 Abstract Finite Groups  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to finite groups  their internal properties: all those results about group theory for which a consideration of the order of elements is a central part of the question. History, applications and related
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 Algebraic Combinatorics Via Finite Group Actions  A. Betten, H. Fripertinger, A. Kerber
An Internet book with chapters on Actions: Actions of Groups; Bilateral classes, symmetry classes of mappings; Finite symmetric groups; Complete monomial groups; Enumeration of symmetry classes; The involution principle; and Special symmetry classes;
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 Algebra  University of Wales, Bangor
A paper describing research interests in algebra at Bangor, which have to a large extent been motivated by problems in algebraic topology and homological algebra. The recent spate of new and exciting concepts (crossed modules, crossed ncubes, nonabelian
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 arXiv.org ePrint archive  Los Alamos National Laboratory (LANL)
A major site for mathematics preprints that has incorporated many formerly independent specialist archives including alggeom, functan, dgga, qalg, autofms, cdhg, MAGNUS, Several Complex Variables, Logic Eprints, Commutative Algebra, Dynamical Systems,
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 ATLAS of Finite Group representations  R. A. Wilson
Representations of many finite simple groups and related groups such as covering groups and automorphism groups of simple groups. Contents: groups: Alternating & Symmetric, Lie type, and sporadic. Includes experimental generic group pagemaker and an experimental
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 Books: Professional & Technical: Professional Science: Mathematics  Amazon.com
Browse bestselling math books from the Professional and Technical Bookstore at Amazon.com, in such categories as Applied; Chaos & Systems; Geometry & Topology; Mathematical Analysis; Mathematical Physics; Number Systems; Pure Mathematics; Transformations;
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 Commutative Semigroups (Catalogue of Algebraic Systems)  John Pedersen, W. Edwin Clark; Dept. of Mathematics, University of South Florida
Definition and examples of commutative semigroups. A link to general information about semigroups.
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 Completing Latin Squares  Ivars Peterson (MathTrek)
Using only the numbers 1, 2, 3, and 4, arrange four sets of these numbers into a fourbyfour array so that no column or row contains the same two numbers. The result is known as a Latin square... in Latin squares of order 4, each row (and each column)
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 Computer Lab Courseware  University of Toronto
Courseware to help in the teaching of various mathematical concepts. Most is made up of Mathematica notebooks and packages, but some consists of C programs written to run under XWindows. A lab manual in TeX beginning with an introduction to UNIX and
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 Course Notes  J. S. Milne
Full course notes in dvi, pdf, and postscript formats for all the advanced courses J. S. Milne taught at the University of Michigan between 1986 and 1999: Group Theory; Fields and Galois Theory; Algebraic Number Theory; Class Field Theory; Modular Functions
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 CT Category Theory (Front for the Mathematics ArXiv)  Univ. of California, Davis
Category Theory preprints, from the U.C. Davis front end for the xxx.lanl.gov ePrint archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives. Search by keyword or browse by topic.
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 David Marius Bressoud
David Bressoud has written several undergraduate textbooks that use physics and the history of mathematics to motivate the study of multivariable calculus, number theory, real analysis. Other books include A Course in Computational Number Theory and
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 Entropic Groupoids (Catalogue of Algebraic Systems)  John Pedersen, W. Edwin Clark; Dept. of Mathematics, University of South Florida
Definition, examples, and references about entropic or medial groupoids. Links to related terms in the Catalogue.
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 An essay on patterns in musical composition, transformation, mathematical groups and the nature of musical substance  Bill Hammel
An article on music composition and history, with a discussion of the organizing principles of various musical scales as they affect musical composition and links to related sites.
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 Field Theory and Polynomials  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to field theory and polynomials. Field theory looks at sets, such as the real number line, on which all the usual arithmetic properties hold, including, now, those of division. The study of multiple
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 Finite Rank Torsion Free Modules Over Dedekind Domains  E. Lee Lady; University of Hawaii
A book that discusses abelian group theory as not just another variety of group theory but the study of modules over principal ideal domains, a highly specialized branch of commutative ring theory. Postscript and DVI versions. Chapters: Modules Over Commutative
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 Freaky Links  Cut the Knot!, Alexander Bogomolny with William A. McWorter Jr.
Mathematics impinges on itself and the sciences in unexpected and bizarre ways. This page is a small illustration of this phenomenon, taking up recreational mathematics and the game of Chinese checkers, the strategy game called Hex, quasigroups, and block
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 Front for the Mathematics ArXiv  Univ. of California, Davis
U.C. Davis front end for the xxx.lanl.gov ePrint archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives including alggeom, functan, dgga, qalg, autofms, cdhg, MAGNUS, Several Complex
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 The Galois Story  Ivars Peterson (MathTrek)
The life and death, myth and reality, of Evariste Galois, with a short bibliography.
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 GAP: Groups, Algorithms, and Programming  GAP Group; UK, Germany, USA, Australia
A system for computational discrete algebra with particular emphasis on, but not restricted to computational group theory. GAP and its sources, including share packages, data library and a manual, are distributed freely, subject to conditions detailed
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 The Generalized Theory of Life  Vyacheslav L. Kalmykov; Institute of Cell Biophysics, Russian Academy of Sciences
A paper that presents an integrally generalized theory or conceptualization of life that includes elements of an axiomatic approach and is physically interpretable, formulated as the result of attempts to invent a holistic system of creative synthetic
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 The Geometry Junkyard  David Eppstein, Theory Group, ICS, Univ. of California at Irvine
A collection of usenet clippings, web pointers, lecture notes, research excerpts, papers, abstracts, programs, problems, and other stuff related to discrete and computational geometry  some serious and much also entertaining. Junk sorted into piles (Topics):
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 Graph Theory  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to graph theory. A graph is a set V of vertices and a set E of edges  pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on
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 Groupoids (Catalogue of Algebraic Systems)  John Pedersen, W. Edwin Clark; Dept. of Mathematics, University of South Florida
Definition, examples, decision problems, spectra and growth, references, and subsystems about groupoids.
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 Groups32  John J. Wavrik, University of California at San Diego
A group theory calculator. Groups32 computes information about groups of orders 132; has a permutation group package; and provides a search for groups with given generators and relations. Site includes documentation as well as course handouts in PDF
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 Groups (Catalogue of Algebraic Systems)  John Pedersen, W. Edwin Clark; Dept. of Mathematics, University of South Florida
Definition, examples, decision problems, spectra and growth, references, subsystems about groups. Links to related terms in the Catalogue.
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 Groups & Graphs Home Page  Bill Kocay
A software package for graphs, digraphs, combinatorial designs, and their automorphism groups. Features include automorphism group computation; graph certificate which identifies a graph uniquely up to isomorphism; Hamiltonian cycles; planarity test and
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 HAKMEM  Beeler, Gosper, Schroeppel; Artificial Intelligence Laboratory, MIT
A list of math and computerrelated problems, unsolved in 1972 when the list originated, compiled "with the hope that a record of the random things people do around here can save some duplication of effort  except for fun." Topics include: Geometry,
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 A history of the Burnside problem  MacTutor Math History Archives
Linked essay on the development of the questions: Is a finitely generated periodic group necessarily finite? Is a finitely generated periodic group of bounded exponent necessarily finite?
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 Ido Efrat
A mathematics professor at Ben Gurion University of the Negev in Israel. Site includes the syllabi for current courses and a list of Efrat's publications in abstract algebra, especially group theory. Some articles may be downloaded in PDF or DVI format.
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 Introducing Mathematics
This website looks at some areas of mathematics that are not familiar to most people, such as Ramsey theory and set theory, but introduces them in an uncomplicated manner.
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 Inverse Property (IP) Quasigroups (Catalogue of Algebraic Systems)  John Pedersen, W. Edwin Clark; Dept. of Mathematics, University of South Florida
Definition, examples, and references about IP quasigroups, and links to related terms in the Catalogue.
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 Jaap's Scratch Pad  Jaap Scherphuis
Java applets, generators, and solutions for sudoku, Rubik's Cube, "moving pieces" puzzles, permutation puzzles, and more, including sphere symmetries, polyform, Towers of Hanoi, and many lesser known puzzles from this collector. Scherphuis' articles range
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 John Stembridge
John Stembridge researches algebra and combinatorics. His papers on these subjects are available online as gzipped PostScript files. The site contains an archive of related research data such as lists of posets on 8 or fewer vertices and Coxeter graph
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 Jon McCammond
A mathematician at Texas A&M University. Research interests include geometric group theory and lowdimensional topology, as well as combinatorics, graph theory, and computational geometry. Preprints can be downloaded in PostScript format. Current
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 Library of Math  David A. Smith
Definitions, comments, examples, propositions, and proofs on Business Algebra, Business Calculus, Calculus I, Calculus III, Euclidean Geometry, Financial Mathematics, Group Theory, and Trigonometry. The Library of Math website was designed to be a "browserquiet"
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 Magnus: A System for Exploring Infinite Groups  New York Group Theory Cooperative, CCNY
A free, intuitive, graphically driven objectoriented package for computational group theory, exploring infinite groups. From the New York Group Theory Cooperative at CCNY, which also provides links to an archive of preprints and open problems in combinatorial
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 Margo Lynn Mankus  Margo Lynn Mankus
Talks include Using Virtual Manipulatives on the Web to Develop Number Sense, Connecting Whole Number Arithmetic to Algebra: HandsOn/Number Sense Activities, and Learning About Nutrition Using the TI73 and the Web. Also, online or downloadable classroom
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 Mathematical BBS (Mathematics)  Mathematics Dept., Univ. of Ferrara, Italy
Collections of resources: Associations, Departments, Disciplines, Journals, Industrial mathematics, the mathematician. Disciplines include: Algebra; Algebraic geometry; Analysis; Applied Mathematics; Categories; Combinatorics; Complex analysis; Computational
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 Mathematics by Somos  Michael Somos
A mathematician at Cleveland State University and the originator of Somos Polynomials and the Somos Sequence. Brief discussions of these objects, as well as rational triangles and Pythagorean triples, may be found on this site along with links to resources
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 Mathematics  John Savard
A collection of essays and illustrations: pentagonal tilings, infinity (Cantor's theory of transfinite numbers), rotations of the dodecahedron, Archimedean solids, the fourth dimension (regular polytopes), Gödel's proof and the halting problem, and
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 Mathematics Museum (Japan)
Exhibits: Deformation of Catenoid to Helocoid; Geometry of wallpaper patterns (with interactive examinations); MathCut Studium; SolitonLab Art Gallery; Sangaku (Japanese temple geometry problem); The beauty of surfaces; Kodawari House, Keiichi Suzuki's
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 Mathematics Preprints  Mathematics Dept., Penn State University
Preprints: general (American Mathematical Society Preprints; Hypatia; xxx Eprint Archives; and the Front End for the xxx Mathematics Archive), and by subject area.
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 Math WWW VL: Bibliographies  Dept. of Mathematics, Florida State University
Links to bibliographies in collegelevel mathematics.
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 Medial Quasigroups (Catalogue of Algebraic Systems)  John Pedersen, W. Edwin Clark; Dept. of Mathematics, University of South Florida
Definition, examples, and references about medial quasigroups. Links to related terms in the Catalogue.
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 Moufang Quasigroups (Catalogue of Algebraic Systems)  John Pedersen, W. Edwin Clark; Dept. of Mathematics, University of South Florida
Definition, examples, and references about Moufang Quasigroups. Links to related terms in the Catalogue.
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 A New Proof of The Four Colour Theorem  Ashay Dharwadker
An article presenting a proof of the four color theorem that uses group theory and Steiner systems, illustrated using a map of Madhya Pradesh and adjoining states in India. Introduction; Map Colouring; Steiner Systems; Eilenberg Modules; Hall Matchings;
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 New York Group Theory Cooperative at CCNY
Genetic algorithms, open problems and preprints in combinatorial and geometric group theory, meetings, links, and MAGNUS, a free (GPL) graphically oriented system, based on Tcl/Tk, for computational group theory designed to allow for exploration and experimentation
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 On the Puzzles with polyhedra and numbers  Jorge Rezende
Several articles in PDF format, with related links: one on a set of didactic puzzles published by the Portuguese Mathematical Society (SPM); "Jogos com poliedros e permutações", an article in Portuguese describing puzzles with polyhedra
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 Pattern  Drew, Wallace; Mathematics Across the Curriculum, Dartmouth College
An interdisciplinary course in textile design and elementary group theory. Syllabus, course pages (notes, figures, questions, group work and homework), final project and class artworks from a 1996 math and art crosscurricular class at Dartmouth College.
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