- Linear Methods of Applied Mathematics - http://www.mathphysics.com/pde/
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.
- Algebraic Topology - http://www.math.cornell.edu/~hatcher/
Basic core material along with a number of optional topics of a relatively elementary nature by Allen Hatcher. PDF and Postscript.
- Generatingfunctionology - http://www.math.upenn.edu/~wilf/DownldGF.html
By Herbert S. Wilf. Published by Academic Press. PDF.
- Euclid's Elements - http://aleph0.clarku.edu/~djoyce/java/elements/toc.html
Edited by D.E. Joyce. HTML text with Java applets.
- Fundamentals of Model Theory - http://at.yorku.ca/i/a/a/i/10.htm
Introductory textbook by William Weiss and Cherie D'Mello. PostScript, DVI, GIF.
- Probability - http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
"Introduction to Probability" by Charles M. Grinstead and J. Laurie Snell in PDF. Published by the AMS. The site also contains additional teaching resources.
- A=B - http://www.cis.upenn.edu/~wilf/AeqB.html
Combinatorics text by Marko Petkovsek, Herbert Wilf and Doron Zeilberger. Published by A. K. Peters. PDF.
- Abstract Algebra - http://www.math.uiuc.edu/~r-ash/
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.
- Numerical Recipes Books On-Line - http://www.nr.com/nronline_switcher.html
The complete Numerical Recipes books in C, Fortran 77, and Fortran 90 On-Line, in both PostScript and Adobe Acrobat formats.
- Mixed Motives - http://www.ams.org/online_bks/surv57/surv57.pdf
Monograph by Marc Levine published by AMS in 1998. Whole book or chapters in PDF.
- Practical Foundations of Mathematics - http://www.dcs.qmw.ac.uk/~pt/Practical_Foundations/html/summary.html
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.
- Elements of Abstract and Linear Algebra - http://www.math.miami.edu/~ec/book/
Foundational textbook on abstract algebra with emphasis on linear algebra by Edwin H. Connell. Whole book or chapters in DVI, PostScript, and PDF.
- Complex Analysis - http://www.math.gatech.edu/~cain/winter99/complex.html
Textbook for an introductory course in complex analysis by George Cain. Chapters in PDF.
- Universal Algebra - http://www.thoralf.uwaterloo.ca/htdocs/ualg.html
"A Course in Universal Algebra" by Stanley Burris and H. P. Sankappanavar. PostScript and PDF.
- C*-Algebras - http://www.unige.ch/math/biblio/preprint/cstar/liste.html
"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.
- Linear Algebra - http://joshua.smcvt.edu/linalg.html
Textbook by Jim Hefferon covering the material of any undergraduate first linear algebra course. Book or chapters in PDF.
- Abstract Algebra - http://www.maths.tcd.ie/~dwilkins/Courses/311/
Lecture notes by David Wilkins at Trinity College, Dublin.
- Abstract Algebra II - http://www.math.niu.edu/~beachy/abstract_algebraII/
A companion volume to "Abstract Algebra" by John A. Beachy and Bill Blair published by Waveland Press in 1995. Chapters in PostScript.
- Multivariable Calculus - http://www.math.gatech.edu/~cain/notes/calculus.html
Textbook by George Cain and James Herod. Chapters in PDF.
- Topology Course Lecture Notes - http://at.yorku.ca/i/a/a/b/23.htm
By Aisling McCluskey and Brian McMaster. HTML with symbol fonts, DVI and PostScript.
- Trigonometry - http://aleph0.clarku.edu/~djoyce/java/trig/
"Dave's Short Trig Course" by D. E. Joyce. HTML with Java.
- Analysis WebNotes - http://www.math.unl.edu/~webnotes/home/home.htm
Online course by John Lindsay Orr. Chapters also available in LaTeX.
- Advanced Calculus and Analysis - http://www.maths.abdn.ac.uk/~igc/tch/ma2001/notes/notes.html
Lecture notes by Ian Craw from a course at the Univ. of Aberdeen. HTML with GIFs.
- Interactive Real Analysis - http://www.shu.edu/html/teaching/math/reals/reals.html
"Interactive Real Analysis" by Bert G. Wachsmuth. HTML and Java.
- Complex and Functional Analysis - http://www.math.psu.edu/dna/502.s97/
Lecture notes by Douglas N. Arnold for a course at Penn State. Two parts in TeX, DVI, PostScript and PDF.
- Category Theory - http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html
"A Gentle Introduction to Category Theory - the calculational approach" by Maarten M. Fokkinga in PostScript.
- Dynamical Systems - http://www.ams.org/online_bks/coll9/
1927 classic by George D. Birkhoff published by AMS. Scanned chapters in PDF.
- Differential Geometry - http://www.cs.elte.hu/geometry/csikos/dif/dif.html
Notes by Balázs Csikós. Chapters in PostScript.
- Global Analysis - http://www.ams.org/online_bks/surv53/
"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.
- Complex Dynamics in Higher Dimensions - http://www.math.lsa.umich.edu/~fornaess/complexdynamicspapers.html
CBMS lecture notes by John Erik Fornæss at the bottom of page with other papers by the author and Nessim Sibony. PostScript.
- Several complex variables - http://www-fourier.ujf-grenoble.fr/~demailly/lectures.html
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.
- Algebraic Topology - http://www.ams.org/online_bks/coll27/
1942 classic by Solomon Lefschetz published by AMS. Chapters in scanned PDF.
- Differential Geometry - http://www.mat.univie.ac.at/~michor/listpubl.html
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 Topology - http://www.math.binghamton.edu/matt/
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".
- History of Calculus - http://occ.awlonline.com/bookbind/pubbooks/thomas_awl/chapter1/medialib/custom3/deluxe-content.html
Guide To History of Calculus. Topic essays and biographies keyed to the chapters and content of the 10th edition of Thomas's Calculus.
- Mathematical Methods of Engineering Analysis - http://www.sor.princeton.edu/~rvdb/506book/book.pdf
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.
- Numerical Analysis - http://www.cs.laurentian.ca/badams/numeric/intro/intro.html
"Introduction to Numerical Analysis Using Maple" by Barry G. Adams in HTML.
- Geometric Constraint Solving - http://www.cs.purdue.edu:80/homes/cmh/electrobook/intro.html
An electronic primer by William Bouma, Xiangping Chen, Ioannis Fudos, Christoph Hoffmann, and Pamela J. Vermeer.
- Abstract Algebra - http://www.math.umn.edu/~garrett/m/intro_algebra/
"Intro to Abstract Algebra" by Paul Garrett in PostScript and PDF.
- The FEMCI Book - http://analyst.gsfc.nasa.gov/FEMCI/femcibook.html
Finite Element Modeling Continuous Improvement. A web text by Ryan Simmons.
- Algebraic K-theory - http://math.rutgers.edu/~weibel/Kbook.html
"An introduction to algebraic K-theory" by Charles Weibel. Chapters in DVI.
- Complex Analysis - http://delta.cs.cinvestav.mx/~mcintosh/comun/complex/complex.html
Course notes by Harold V. McIntosh in HTML.
- The Limits of Mathematics - http://www.umcs.maine.edu/~chaitin/lm.html
An online course on information theory and the limits of formal reasoning by G.J. Chaitin.
- Plane Geometry - http://www.math.rutgers.edu/~zeilberg/GT.html
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.
- Differential Gometry and General Relativity - http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/tc.html
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.
- Basic Concepts of Mathematics - http://www.trillia.com/zakon1.html
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.
- Numerics - interactive - http://www.weblearn.hs-bremen.de/risse/MAI/docs/numerics.pdf
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.
- Geometric Asymptotics - http://www.ams.org/online_bks/surv14/
This book by Guillemin and Sternberg includes the method of stationary phase, geometrical optics, quantization.
- Applied Cryptography - http://cacr.math.uwaterloo.ca/hac/
1996 CRC Handbook of Applied Cryptography by Menezes, van Oorschot and Vanstone in PDF.
- Graph Theory - http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/download.html
Hyperlinked PDF version of a book by Reinhard Diestel.
- Homeomorphisms in Analysis - http://www.ams.org/online_bks/surv54/
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.
- Finite Simple Groups - http://www.ams.org/online_bks/surv40-1/
"The classification of the finite simple groups" by D. Gorenstein, R. Lyons, and R. Solomon in PDF.
- Matrices - http://www.ams.org/online_bks/coll17/
The 1934 classic "Lectures on Matrices" by Wedderburn in scanned PDF.
- Stochastic Calculus - http://www.statslab.cam.ac.uk/~afrb2/
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.
- Algebraic Geometry - http://modular.fas.harvard.edu/sga/sga/
A. Grothendieck's "Séminaire de Géometrie Algébrique" produced by F. Calegari, J. Borger and W. Stein. JPEG scans of typewritten material.
- Linear Algebra - http://www.numbertheory.org/book/
"Elementary Linear Algebra" by Keith Matthews. Lecture notes and solutions from 1991 in PDF or PostScript.
- Numerical Grid Generation - http://www.erc.msstate.edu/publications/gridbook/
A book by Thompson, Warsi, and Mastin, previously published by Elsevier, in HTML.
- Wavelets - http://www.amara.com/IEEEwave/IEEEwavelet.html
An Introduction to Wavelets by Amara Graps in HTML, PDF or Postscript.
- Toposes, Triples and Theories - http://www.cwru.edu/artsci/math/wells/pub/ttt.html
A book by Michael Barr and Charles Wells originally published by Springer Verlag.
- Dynamical Systems and Ergodic Theory - http://www.ma.man.ac.uk/~mp/book.html
"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).
- Optimization - http://www-path.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf
"Lecture Notes on Optimization" by Pravin Varaiya. This book is an introduction to mathematical programming, optimal control, and dynamic programming.
- Multigrid Methods - http://www.mgnet.org/mgnet-books-wesseling.html
"An Introduction to Multigrid Methods" by Pieter Wesseling.
- Calculus - http://www.math.byu.edu/Math/CalculusBible/
"The Calculus Bible" by G. S. Gill.
- Dynamics and Chaos - http://www.mathphysics.com/dynam/
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.
- Abstract Algebra - http://www.jmilne.org/math/CourseNotes/
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.
- Differential Geometry - http://www.wisdom.weizmann.ac.il/~yakov/Geometry/
Lecture notes for a course at the Weizmann Institute of Science by Sergei Yakovenko. Chapters in DVI.
- Complex Numbers - http://www.clarku.edu/~djoyce/complex/
Dave's Short Course on Complex Numbers (David Joyce).
- Discrete Mathematics - http://research.microsoft.com/users/lovasz/notes.htm
Lecture notes by László Lovász in Postscript. Includes "Discrete Mathematics", "Semidefinite optimization", "Topological methods in combinatorics", and "Complexity of algorithms".
- Topology - http://www.math.uu.se/~oleg/educ-texts.html
"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.
- Splines and Wavelets - http://www.iam.uni-bonn.de/~scherer/wavelets.html
A monograph by Karl Scherer in German (DVI and Postscript).
- Riemannian Geometry - http://www.maths.lth.se/publications/Pure-Lecture-Notes.html
"An Introduction to Riemannian Geometry" by S. Gudmundsson in postscript (1996).
- Harmonic Analysis and Partial Differential Equations - http://www.math.chalmers.se/Math/Research/GeometryAnalysis/Lecturenotes/
A book by Dahlberg and Kenig in postscript (bitmapped fonts). The page also contains another book by Dahlberg: "Icke Linjära Evolutionsekvationer" (Swedish).
- Topology Without Tears - http://www.theassayer.org/cgi-bin/asauthor.cgi?author=430
A course in topology by Sidney A. Morris in HTML with embedded GIFs. Must purchase to view.
- Potential Theory - http://www.geocities.com/fabrikant_books/
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.
- Abstract Algebra with GAP - http://euler.slu.edu/Dept/Faculty/rainbolt/manual.html
A laboratory manual by J. G. Rainbolt and J. A. Gallian.
- Abstract Algebra - http://web.usna.navy.mil/~wdj/book/
A book draft: "Applied Abstract Algebra" by D. Joyner, R. Kreminski, J. Turisco in HTML.
- Abstract Algebra Notes - http://www.millersv.edu/~bikenaga/absalg/absanote.html
A collection of short notes by Bruce Ikenaga in PostScript.
- Calculus Using Infinitesimals - http://www.math.wisc.edu/~keisler/calc.html
Elementary Calculus: An Approach - a book by H. Jerome Keisler originally published by Prindle, Weber & Schmidt (2nd ed: 1986)
- Flatland - http://www.geom.uiuc.edu/~banchoff/Flatland/
A romance of many dimensions. With Illustrations by the Author, A SQUARE (Edwin A. Abbott 1838-1926). HTML.
- Geometry and the Imagination - http://www.geom.uiuc.edu/docs/education/institute91/
An online course by John Conway, Peter Doyle, Jane Gilman and Bill Thurston in HTML and PostScript.
- Sheaf Cohomology - http://sierra.nmsu.edu/morandi/notes/mathematicalnotes.html
Mathematical notes on sheaves and other topics by P. Morandi.
- Description Logics Handbook - http://www.inf.unibz.it/~franconi/dl/course/
A course on Description Logics (the Semantic Web underlying formalism) by E. Franconi (modules in pdf)
- Number Theory - http://www.trillia.com/moser-number.html
"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.
- Wavelet Tutorial - http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html
Guide to wavelet analysis by Robi Polikar.
- Meta Math! The Quest for Omega - http://www.umcs.maine.edu/~chaitin/omega.html
A mathematical and philosophical book by Gregory Chaitin on logic, information theory, complexity, etc. (available in html or pdf).
- Mathematical Analysis I - http://www.trillia.com/zakon-analysisI.html
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 - http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
A manual of geometry and PostScript by Bill Casselman, including code samples and packages.
- Differentiable manifolds - http://math.berkeley.edu/~wodzicki/214/
Lecture notes by Mariusz Wodzicki in postscript or pdf.
- Partial Differential Equations - http://www.mapleapps.com/powertools/pdes/pdes.shtml
Maple lessons for an undergraduate course in Differential Equations by Jim Herod.
- Mechanism of the Heavens - http://www.malaspina.com/etext/heavens.htm
A book on celestial mechanics by Mary Somerville (1831).
- Algorithms and Complexity - http://www.cis.upenn.edu/~wilf/AlgComp3.html
By Herbert S. Wilf. In print 1986-1994. Single PDF file.
- Linear Algebra Notes and Exercises - http://www.mathphysics.com/spingarn/lane/
A collection of mini-lessons in pdf format designed for self-instruction over the web by Jonathan Spingarn.
- Fourier Analysis - http://www.mth.kcl.ac.uk/~ysafarov/Lectures/Fourier/index.html
Lecture notes by Yuri Safarov.
- Real Analysis - http://www.mth.kcl.ac.uk/~ysafarov/Lectures/CM321A/
Lecture notes by Yuri Safarov.
- Inverse Problems - http://www.phy.auckland.ac.nz/Staff/smt/453707SC.html
Lecture notes by Sze Tan.
- Topology - http://www.maths.tcd.ie/~dwilkins/Courses/212/
Lecture notes by David R. Wilkins at Trinity College, Dublin.
- Differential forms - http://www.math.purdue.edu/~dvb/
An introduction to differential forms and other notes by Donu Arapura.
- Chaos - http://www.cmp.caltech.edu/~mcc/Chaos_Course/Outline.html
Introduction To Chaos by Michael Cross. An online course at Caltech.
- Analytic Differential Equations - http://www.wisdom.weizmann.ac.il/~yakov/thebook.pdf
Lectures on Analytic Differential Equations by Sergei Yakovenko at the Weizmann Institute.
- Differential Equations - http://marauder.millersville.edu/~bikenaga/diffeq/deqnote.html
Postscript notes on various topics in differential equations by Bruce Ikenaga.
- Matroid Decomposition - http://www.emis.de/monographs/md/
Monograph by Klaus Truemper published by Academic Press in 1992. Chapters in PostScript.
- Theory of Symmetry and Ornament - http://www.emis.de/monographs/jablan/
Monograph by Slavik V. Jablan published by the Serbian Academy of Science and Arts in 1995. HTML
- Mathematical Logic - http://euclid.trentu.ca/math/sb/pcml/
"A Problem Course in Mathematical Logic" by Stefan Bilaniuk in LaTeX, PostScript or PDF.
- Differential geometry - http://www.geocities.com/r-sharipov/r4-b3.htm
A textbook by Ruslan Sharipov (English and Russian versions).
- Tensor analysis - http://www.geocities.com/r-sharipov/r4-b6.htm
A quick introduction to tensor analysis by Ruslan Sharipov (English and Russian versions).
- Calculus - http://www.math.harvard.edu/people/SternbergShlomo.html
"Advanced Calculus" by Shlomo Sternberg covers analysis on linear spaces and manifolds extending through introductory differential geometry.
- Math Wizard - http://home.earthlink.net/%7esusankennison/mathwizard/
E-book gives some ideas on alternative approaches to teaching and learning math. Page includes table of contents. Requires a purchase.
- Differential Geometry - http://internal.maths.adelaide.edu.au/people/mmurray/dg_hons/dg_hons.html
Lecture notes for an honors course at the University of Adelaide by Michael Murray in HTML with GIFs.
- Finite Fields - http://www-math.cudenver.edu/~wcherowi/courses/finflds.html
An Introduction to Finite Fields by Bill Cherowitzo (html).
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