 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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 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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 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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 Brief Course Materials for Various Courses  E. Lee Lady; University of Hawaii
A collection of short handouts: files are in PDF and DVI formats. Contents include: The Fundamental Theorem of Arithmetic, the division algorithm, solutions of linear congruences, solving the Chinese Remainder problem, an example of a continued fraction,
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 Categories and Combinatorics Group  Mathematics and Statistics, Univ. of Sydney, Australia
Category theory is a recent branch of mathematics originating in algebraic topology, but rapidly establishing connections with algebra, logic, algebraic and differential geometry, and most recently computer science. Category theory is particularly suited
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 Center for Geometry Analysis Numerics and Graphics (GANG)  Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
An interdisciplinary Differential Geometry research team. The GANG Geometry Archive is an online library of papers, preprints, images, animations and software connected with their research. The Library includes: Knot (energyminimizing knots and links);
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 Conformal Maps of Nonsmooth Surfaces and Their Applications  Vladimir M. Miklyukov
"In contrast with classic mathematical analysis that relies on ancient magical rites and overidealized relations, mathematical problems arising from the theory of micro and nanoflows require more real logical constructions such as investigations of functions
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 Conic Sections (Visual Dictionary of Special Plane Curves)  Xah Lee
A discussion of the history of conic sections, one of the oldest math subjects studied systematically and thoroughly, with a description, formulas, properties, a proof, Mathematica notebooks, the ellipse seen as a circle, second degree curves, intersection
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 C.T.J. Dodson  Christopher Dodson
Dodson provides notes and Maple or Mathematica packages for many different mathematics courses, including algebra and precalculus, calculus, differential equations, using computers for mathematics and statistics, and an introductory course on curves,
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 Cubic surfaces  MacTutor Math History Archives
Linked essay on the history of surfaces of order three.
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 Curvature of Surfaces (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
If you take a flat piece of paper and bend it gently, it bends in only one direction at a time. At any point on the paper, you can find at least one direction through which there is a straight line on the surface. You can bend it into a cylinder, or into
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 Differential Geometry (Graphics Archive, Special Topics)  The Geometry Center
Using differential calculus to study curves and surfaces in space.
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 Differential Geometry Images  Walter Seaman
Animations of differential geometry topics: images constructed by Seaman using the programs in Modern Differential Geometry of Curves and Surfaces with Mathematica (Second Edition) by Alfred Gray. Topics include: Curves with prescribed curvature and torsion;
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 DigiArea Group  Helen Golovina
Makers of atlas™, a Maple package for differential geometry calculations that works with manifolds, mappings, embeddings, submersions, pforms, and tensor fields; and LdeApprox™, a toolbox for Maple or Mathematica that finds analytical polynomial
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 EG Models (Electronic Geometry Models)  Michael Joswig, Konrad Polthier
A refereed archive of interesting geometric examples and visualizations, open for any geometer to publish new geometric models, or to browse the models for material to be used in education and research. The geometry models cover a broad range of mathematical
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 Electric Currents in Infinite Networks [PDF]  Peter G. Doyle
Networks as Riemann surfaces. A paper that shows how to get a more complete theory of conduction in infinite networks by paralleling the welldeveloped theory of conduction on open Riemann surfaces. PostScript and source file are available from Doyle's
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 Espaces Fibrés et Connexions  Robert Coquereaux
Un livre de géométrie différentielle en hypertexte; une introduction a la théorie des espaces fibrés et des connexions. A hypertext book in French on differential geometry.
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 The Euler Number (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
If we have a polyhedron, we can compute its Euler number, x=VE+F. In fact, we computed Euler numbers ad delectam. Why did we do this? One reason is that they are is easy to compute. But that is not obviously a compelling reason for doing anything in
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 Famous Curves Applet Index  MacTutor Math History Archive
From Astroid, Cardiod, Catenary, and Cayley's Sextic to the Trisectrix of Maclaurin, Tschirnhaus' Cubic, Watt's Curve, the Witch of Agnesi  and many more  click on the name of a curve to experiment with some of its associated curves.
(Your browser
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 Famous Curves Index  MacTutor Math History Archive
Links to pages illustrating more than 60 mathematical curves, with information on their history and associated curves. Anyone with the Mathematical MacTutor system or a Javaenabled browser can investigate these curves and their associated curves interactively.
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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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 GANG Discrete Library  Ian McIntosh; Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
A library of discrete conformal maps as discrete integrable systems. A discrete conformal map is a map z : z^2 > p^1 with the property that the
crossratio of four adjacent points is constant... Illustrations show how a Riemann surface arises, considering
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 GANG Knot Library  Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
A library of Energy Minimizing Knots and Links. Select a knotimage or category to see more members of the knot's family. The catalog contains knots up to 8 crossings. 2,q torus knots and links; Rational link with two, three, and fourterm continued
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 GANG Symmetry Library  James M. Lawrence; Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
Symmetry detection software. Input file, sample output, graphs, and download. From the Center for Geometry Analysis Numerics and Graphics.
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 Geometry and Topology: Recent Papers 19891993  Univ. of Melbourne, Australia
A bibliography of eprints from the Dept. of Mathematics and Statistics, Univ. of Melbourne, Australia.
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 Geometry of Harmonic Maps  Y. L. Lin, Fudan University, Shanghai, China
A book which, though not a complete description of the theory, provides an introduction and an approach useful to researchers and graduate students in differential geometry, geometric analysis, differential equations and theoretical physics. Harmonic
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 Georg Friedrich Bernhard Riemann (History of Mathematics Archive)  David R. Wilkins
A biography and selected papers of Bernhard Riemann, available online or for download in various formats. A lecture on geometry and the paper which contains the Riemann Hypothesis are available in English translation; the other papers remain in the original
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 Great Math Programs  Xah Lee
A listing about 40 excellent recreational math programs for Macintosh that do: polyhedra and Rubic cubes, curves and surfaces, fractals and Lsystems, tilings and symmetry, game of hex and game of life, chess and fiveinarow, peg solitare and polyominos,
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 Harmonic Maps Bibliography  Burstall, Lemaire, Rawnsley
An ongoing project to provide a searchable, comprehensive, and uptodate bibliography in the area of harmonic maps. The bibliography is in TiB format (a bibliographical preprocessor for TeX, LaTeX etc.) from which BiBTeX, TeX and PostScript versions
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 Harmonic Maps Bibliography  Department of Mathematics, University of Florida
The Tib formatted bibliography on harmonic mappings between Riemannian manifolds maintained and offered for anonymous ftp at ftp.maths.bath.ac.uk and at ftp.maths.warwick.ac.uk in England. Formats other than Tib are also available.
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 Helmer Aslaksen
A mathematics professor at the National University of Singapore. Research involves abstract algebra, including the trigonometry of symmetric spaces, and calculations for the Chinese, Islamic, and Indian calculators. Papers about these topics may be
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 Imaging Raytracer  Paul Flavin
A raytracing applet with which you can generate the six quadric surfaces  sphere (ellipsoid), cone, hyperboloid of one and two surfaces, paraboloid, hyperboloic paraboloid  and the cylinder.
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 Imaging the Imagined  Paul Flavin
Modeling with Math and a Keyboard: the art and science of modeling; the math, theory and practice of rendering, imaging, and animation. An introduction to raytracing and the Quadric surfaces; Platonic Solids and Polyhedra; 'Tensegrity' (tension) structures;
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 Institute for Gravitational Physics and Geometry  Dept. of Physics, Penn State University
The Institute fosters research of an interdisciplinary character linking astrophysics, gravitational wave physics and experimental gravitational wave detection in the pursuit of the scientific understanding of gravity and the development of gravitational
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 International Snow Sculpture Championships: Team Minnesota  Department of Mathematics and Computer Science, Macalester College
Team Minnesota's Enneper surface entry earned second place in the Breckenridge International Snow Sculpture Championships of 2000. The site also includes photos of their planning, design, and implementation stages, the acceptance speech, and the team's
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 Ken Brakke's home page
Home page of the Susquehanna University mathematics professor who coauthored The Physics of Microdroplets and developed Surface Evolver, a free interactive program for modeling liquid surfaces shaped by various forces and constraints. Brakke also offers
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 Level Set Methods Applied to Microchip Manufacturing  J. A. Sethian
A paper and movies on microchip manufacturing. Part of the process of manufacturing a computer chip consists of digging holes in silicon wafers and coating them with materials. At various stages, level set methods can be used to track the evolution of
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 Level Set Methods for Shape Recovery  J. A. Sethian
Overview of a movie on medical imaging. Imagine that you are given an image, say a medical (MRI or CT) scan. Suppose you want to extract the important feature within the image of a digital subtraction angiogram (DSA); in this case, the outline of the
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 Macpurity's Earth Science, Geodesy and Geophysics web site  John W. Robbins
A site with information in the areas of Potential Theory, Theoretical Geodesy, Theoretical Geophysics and Celestial Mechanics and Dynamics.
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 Maple Application Center  Waterloo Maple, Inc.
Software you can order to explore, share, and publish math on the Internet. Interactive media for exploring and exchanging mathematical ideas, with content on a variety of subjects at the high school, university, and graduate level. (There are high school
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 Math Bibliographies  Dept. of Mathematics, University of Florida
A collection of bibliographies, with two distinct search mechanisms. Contents: Introduction; More about WAIS; More about Glimpse; Bibliography on ergodic theory and dynamical systems; Bibliography on harmonic maps; Journal of Differential Geometry; VAF
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 Mathematica Courseware Catalog  Wolfram Research, Inc.
Developed as a resource for the academic community, the Mathematica Courseware Catalog is an evergrowing and broadranging collection of course materials that make significant use of Mathematica. Search by keyword or browse by subject: see, in particular,
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 Mathematical Analysis for Beginners in Mathematics and Engineering  Vladimir M. Miklyukov
A set of lectures and sample test questions, in Russian language with English captions.
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 Mathematical Snippets  Mathematics Dept., Bellevue Community College, Bellevue, WA
Illustrated descriptions of six mathematical concepts: the Pythagorean Theorem, Archimedes' Tombstone, the Möbius Strip, the Koch Snowflake Curve, Plateau's Problem (minimal surfaces), and Counting to Infinity. Each snippet contains a very brief
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 Mathematica Packages  Xah Lee
A dozen Mathematica programs, mostly geometry or graphics related. Mathematica is a computer algebra system sold by Wolfram Research Inc. To use these notebooks, you need to have a copy of Mathematica. Mathematica packages and notebooks are plain ASCII
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 Mathematics Archives  University of Tennessee, Knoxville (UTK)
A comprehensive site for finding mathematics on the Internet; particularly strong in its collection of educational software and links to other sites of interest to mathematicians that provide access to electronic journals, preprint services, grant information,
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 Mathematics Graphics Gallery  Xah Lee
A collection of mathematical images. Links to files on Xah Lee's sites that contain attractive mathematics graphics: Nested Inversion of Circles; Conic Sections; Epicycloid and Hypocycloids; Rose Curves; wallpaper designs; Transformation of the Plane;
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 Mathematics in John Robinson's Symbolic Sculpture  University of Wales, Bangor
Art and mathematics are combined in this site, which explores Borromean Rings, The Möbius Band, Bernard Morin and the Brehm Model, The Projective Plane, Fibre Bundles, Knots and Links, Torus Knots, and Fractals through the work of sculptor John Robinson.
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 Mathematics Journals (AMS)  American Mathematical Society
A list of mathematics journals with articles on the Web and a list of Web sites for printed journals, with tables of contents of issues, abstracts of papers, actual papers, information about submissions and subscriptions, etc. See also the Annual Listing
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 Mathematics Journals: Electronic and Printed  Mathematics Dept., Penn State University
Links to dozens of journals, from the Academic press electronic journal library to the Ulam Quarterly, and spanning printed journals from Abstract and Applied Analysis to the Zentralblatt für Mathematik. A link to the Bibliothèque Mathématique
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