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Lattice Theory and Geometry of Numbers (The Geometry Junkyard) - David Eppstein, Theory Group, ICS, UC Irvine An extensive annotated list of links to material on lattices. A lattice is an infinite arrangement of points spaced with sufficient regularity that one can shift any point onto any other point by some symmetry of the arrangement. More formally, a lattice can be defined as a discrete subgroup of a finite-dimensional vector space (the subgroup is often required not to lie within any subspace of the vector space, which can be expressed formally by saying that the quotient of the space by the lattice is compact). more>> Order, Lattices, Ordered Algebraic Structures - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to ordered sets. Ordered sets, or lattices, give a uniform structure to, for example, the set of subfields of a field. Various special types of lattices have particularly nice structure and have applications in group theory and algebraic topology, for example. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>>

All Sites - 21 items found, showing 1 to 21

Application of Rayleigh's Short-Cut Method to Polya's Recurrence Problem [PDF] - Peter Doyle Doyle's Ph.D. thesis at Dartmouth College, June 1982. The goals of the presentation are to explain why Polya's theorem is true and to develop techniques for applying Rayleigh's method. The main results make sense of the notion that if two graphs look ...more>> 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; ...more>> Catalogue of Lattices - Neil Sloane, Gabriele Nebe A catalogue of different types of lattices, combinatorial objects with direct applications to packing spheres into a limited amount of space. ...more>> Cracking Kepler's sphere-packing problem - Ivars Peterson; Science News Online The familiar piles of neatly stacked oranges at a supermarket represent a practical solution to the problem of packing spheres as tightly as possible. Now, a mathematician has proved that no other arrangement of identical spheres fills space more efficiently. ...more>> Discrete Mathematics & Theoretical Computer Science (DMTCS): An Electronic Journal - Jens Gustedt DMTCS is an electronic journal published by the Maison de l'Informatique et des Mathématiques Discrètes, MIMD. It is a peer-reviewed publication devoted to rapid publication of innovative research which covers discrete mathematics and theoretical computer ...more>> Elementary Math Enrichment - Beth Schaubroeck Free mathematics enrichment materials for accelerated 4th and 5th graders. The 70 lessons, grouped into 12 different units, include solutions and teacher guides: Ancient Mathematics (Mayan math, in base 20; and Egyptian math, which lacks zero), Baseball ...more>> 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 ...more>> 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): ...more>> Herbert Wilf Herbert Wilf is a combinatorialist. The entire text of his books generatingfunctionology, A = B, and Algorithms and Complexity may be downloaded in PDF format, as may his "East Side, West Side" lecture notes on combinatorial objects and Maple programming. ...more>> Illustrated 4D Computer Graphics - Kirby Urner, 4D Solutions Curriculum Concepts from the Fuller School. Primitive topologies: non-Euclidean definitions of points, lines, planes as non-zero, parameterized entities, with light affecting properties in ray traced views; Concentric hierarchy: a reference frame relating ...more>> 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 ...more>> The Kepler Conjecture - Thomas C. Hales, Samuel P. Ferguson The authors claim to have proved the Kepler Conjecture, that no packing of equal-sized spheres in space can have greater density than that of the face-centered-cubic packing. The full proof is included in over 250 pages of postscript format, with in addition ...more>> Manipula Math with Java - International Education Software (IES) Hundreds of interactive Java applets for middle school through early college years on subjects such as geometry, calculus, trigonometry, linear transformations, vectors, complex numbers, and conics. Applets and animations often include introductions to ...more>> Mathematical Ideas in Science - Seven Stones Multimedia A series of tutorial modules using JavaScript, Shockwave for Director, or Shockwave Flash: sphere packings, shapes and lattices; waves described, longitudinal and transverse wave lab, 2-dimensional harmonic disturbance; 2-dimensional vector components ...more>> A Mathematica Package for Studying Posets - Curtis Greene, Haverford College Download Macintosh, Windows, or ASCII versions of posets22d, a Mathematica package for generating, displaying, and exploring partially ordered sets (also known as "posets"), with an emphasis on combinatorics. The package can generate a poset directly ...more>> Math e-Print Archive - Dept. of Mathematics, Florida State University Papers/abstracts to view and download (the files are in gzipped postscript format) by members of the Mathematics Department at Florida State University. Papers are listed in reverse chronological order. ...more>> The Quadray Papers - Kirby Urner, 4D Solutions An Introduction to Quadrays. The game of quadrays starts with a regular tetrahedron and four rays pointing from its center to the four corners; these or any ray built from these rays are labelled 4-tuples - i.e. four numbers separated by commas and enclosed ...more>> Richard E. Borcherds Preprints, papers, and the author's thesis, in HTML, plain TeX, dvi, and pdf formats; problem sheets for Lie algebras or Modular forms, and solutions to some problems in Hartshorne's book; tables of positive definite lattices and coefficients of some ...more>> RT Representation Theory (Front for the Mathematics ArXiv) - Univ. of California, Davis Representation Theory 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. ...more>> Secrets of the Beehive - Keith Devlin; Guardian Unlimited Archive The 4th century geometer Pappus was one of several ancient Greek mathematicians who suspected that the elegant shape of the honeycomb was a result not of an innate bee-sense of geometric beauty but of nature's efficiency. The repeating pattern of six-sided ...more>> Theory of Tieknots - Yong Mao The mathematical theory behind tying a necktie, with illustrations of the Four in Hand, the Pratt Knot, the Half-Windsor, and the Full-Windsor, and a classification of necktie knots with respect to size and shape. Tying a tie knot is equivalent to a persistent ...more>>

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