- A 27-Vertex Graph That Is Vertex-Transitive and Edge-Transitive But Not 1-Transitive [PDF] - Peter Doyle
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. PostScript, source, and PDF picture are available
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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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- 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 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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- 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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- 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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- 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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- 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 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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- Ideals, Varieties, and Algorithms - Cox, Little, O'Shea
An introduction to computational algebraic geometry and commutative algebra at the undergraduate level, with discussions of systems of polynomial equations ("ideals"), their solutions ("varieties"), and how these objects can be manipulated ("algorithms").
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- Innovative Teaching of Mathematics - ITM 2003 - Eckhard Hitzer
September 20-21, 2003, Research Institute for Mathematical Sciences, Kyoto, Japan. An international symposium with an explicit focus on Clifford geometric algebra for teaching. A second major focus is to present new ways of innovative cooperation between
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- Jim Loy's Mathematics Page - Jim Loy
This is an informal collection of articles on many different mathematics problems. Topics include Algebra, Geometry, Calendars, Number Theory, and reviews of mathematics-related books. See also Jim Loy's Puzzle Page and Jim Loy's Logic Page.
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- Joseph H. Silverman
Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves. Silverman's research interests include number theory, elliptic curves, arithmetic and Diophantine geometry, number theoretic aspects
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- Journal Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry
A yearly journal founded in 1971 on the occasion of the 65th birthday of O.-H. Keller. It publishes research articles in the areas of algebra, geometry, algebraic geometry and related fields, preferably in English language. Issues since 1993 are on the
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- Journal of Algebra (Academic Press) - Harcourt, Inc.
The Journal of Algebra presents carefully selected articles concerning original research in the field of algebra. Articles from related research areas that have a significant bearing on algebra are also included. Topics covered include: Structure of finite
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- Journal of Algebraic Combinatorics - Kluwer Online
The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial
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- Journal of Combinatorial Designs - John Wiley & Sons, Inc.
An international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory.
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- Kolyvagin's Application of Euler Systems to Elliptic Curves - Kedlaya, Osserman; Massachusetts Institute of Technology
A semester-long seminar studying Kolyvagin's application of Euler systems to elliptic curves (i.e., to the conjecture of Birch and Swinnerton-Dyer), focused around the expository paper Kolyvagin's Work on Modular Elliptic Curves by Professor Gross. Includes
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