Academics

Useful Links for Branches of Mathematics

Algebra | Analysis | Combinatorics & Graph Theory | Differential Equations | Geometry | History | Nonlinear Studies | Number Theory | Probability & Statistics | Topology

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The links on this page were selected to provide a starting point for undergraduate college students with an interest in mathematics.

Algebra

Catalogue of Algebraic Systems
Definitions, examples, and discussion of most algebraic structures. (U. of South Florida.)

Simple Algebraic Structures
Definitions and examples of groups and simpler structures. Discussion of associated concepts. (MathPro Press)

Group Pub Forum
"The reason for the name is that the spirit is supposed to be that of a conversation in a pub at a Group Theory conference." Book and journal announcements, conference information, direct links, folk in the forum, jobs & scholarships, mathematical resources, newsflashes and new announcements, problem book, research announcements, mailing list, travel information exchange. (U. of Bath, United Kingdom)

Analysis

Analysis Webnotes
An online real analysis course of 60 interactive lessons at the level of MAT 421. Includes interactive applet-powered demonstrations, proof techniques, labs, and a student discussion board. (J. Orr, U. of Nebraska-Lincoln)

Interactive Real Analysis
An online, interactive textbook for Real Analysis in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, and more. Interactive Java applets and a nice historical tidbits section. (B. Wachsmuth, Seton Hall U.)

Combinatorics & Graph Theory

Graphs: Theory-Algorithms-Complexity (in English)
Related link collections, online forums, open problems, topics, search & find, software, books & lecture notes, people in graph theory. (Institut für Informatik, Humboldt Universität, Berlin, Germany)

Differential Equations

Web Study Guide for Ordinary Differential Equations
For Sophomores studying ODE. Mathematical notation, review of integration techniques, methods for solving first-order and second-order ODE's, a detailed discussion of the Laplace transform, and references. (Department of Mathematics, Oregon State U.)

Consortium for Ordinary Differential Equations Experiments
For professors and students. C*ODE*E newsletter, ODE experiments, graphics gallery, ODE software, workshops, and links. (Harvey Mudd College, Claremont, CA)

Geometry

Geometry in Action
Applications of discrete and computational geometry (mainly low-dimensional Euclidean geometry) to design and manufacturing, graphics and visualization, information systems, medicine and biology, physical sciences, robotics, and others. "Contains brief descriptions of those applications and the geometric questions arising from them, as well as pointers to web pages on the applications themselves and on their geometric connections." (D. Eppstein, UC Irvine, California)

The Geometry Center
Center for the computation and visualization of geometric structures. "It is funded by the National Science Foundation as part of the Science and Technology Center program. The Center has a unified mathematics computing environment supporting math and computer science research, mathematical visualization, software development, application development, video animation production, and K-16 math education." Geometry Center Web Resources: current projects, interactive web and Java applications, multimedia documents (hypertext papers, preprints, forum), geometry reference archives (graphic images, formulas), downloadable software, video productions, course materials, and MnSCU/UM Distance Learning Initiative. (U. of Minnesota)

Center for Geometry, Analysis, Numerics & Graphics
The Center for Geometry, Analysis, Numerics & Graphics (GANG ) is an interdisciplinary Differential Geometry research team. Site includes library of images, software, and quicktime movies; seminars and preprints (DVI and PostScript). (U. of Massachusetts, Amherst)

History

History of Mathematics Archive
Excellent source for biographies of mathematicians, topics in the history of mathematics, chronologies, and historical links. (Award winning site at the University of St. Andrews, Scotland)

Mathematical Quotations
More than 80 printed pages of mathematical quotations. (Mark Woodard, Furman University, Greenville, SC)

Nonlinear Studies

Nonlinear studies is a rapidly growing area. Although not a traditional branch of mathematics, it is included here for those students interested in fractals, chaos, or nonlinear dynamical systems.

Sci.nonlinear FAQ
Excellent quick overview of nonlinear science, applications, computational resources, and references. (U. of Colorado, Boulder, CO)

Dynamical Systems Homepage
Past conferences (and some upcoming conferences in the field), dynamical systems electronic preprint server (and several other electronic preprint servers), links to some survey articles in dynamical systems, open problems in dynamical systems, a searchable list of people working in the field (and some other similar lists), recent job postings in the field, seminar schedules in the Greater Long Island area, links to some similar pages. (SUNY at Stony Brook)

Spanky Fractal Database
Extensive collection of links to fractals and related sites. (Noel Giffin, TRIUMF (TRI-University Meson Facility), Vancouver, BC, Canada)

Nichtlineare Dynamik--Chaosgruppe (in English and German)
Handbook of who is doing what in nonlinear dynamics. (Technische Universität München, Germany)

Centers and Institutes conducting research in chaos and nonlinear dynamics:

Arizona Center for Mathematical Sciences (U. of Arizona, Tucson)

Center for Nonlinear Analysis (Carnegie-Mellon)

Center for Nonlinear Dynamics (U. of Texas at Austin)

Center for Nonlinear Studies (Los Alamos National Laboratory)

Chaos at Maryland (U. of Maryland at College Park)

Institute for Nonlinear Science (UC San Diego, California)

Number Theory

Number Theory Web
Seeks to "collect and disseminate information of interest to number theorists everywhere." This is the American mirrow site at U. of Georgia, Athens. (Keith Matthews, Dept. of Mathematics, University of Queensland, Brisbane, Australia)

The Largest Known Primes
What are primes and who cares? Excellent introduction to number theory. Award winning site. (Chris Caldwell, Dept. of Mathematics and Computer Science, University of Tennessee at Martin)

The Mathematics of Fermat's Last Theorem
How did Andrew Wiles prove it? Beautiful overview of the proof. Prerequisites for following the discussion: at least one course each in linear algebra, abstract algebra, and complex analysis. (Charles Daney)

Probability & Statistics

The Probability Web
"...to serve people with interests in probability theory and its applications. Information is presented under the following headings: Probability links, Abstracts, Listservers, Newsgroups, People, Jobs, Journals, Software, Books, Booksellers, Conferences, Publishers and Miscellaneous." (Phil Pollett, Department of Mathematics, U. of Queensland, Brisbane, Australia)

Center For Statistical and Mathematical Computing
Stat/Math software information: tutorials, examples, resources, and on-line documentation. (Indiana U., Bloomington)

Center for Statistical Consultation and Research
On-line statistical software documentation and links to resources in statistics. (U. of Michigan at Ann Arbor)

Topology

Topology Atlas: A Brief Introduction
A "one-stop information shopping center" for mathematicians and others interested in topology. Sponsored by 5 universities. (Nipissing U., Ontario, Canada)

British Topology Home Page
Designed primarily for British and European users. Topologists' home pages, topology groups, topology seminars and other activities, conferences and meetings on topology and related topics, topology resources, job seekers in algebraic topology. (Andy Baker, Dept. of Mathematics, U. of Glasgow, Scotland, UK)