- A 27-Vertex Graph That Is Vertex-Transitive and Edge-Transitive But Not 1-Transitive - Peter Doyle
Hypertext and Postscript versions of a paper describing a 27-vertex graph that is vertex-transitive and edge-transitive but not 1-transitive. While all vertices and edges of the graph are similar, there are no edge-reversing automorphisms.
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- Advanced Geometry - Math Forum
Links to some of the best Internet resources for advanced geometry: Web sites, software, Internet projects, publications, and public forums for discussion.
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- AG Algebraic Geometry (Front for the Mathematics ArXiv) - Univ. of California, Davis
Algebraic Geometry preprints, from the U.C. Davis front end for the xxx.lanl.gov e-Print 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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- AGATHOS - Algebraic Geometry: A Total Hypertext Online System - Kevin R. Coombes; Department of Biostatistics, University of Texas M.D.Anderson Cancer Center
This course assumes that the reader has completed a year-long graduate course in abstract algebra. It can be approached as a linear text, a list of interesting examples, a list of important theorems in algebraic geometry, key concepts, or exercises that
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- Algebraic Curves - Silvio Levy; The Geometry Center
Curves that can be given in implicit form as f(x,y)=0, where f is a polynomial, are called algebraic. This site provides an overview, with illustrations.
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- Algebraic Geometry - Peter Stiller; Dept. of Mathematics & Computer Science, Texas A&M Univ.
This page answers the question, "What is Algebraic Geometry?" - a subject with historical roots in analytic geometry, concerned with the geometry of the solutions of a system of polynomial equations. With a link to a bibliography of related publications.
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- Algebraic Geometry Seminar - Michael Harrison; Univ. of Washington
Online notes for a seminar, including handouts in dvi and postscript formats, solutions to the problems in Chapter 1 of Hartshorne's Algebraic Geometry, and notes on algebraic geometry by Professor J. S. Milne, Univ. of Michigan.
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- Algebraic Geometry - Tayler Jarvis
A page of links to general algebraic geometry sites, sites on algebraic curves, algebraic surfaces, algebraic geometers and the like, and related sites.
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- Algebraic Number Theory and Elliptic Curves - Ghitza, Osserman; Massachusetts Institute of Technology
A semester-long seminar giving a rapid introduction to algebraic number theory and elliptic curves. Topics: Dedekind domains, rings of integers, scheme-theoretic curves, finite morphisms thereof, splitting and ramification, the Tchebotarov density theorem
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- Algebraic Number Theory Archives - Boston, Grayson
Preprints about algebraic number theory and arithmetic geometry are accepted in electronic form for storage until publication. There are instructions for authors who wish to submit preprints to the archives and for for joining the mailing list (members
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- Algorithms for Modular Elliptic Curves - John Cremona
View parts of the second edition of the book, with introduction, tables and software. Download the errata list for the second edition, available as a dvi file or a postscript file.
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- Analytic and Descriptive Geometry - Dave Rusin; The Mathematical Atlas
An introduction to ordinary analytic geometry as studied in secondary school. (Also included here is a rather lengthy analysis of a result known as Poncelet's Porism.) History; applications and related fields and subfields; textbooks, reference works,
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- Arbeitsgruppe Bachem/Schrader - University of Köln
A working group of the Center for Parallel Computing (ZPR) at Köln. Site includes a list of members and contact address; informative write-ups on its projects, some in English. Topics include: Basic Research (meaning "pure" as opposed to "applied");
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- Arithmetic Algebraic Geometry (AAG) - Training and Mobility of Researchers; European Community
A partnership of 12 working groups from 5 European countries (England, France, Germany, Italy, Spain) working to develop methods taken from geometry to study the arithmetical properties of algebraic equations. Main research themes: p-adic cohomology theory;
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- arXiv.org e-Print archive - Los Alamos National Laboratory (LANL)
A major site for mathematics preprints that has incorporated many formerly independent specialist archives including alg-geom, funct-an, dg-ga, q-alg, auto-fms, cd-hg, MAGNUS, Several Complex Variables, Logic E-prints, Commutative Algebra, Dynamical Systems,
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- Automated Deduction - William McCune
Research on applications of automated deduction to problems in abstract algebra and algebraic geometry, algorithms and strategies for searching for proofs and for counterexamples, high-performance implementation of automated deduction algorithms, and
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- Automorphic Forms and Representations Virtual Study Group - Michael Harrison
A virtual study group formed to explore the Langland's Program by reading Automorphic Form and Representations by Daniel Bump.
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- Basic Geometry of Voting - Donald G. Saari
A book that offers a large number of new results about voting theory, its emphasis purposely placed on three candidate settings so that the book can be read by almost everyone. (With four or more candidates, the results need more advanced mathematical
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- Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory - Paul Garrett
A 1996 bibliography compiled for the author's Ph.D. students at the University of Minnesota.
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- The Birch and Swinnerton-Dyer Conjecture - Clay Mathematics Institute
A Clay Mathematics Institute Prize problem, with a description in pdf format by Andrew Wiles. The conjecture addresses the problem of enumerating rational points, such as on elliptic curves.
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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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- Calabi-Yau Homepage - Sheldon Katz
A page of information about Calabi-Yau manifolds: threefolds, fourfolds, software.
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- Categorical Geometry - Zhaohua Luo
See a brief tour of categorical geometry, which studies the geometric properties of unitary categories. The categorical approach to algebraic geometry was initiated by Yves Diers in his pioneer book Categories of Commutative Algebras (Oxford University
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- Counting Points on Elliptic Curves - Fouquet, Harley, Gaudry, Morain
The authors, Ph.D. students at the Laboratoire d'informatique de l'École polytechnique, Paris, have established new records for point counting in characteristic 2, using a new algorithm due to Takakazu Satoh.
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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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- David Pollack
Download the author's thesis, "Explicit Hecke Actions on Modular Forms" (Harvard, 1998) in DVI format.
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- Diophantine geometry in characteristic p: a survey - José Felipe Voloch
An article that appeared in Arithmetic Geometry, F. Catanese, ed., Symposia Mathematica XXXVII, Cambridge Univ. Press, 1997, pp. 260-278. Introduction; Curves; Abelian varieties and their subvarieties; Diophantine Approximation in characteristic p; Omitted
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- Discrete and Computational Geometry - Springer-Verlag
An international journal of mathematics and computer science that accepts research articles of high quality in discrete geometry and on the design and analysis of geometric algorithms; more specifically, DCG publishes papers on such topics as configurations
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- EAGER (European Algebraic Geometry Research Training Network) - Wolfram Decker
The members of EAGER are algebraic geometers in mathematical centres spreading among most European countries. These centres are grouped into twelve geographical nodes which are responsible for the management of joint research projects and for the training
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- The ECMNET Project - Charron, Daminelli, Granlund, Leyland, Zimmermann
The goal of the ECMNET Project is to find large factors using the elliptic curve method, mainly Cunningham numbers.
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- Elliptic Curve Discrete Logarithms (ECDL) Project - Robert Harley; 4K Associates
The Project has solved ECC2K-108.
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- Elliptic Curves and Cryptography - Andreas Enge
Includes the test of the author's introductory book on elliptic curves and their applications in cryptography. Also links to further publications; the personal pages of number theorists and cryptographers; and companies, organisations and miscellaneous
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- Elliptic Curves and Cryptology - Marc Joye
Links to elliptic curve resources: people (an extensive list of personal pages), bibliography, software, and links to relevant Web pages. Many preprints are available from the site.
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- Elliptic Curves and Elliptic Functions - Charles Daney
From The Mathematics of Fermat's Last Theorem. With a glossary; contents include: What is an elliptic curve?; The group structure of an elliptic curve; Arithmetic on elliptic curves; Further basic concepts and results.
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- Elliptic Curves and Formal Groups - Lubin, Serre, Tate
Lecture notes from a seminar, part of the Lecture notes prepared in connection with the seminars held at the Summer Institute on Algebraic Geometry, Whitney Estate, Woods Hole, Massachusetts, July 6-July 31, 1964.
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- Elliptic Curves and Right Triangles - Karl Rubin; Stanford University
Slides (GIF) of lectures.
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- Elliptic Curves - Dave Rusin; The Mathematical Atlas
An area of algebraic geometry that deals with nonsingular curves of genus 1 - in
English, solutions to equations y^2 = x^3 + A x + B. It has important connections to number theory and in particular to factorization of ordinary integers (and thus to cryptography).
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- Elliptic Curves II - Johan P. Hansen; Dept. of Mathematics, Ny Munkegade, Aarhus
Lecture notes in English and German, a continuation of the course: "Elliptic curves over Q and C," on modular forms and elliptic curves.
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- Elliptic Curves - Stéfane Fermigier
A collection of links to research articles on elliptic curves and related topics (applications, modular forms, Fermat's last theorem).
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- Euler Systems - Karl Rubin
One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Here, in the first
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- Explicit Approaches to Modular Abelian Varieties - William Stein
Stein's Ph.D. thesis (Berkeley, 2000). An investigation of the Birch and Swinnerton-Dyer conjecture, which ties together the constellation of invariants attached to an abelian variety. The author attempts to verify this conjecture for certain specific
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- Front for the Mathematics ArXiv - Univ. of California, Davis
U.C. Davis front end for the xxx.lanl.gov e-Print archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives including alg-geom, funct-an, dg-ga, q-alg, auto-fms, cd-hg, MAGNUS, Several Complex
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- Geometric Algorithms - Susan Landau; Univ. of Massachusetts at Amherst
Landau's interest in geometric algorithms has been in problems of an algebraic flavor: computer-aided design, robotics, and other geometric-related applications that have created a need for methods for embeddings, visualization, and algorithms for construction
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- Geometry and Topology: Recent Papers 1989-1993 - Univ. of Melbourne, Australia
A bibliography of e-prints from the Dept. of Mathematics and Statistics, Univ. of Melbourne, Australia.
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- Grothendieck Circle - Leila Schneps
Alexandre Grothendieck's published articles, unpublished research, letters, and translations: The Cohomology Theory of Abstract Algebraic Varieties, Standard Conjectures on Algebraic Cycles, Hodge's General Conjecture Is False for Trivial Reasons, Groupes
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- Helena A. Verrill - Department of Mathematics, Louisiana State University
Notes, links, handouts, and other materials from the courses that Verrill teaches, such as Solving Discrete Problems, Calculus, Elliptic Curves, and Modular Forms. She also provides a Java applet for a wallpaper drawing program and step-by-step illustrations
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- High Rank Elliptic Curves with Prescribed Torsion - Andrej Dujella, Zagreb
The highest rank currently known for an elliptic curve over Q with each of
the possible torsion groups.
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- The history of voting
- MacTutor Math History Archives
Linked essay on the history of electoral systems.
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- Homogeneous Transformation Matrices - Daniel W. VanArsdale
Explicit n-dimensional homogeneous matrices for projection, dilation, reflection, shear, strain, rotation and other familiar transformations.
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- How to Fix an Election - Ivars Peterson (MathTrek)
Voting sounds like a simple matter. Just pick a candidate, then count the ballots and announce the tally. When there are three or more candidates (or choices), however, the results may not actually reflect the true preferences of the voters.
Suppose
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