. Morris in HTML with embedded GIFs. Must purchase to view. - http://www.theassayer.org/cgi-bin/asauthor.cgi?author=430 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/ Riemannian Geometry - "An Introduction to Riemannian Geometry" by S. Gudmundsson in postscript (1996). - http://www.maths.lth.se/publications/Pure-Lecture-Notes.html Splines and Wavelets - A monograph by Karl Scherer in German (DVI and Postscript). - http://www.iam.uni-bonn.de/~scherer/wavelets.html Complex Numbers - Dave's Short Course on Complex Numbers (David Joyce). - http://www.clarku.edu/~djoyce/complex/ Matrix Analysis and Applied Linear Algebra - By Carl D. Meyer. Full text in PDF with errata, updates and solutions. - http://www.matrixanalysis.com/ 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 - http://www.mathphysics.com/dynam/ Multigrid Methods - "An Introduction to Multigrid Methods" by Pieter Wesseling. - http://www.mgnet.org/mgnet-books-wesseling.html Optimization - "Lecture Notes on Optimization" by Pravin Varaiya. This book is an introduction to mathematical programming, optimal control, and dynamic programming. - http://www-path.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf Toposes, Triples and Theories - A book by Michael Barr and Charles Wells originally published by Springer Verlag. - http://www.cwru.edu/artsci/math/wells/pub/ttt.html Wavelets - An Introduction to Wavelets by Amara Graps in HTML, PDF or Postscript. - http://www.amara.com/IEEEwave/IEEEwavelet.html Numerical Grid Generation - A book by Thompson, Warsi, and Mastin, previously published by Elsevier, in HTML. - http://www.erc.msstate.edu/publications/gridbook/ Linear Algebra - "Elementary Linear Algebra" by Keith Matthews. Lecture notes and solutions from 1991 in PDF or PostScript. - http://www.numbertheory.org/book/ Matrices - The 1934 classic "Lectures on Matrices" by Wedderburn in scanned PDF. - http://www.ams.org/online_bks/coll17/ Monotone Operators in Banach Space and Nonlinear Partial Differential Equations - A monograph by Ralph Showalter in PDF. - http://www.ams.org/online_bks/surv49/ 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/ 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/ Linear Algebra, Infinite Dimensions, and Maple - A textbook by James Herod. - http://www.math.gatech.edu/~herod/Hspace/Hspace.html Geometric Asymptotics - This book by Guillemin and Sternberg includes the method of stationary phase, geometrical optics, quantization. - http://www.ams.org/online_bks/surv14/ 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 - http://www.weblearn.hs-bremen.de/risse/MAI/docs/numerics.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. - http://www.trillia.com/zakon1.html Algebraic Combinatorics via Finite Group Actions - HTML book by A. Betten, H. Fripertinger, and A. Kerber. - http://www.mathe2.uni-bayreuth.de/frib/html/book/hyl00.html 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. - http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/tc.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 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 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 Algebraic K-theory - "An introduction to algebraic K-theory" by Charles Weibel. Chapters in DVI. - http://math.rutgers.edu/~weibel/Kbook.html Fundamental Problems in Algorithmic Algebra - Book by Chee Yap published by Oxford University Press in 1999. - http://www.cs.nyu.edu/yap/book/ 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 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 Dynamical Systems and Fractals - Lecture Notes by David J. Wright in HTML. - http://www.math.okstate.edu/mathdept/dynamics/lecnotes/lecnotes.html Linear Programming: Foundations and Extensions - Book by Robert J. Vanderbei in PDF. - http://www.princeton.edu/~rvdb/LPbook/ 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, roo - http://www.math.binghamton.edu/matt/ Computational Geometry and Computational Optimization - Lecture notes by Jianer Chen in PostScript. - http://www.cs.tamu.edu/faculty/chen/notes/ 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/ Algebraic Topology - 1942 classic by Solomon Lefschetz published by AMS. Chapters in scanned PDF. - http://www.ams.org/online_bks/coll27/ 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 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. - http://www.math.lsa.umich.edu/~fornaess/complexdynamicspapers.html 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 - http://www.ams.org/online_bks/surv53/ Functional Analysis and Semi-Groups - Book by Einar Hille and Ralph S. Phillips published by AMS in 1957. Scanned chapters in PDF. - http://www.ams.org/online_bks/coll31/ 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 Complex analytic and algebraic geometry - Book by Jean-Pierre Demailly in PostScript. - http://www-fourier.ujf-grenoble.fr/~demailly/books.html Dynamical Systems - 1927 classic by George D. Birkhoff published by AMS. Scanned chapters in PDF. - http://www.ams.org/online_bks/coll9/ 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/ Category Theory - "A Gentle Introduction to Category Theory - the calculational approach" by Maarten M. Fokkinga in PostScript. - http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html Complex and Functional Analysis - Lecture notes by Douglas N. Arnold for a course at Penn State. Two parts in TeX, DVI, PostScript and PDF. - http://www.math.psu.edu/dna/502.s97/ Advanced Calculus and Analysis - Lecture notes by Ian Craw from a course at the Univ. of Aberdeen. HTML with GIFs. - http://www.maths.abdn.ac.uk/~igc/tch/ma2001/notes/notes.html Analysis WebNotes - Online course by John Lindsay Orr. Chapters also available in LaTeX. - http://www.math.unl.edu/~webnotes/home/home.htm Trigonometry - "Dave's Short Trig Course" by D. E. Joyce. HTML with Java. - http://aleph0.clarku.edu/~djoyce/java/trig/ Topology Course Lecture Notes - By Aisling McCluskey and Brian McMaster. HTML with symbol fonts, DVI and PostScript. - http://at.yorku.ca/i/a/a/b/23.htm 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/ Multivariable Calculus - Textbook by George Cain and James Herod. Chapters in PDF. - http://www.math.gatech.edu/~cain/notes/calculus.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. - http://www.math.niu.edu/~beachy/abstract_algebraII/ 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://www-physics.lbl.gov/~rncahn/book.html 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 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 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. - http://www.unige.ch/math/biblio/preprint/cstar/liste.html Universal Algebra - "A Course in Universal Algebra" by Stanley Burris and H. P. Sankappanavar. PostScript and PDF. - http://www.thoralf.uwaterloo.ca/htdocs/ualg.html 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. - http://www.math.miami.edu/~ec/book/ 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.dcs.qmw.ac.uk/~pt/Practical_Foundations/html/summary.html 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 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 A=B - Combinatorics text by Marko Petkovsek, Herbert Wilf and Doron Zeilberger. Published by A. K. Peters. PDF. - http://www.cis.upenn.edu/~wilf/AeqB.html 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. - http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.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 Euclid's Elements - Edited by D.E. Joyce. HTML text with Java applets. - http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Generatingfunctionology - By Herbert S. Wilf. Published by Academic Press. PDF. - http://www.math.upenn.edu/~wilf/DownldGF.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/ |
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