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Introduction to Dynamical Systems by Michael Brin and Garrett Stuck An Introduction to Dynamical Systems by R. Clark Robinson An Introduction to Dynamical Systems by D. K. Arrowsmith and C. M. Place

ArXiv -
Recent papers in dynamical systems at the ArXiv preprint server.

Turbulent Landscapes -
Turbulent Landscapes is the result of 13 artists' explorations of complexity in nature. The exhibit will travel to museums and science centers in upcoming months.

Dynamical Systems Home Page -
Conference listings, survey articles, open problems, people, jobs, and seminars.

Pages on Dynamical Systems -
A interactive laboratory on dynamical systems, in particular on particle systems.

Society for Nonlinear Dynamics and Econometrics -
The Society seeks to promote the use of nonlinear methods in economics and finance from both a theoretical and empirical perspective.

A First Course in Dynamics : with a Panorama of Recent Developments  by Boris Hasselblatt and Anatole Katok Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications)  by Anatole Katok, Boris Hasselblatt, G.-C. Rota, et al An Introduction to Chaotic Dynamical Systems, 2nd Edition  by Robert L. Devaney

Nonlinear Dynamics Bibliography -
Maintained by Peter E. Beckmann, Johannes Gutenberg Universität.

Surveys in Dynamical Systems -
References to several surveys and papers of introductory character which are available on-line.

Crowd Dynamics -
Crowd and Egress Dynamics by G. Keith Still.

Dynamical Systems Lab -
This set of lectures is designed to explore one-dimensional dynamical systems using the software Chaos and Dynamics.

Java Exploration Tool for Dynamical Systems -
This Java Applet can be used for the exploration on two-dimensional analytical defined dynamical systems. The system is defined by a set of two differential equations, which will be evaluated within adjustable regions forming a two-dimensional vector field.

Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics)  by Stephen Wiggins Differential Equations, Dynamical Systems, and an Introduction to Chaos (Pure and Applied Mathematics (Academic Press), 60.) by Morris W. Hirsch, Stephen Smale and Robert Devaney

Dynamical Systems Data Base -
Data base of around 50,000 planar dynamical systems.

Climate Dynamics, Chaos and Quantum Mechanics -
A general systems theory for chaos, quantum mechanics and climate dynamics applicable to dynamical systems of all space-time scales.

Dynamics in One Complex Variable -
These notes study the dynamics of iterated holomorphic mappings from a Riemann surface to itself. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry.

Dynamical Systems Websites -
A list of research sites maintained at the University of Warwick.

Evolution Equations and Semigroups -
Bulletin board and preprint archive.

A First Course in Chaotic Dynamical Systems: Theory and Experiment (Studies in Nonlinearity) by Robert L. Devaney Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering by Steven H. Strogatz

Chaos, Limit Cycles and Twisted Rods -
Integrability and chaotic attractors. Limit cycles of the Lienard systems. Elastic instabilites : twisted rods. Path and surface following : continuation algorithms.

Ergodic Theory and Dynamical Systems -
With a particular emphasis on applications to other areas of mathematics. Mark Pollicott.

Population Dynamics with Hysteresis Effect -
Papers on population dynamics with hysteresis based on phase transition phenomena, by Emil Minchev (PDF/PS).

Discrete And Continuous Dynamical Systems

Journal Of Dynamical Systems & Geometric Theories


Trigonometry -
"Dave's Short Trig Course" by D. E. Joyce. HTML with Java.

Mathematical Principles of Natural Philosophy -
Principia by Isaac Newton (1687) translated by Andrew Motte (1729) in HTML (incomplete).

Description Logics Handbook -
A course on Description Logics (the Semantic Web underlying formalism) by E. Franconi (modules in pdf)

A=B -
Combinatorics text by Marko Petkovsek, Herbert Wilf and Doron Zeilberger. Published by A. K. Peters. PDF.

Wavelets -
An Introduction to Wavelets by Amara Graps in HTML, PDF or Postscript.

Complex Numbers -
Dave's Short Course on Complex Numbers (David Joyce).

Euclid's Elements -
Edited by D.E. Joyce. HTML text with Java applets.

Flatland -
A romance of many dimensions. With Illustrations by the Author, A SQUARE (Edwin A. Abbott 1838-1926). HTML.

Algebraic Topology -
Basic core material along with a number of optional topics of a relatively elementary nature by Allen Hatcher. PDF and Postscript.

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.

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.

Algebraic Geometry -
Various lecture notes by J.S. Milne.

Algebraic Topology -
1942 classic by Solomon Lefschetz published by AMS. Chapters in scanned PDF.

Geometric Asymptotics -
This book by Guillemin and Sternberg includes the method of stationary phase, geometrical optics, quantization.

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.

Monotone Operators in Banach Space and Nonlinear Partial Differential Equations -
A monograph by Ralph Showalter in PDF.

Matrices -
The 1934 classic "Lectures on Matrices" by Wedderburn in scanned PDF.

Dynamical Systems -
1927 classic by George D. Birkhoff published by AMS. Scanned chapters in PDF.

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.

Templates for the Solution of Linear Systems -
Book on iterative methods by Richard Barrett et al. in HTML and Postscript.

Functional Analysis and Semi-Groups -
Book by Einar Hille and Ralph S. Phillips published by AMS in 1957. Scanned chapters in PDF.

Mechanism of the Heavens -
A book on celestial mechanics by Mary Somerville (1831).

Differential Algebra -
Scans of Ritt's 1950 classic in PDF.

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.

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.

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.

Geometry and the Imagination -
An online course by John Conway, Peter Doyle, Jane Gilman and Bill Thurston in HTML and PostScript.

Applied Cryptography -
1996 CRC Handbook of Applied Cryptography by Menezes, van Oorschot and Vanstone in PDF.

Tensor Calculus and Continuum Mechanics -
Textbook by John H. Heinbockel. Whole book or chapters in PostScript and 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.

Topology Course Lecture Notes -
By Aisling McCluskey and Brian McMaster. HTML with symbol fonts, DVI and PostScript.

Category Theory -
"A Gentle Introduction to Category Theory - the calculational approach" by Maarten M. Fokkinga in PostScript.

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.

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.

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.

Analysis WebNotes -
Online course by John Lindsay Orr. Chapters also available in LaTeX.

Theory of Symmetry and Ornament -
Monograph by Slavik V. Jablan published by the Serbian Academy of Science and Arts in 1995. HTML

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.

Algebraic Geometry -
A. Grothendieck's "Séminaire de Géometrie Algébrique" produced by F. Calegari, J. Borger and W. Stein. JPEG scans of typewritten material.

Linear Algebra -
"Elementary Linear Algebra" by Keith Matthews. Lecture notes and solutions from 1991 in PDF or PostScript.

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.

Advanced Calculus and Analysis -
Lecture notes by Ian Craw from a course at the Univ. of Aberdeen. HTML with GIFs.

Calculus -
"Advanced Calculus" by Shlomo Sternberg covers analysis on linear spaces and manifolds extending through introductory differential geometry.

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.

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.

Generatingfunctionology -
By Herbert S. Wilf. Published by Academic Press. PDF.

Complex Analysis -
Textbook for an introductory course in complex analysis by George Cain. Chapters in PDF.

Multivariable Calculus -
Textbook by George Cain and James Herod. Chapters in PDF.

Physics, Invariant Theory, Modular Forms, and Algebraic Geometry -
Several lecture note sets by Igor Dolgachev in various formats, including DVI and PostScript.

Toposes, Triples and Theories -
A book by Michael Barr and Charles Wells originally published by Springer Verlag.

Linear Algebra -
Textbook by Jim Hefferon covering the material of any undergraduate first linear algebra course. Book or chapters in PDF.

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".

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.

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.

Abstract Algebra -
Lecture notes by David Wilkins at Trinity College, Dublin.

Graph Theory -
Hyperlinked PDF version of a book by Reinhard Diestel.

Algorithms and Complexity -
By Herbert S. Wilf. In print 1986-1994. Single PDF file.

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.

Functional Analysis -
Lecture notes by Paul Garrett.

Matroid Decomposition -
Monograph by Klaus Truemper published by Academic Press in 1992. Chapters in PostScript.

Linear Algebra and Applications -
Textbook by Thomas Shores. GIFs of pages.

Interactive Real Analysis -
"Interactive Real Analysis" by Bert G. Wachsmuth. HTML and Java.

Multigrid Methods -
"An Introduction to Multigrid Methods" by Pieter Wesseling.

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.

Topology -
Lecture notes by David R. Wilkins at Trinity College, Dublin.

The Limits of Mathematics -
An online course on information theory and the limits of formal reasoning by G.J. Chaitin.

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.

Linear Programming: Foundations and Extensions -
Book by Robert J. Vanderbei in PDF.

Dynamical Systems and Fractals -
Lecture Notes by David J. Wright in HTML.

Calculus Using Infinitesimals -
Elementary Calculus: An Approach - a book by H. Jerome Keisler originally published by Prindle, Weber & Schmidt (2nd ed: 1986)

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 -
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.

Discrete Mathematics -
Lecture notes by László Lovász in Postscript. Includes "Discrete Mathematics", "Semidefinite optimization", "Topological methods in combinatorics", and "Complexity of algorithms".

Complex analysis and dynamics -
Various lecture notes C. McMullen

Geometric Constraint Solving -
An electronic primer by William Bouma, Xiangping Chen, Ioannis Fudos, Christoph Hoffmann, and Pamela J. Vermeer.

Mathematical Modeling in a Real and Complex World -
Online guide book by Frank Wattenberg in HTML.

Universal Algebra -
"A Course in Universal Algebra" by Stanley Burris and H. P. Sankappanavar. PostScript and PDF.

Mixed Motives -
Monograph by Marc Levine published by AMS in 1998. Whole book or chapters in PDF.

Fundamental Problems in Algorithmic Algebra -
Book by Chee Yap published by Oxford University Press in 1999.

Complex Analysis -
Course notes by Harold V. McIntosh in HTML.

Index Theory, Geometric Scattering, and Differential analysis on manifolds with corners -
Several books by Richard Melrose et al. in PostScript.

Mathematical Illustrations -
A manual of geometry and PostScript by Bill Casselman, including code samples and packages.

Algebraic Combinatorics via Finite Group Actions -
HTML book by A. Betten, H. Fripertinger, and A. Kerber.

Dynamics in One Complex Variable: Introductory Lectures -
Lecture notes by John Milnor in TeX and PostScript.

Chebyshev and Fourier Spectral Methods -
A book by John P. Boyd (2nd edition) available from Dover.

Linear Algebra, Infinite Dimensions, and Maple -
A textbook by James Herod.

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).

Analytic Differential Equations -
Lectures on Analytic Differential Equations by Sergei Yakovenko at the Weizmann Institute.

Ordinary Differential Equations -
Informal postscript notes for a course by Sheldon Newhouse at Michigan State.

Chaos -
Introduction To Chaos by Michael Cross. An online course at Caltech.

Algebraic K-theory -
"An introduction to algebraic K-theory" by Charles Weibel. Chapters in DVI.

Inverse Problems -
Lecture notes by Sze Tan.

Differential Geometry -
Lecture notes for a course at the Weizmann Institute of Science by Sergei Yakovenko. Chapters in DVI.

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.

Calculus -
"The Calculus Bible" by G. S. Gill.

Finite Rank Torsion Free Modules Over Dedekind Domains -
Monograph in commutative ring theory by Lee Lady. DVI and PDF.

Partial Differential Equations -
Maple lessons for an undergraduate course in Differential Equations by Jim Herod.

Complex and Functional Analysis -
Lecture notes by Douglas N. Arnold for a course at Penn State. Two parts in TeX, DVI, PostScript and PDF.

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.

Complex Dynamics in Higher Dimensions -
CBMS lecture notes by John Erik Fornćss at the bottom of page with other papers by the author and Nessim Sibony. PostScript.

Complex analytic and algebraic geometry -
Book by Jean-Pierre Demailly in PostScript.

Fractals in the Plane - Ergodic Theory Methods -
A book by F. Przytycki and M. Urbanski in Postscript.

Wavelet Tutorial -
Guide to wavelet analysis by Robi Polikar.

Entropy of Compact Group Automorphisms -
Lecture notes based on a course at Ohio State in 1994 by Thomas Ward in DVI and PostScript.

Matrix Analysis and Applied Linear Algebra -
By Carl D. Meyer. Full text in PDF with errata, updates and solutions.

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.

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.

Abstract Algebra with GAP -
A laboratory manual by J. G. Rainbolt and J. A. Gallian.

Semi-Simple Lie Algebras and their Representations -
Book for particle physicists by Robert N. Cahn. Published by Benjamin-Cummings in 1984. Chapters in PostScript.

Fourier Analysis -
Lecture notes by Yuri Safarov.

Linearization via the Lie Derivative -
By Carmen Chicone and Richard Swanson. LaTeX, DVI, PostScript and PDF.

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.

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.

Distributions, Fourier Transforms and Microlocal Analysis -
A short course by Yuri Safarov

Abstract Algebra -
A book draft: "Applied Abstract Algebra" by D. Joyner, R. Kreminski, J. Turisco in HTML.

Differential Geometry -
Notes by Balázs Csikós. Chapters in PostScript.

Finite Simple Groups -
"The classification of the finite simple groups" by D. Gorenstein, R. Lyons, and R. Solomon in PDF.

Differential Geometry and Physics -
Lecture notes by Gabriel Lugo.

Ordinary Differential Equations -
Course notes by Klaus Schmitt at the University of Utah.

Riemannian Geometry -
"An Introduction to Riemannian Geometry" by S. Gudmundsson in postscript (1996).

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).

Computational Geometry and Computational Optimization -
Lecture notes by Jianer Chen in PostScript.

Math Wizard -
E-book gives some ideas on alternative approaches to teaching and learning math. Page includes table of contents. Requires a purchase.

Finite Fields -
An Introduction to Finite Fields by Bill Cherowitzo (html).

Mathematical Logic -
"A Problem Course in Mathematical Logic" by Stefan Bilaniuk in LaTeX, PostScript or PDF.

Differentiable manifolds -
Lecture notes by Mariusz Wodzicki in postscript or pdf.

Numerical Grid Generation -
A book by Thompson, Warsi, and Mastin, previously published by Elsevier, in HTML.

Real Analysis -
Lecture notes by Yuri Safarov.

Abstract Algebra -
"Intro to Abstract Algebra" by Paul Garrett in PostScript and PDF.
Complex algebraic varieties and their cohomology -
A book of notes by Donu Arapura.

Differential forms -
An introduction to differential forms and other notes by Donu Arapura.

Linear Algebra Notes and Exercises -
A collection of mini-lessons in pdf format designed for self-instruction over the web by Jonathan Spingarn.

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.

Integral And Differential Equations -
Class notes by Jim Herod at Georgia Tech.

Optimization -
"Lecture Notes on Optimization" by Pravin Varaiya. This book is an introduction to mathematical programming, optimal control, and dynamic programming.

Complex-Analytic Geometry of Complex Parallelizable Manifolds -
Monograph by Jörg Winkelmann. Chapters in DVI.

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).

Finite Element Method/Boundary Element Method -
Notes by Peter Hunter and Andrew Pullan in pdf.

Partial Differential Equations -
Lecture notes on Analysis and PDEs by Bruce Driver at UCSD.

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.

The FEMCI Book -
Finite Element Modeling Continuous Improvement. A web text by Ryan Simmons.

Abstract Algebra Notes -
A collection of short notes by Bruce Ikenaga in PostScript.

Topology Without Tears -
A course in topology by Sidney A. Morris in HTML with embedded GIFs. Must purchase to view.

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.

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.

Finite Applied Associative Algebra (semigroups) & Digital Networks -
A compendium of papers by Nico F. Benschop on abstract algebra, number theory, computer science and physics.

Partial Differential Equations -
"PDE Primer" by Ralph Showalter at Oregon State.
Differential geometry -
A textbook by Ruslan Sharipov (English and Russian versions).

Tensor analysis -
A quick introduction to tensor analysis by Ruslan Sharipov (English and Russian versions).

href="">Differential Equations-
Postscript notes on various topics in differential equations by Bruce Ikenaga.

Linear algebra and multidimensional geometry -
A textbook by Ruslan Sharipov (English and Russian versions).

Differential Geometry -
Lecture notes for an honors course at the University of Adelaide by Michael Murray in HTML with GIFs.

Numerical Analysis -
"Introduction to Numerical Analysis Using Maple" by Barry G. Adams in 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).

Fundamentals of Model Theory -
Introductory textbook by William Weiss and Cherie D'Mello. PostScript, DVI, GIF.

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