A Gentle Introduction to Category Theory Lecture notes by Maarten M. Fokkinga introducing some important notions from category theory, in particular adjunctions. Proofs are given in a calculational style, and the (few) examples are taken from algorithmics. The text is a long PostScript file.
A=B Combinatorics text by Marko Petkovsek, Herbert Wilf and Doron Zeilberger. Published by A. K. Peters. 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 Lecture notes by David Wilkins at Trinity College, Dublin.
Abstract Algebra Lecture notes by David Wilkins, Trinity College, Dublin. Topics in Number Theory; Group Theory; Galois Theory.
Abstract Algebra "Intro to Abstract Algebra" by Paul Garrett in PostScript and 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 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.
Algebraic Geometry A. Grothendieck's "Séminaire de Géometrie Algébrique" produced by F. Calegari, J. Borger and W. Stein. JPEG scans of typewritten material.
Allen Hatcher's Homepage Links to online texts and papers (published and unpublished) on Algebraic Topology, K-Theory, and 3-Manifolds.
Analysis WebNotes John Lindsay Orr, University of Nebraska--Lincoln.
Analysis WebNotes Online course by John Lindsay Orr. Chapters also available in LaTeX.
Applied Cryptography 1996 CRC Handbook of Applied Cryptography by Menezes, van Oorschot and Vanstone in PDF.
Ash, Robert University of Illinois. Downloadable texts in Abstract Algebra, Algebraic Number Theory, Commutative Algebra (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.
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.
Calculus "Advanced Calculus" by Shlomo Sternberg covers analysis on linear spaces and manifolds extending through introductory differential geometry.
Calculus Using Infinitesimals Elementary Calculus: An Approach - a book by H. Jerome Keisler originally published by Prindle, Weber & Schmidt (2nd ed: 1986)
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.
Complex and Functional Analysis Course notes and old exams in PDF, PS, DVI, and TeX for a first course in Complex and Functional Analysis.
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).
Course Notes Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.
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.
Dave's Short Course on Complex Numbers An introduction with math and a little history intended for those having a familiarity with ordinary real numbers and algebra.
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 a course at the Weizmann Institute of Science by Sergei Yakovenko. Chapters in DVI.
Differential Geometry Lecture notes for a course at the Weizmann Institute of Science by Sergei Yakovenko. Chapters in DVI.
Differential Geometry Lecture notes for an honors course at the University of Adelaide by Michael Murray in HTML with GIFs.
Differential Gometry 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 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".
Dynamical Systems 1927 classic by George D. Birkhoff published by AMS. Scanned chapters in PDF.
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).
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.
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.
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.
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).
Hatcher, Allen Geometric topology. With textbooks on Algebraic Topology, Vector Bundles and K-theory, and 3-manifolds.
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.
Home Page of J. S. Milne Includes preprints and course notes on Group Theory, Fields and Galois Theory, Algebraic Geometry, Algebraic Number Theory,Modular Functions and Modular Forms, Elliptic Curves, Abelian Varieties, Etale Cohomology, and Class Field Theory.
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.
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.
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.
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.
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).
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 Analysis "Introduction to Numerical Analysis Using Maple" by Barry G. Adams in HTML.
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.
Optimization "Lecture Notes on Optimization" by Pravin Varaiya. This book is an introduction to mathematical programming, optimal control, and dynamic programming.
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.
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.
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.
Stochastic Calculus Notes These notes by Alan Bain provide a complete elementary introduction to stochastic integration with respect to continuous semimartingales.
Tensor analysis A quick introduction to tensor analysis by Ruslan Sharipov (English and Russian versions).
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.
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.
The FEMCI Book Finite Element Modeling Continuous Improvement. A web text by Ryan Simmons.
The Limits of Mathematics An online course on information theory and the limits of formal reasoning by G.J. Chaitin.
Theory of Symmetry and Ornament Monograph by Slavik V. Jablan published by the Serbian Academy of Science and Arts in 1995. HTML
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 Lecture notes by David R. Wilkins at Trinity College, Dublin.
Toposes, Triples and Theories By Michael Barr and Charles Wells, 1983. A revised and corrected version is now available free for downloading. Formats: DVI, PDF, PostScript.
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.
