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Education
- Algebra Helper - Collection of tools created to assist students and teachers of algebra.
- Algebra Story and Word Problems - Collection of problems and solutions, providing a base for Integrated Thematic Instruction in mathematical problem solving.
- Ask Dr. Math - Provides answers to common questions on basic algebra, equations/graphs/translations, linear algebra, linear equations and polynomials.
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Education >
High_School
- Algebra - Mathematical Abstraction from Concrete Experience - Illustrates how the student learns algebra while interacting with manipulatives, physical objects, represented by the numerals and variables of mathematics.
- Algebra - One on One - Educational game for a fun way to learn and practice algebra. With reviews and download link.
- Algebra Homework Help and Solvers - Free tutorials to help create solutions with work shown, write algebra lessons and help solve homework problems.
- Algebra is Arithmetic Backwards - For inheritance, fiduciaries, measures, optimization, topology, history, life, and all "backward" projects (for predicting or planning the future from the past).
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Group_Theory >
Tables
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Linear_Algebra
- Abstract Linear Spaces - Article written by J.J. O'Connor and E.F. Robertson.
- Elementary Linear Algebra - Lecture notes by Keith Matthews. Includes solutions to problems.
- Elements of Abstract and Linear Algebra - Foundational textbook by Edwin H. Connell. Available for download in pdf, dvi, postscript, or gzipped postscript.
- Project Linbox: Exact Computational Linear Algebra - C template library for exact, high-performance linear algebra computation with dense, sparse, and structured matrices over the integers and over finite fields.
- Linear Algebra and Applications Textbook - Topics include linear systems of equations, matrix algebra, vector spaces, geometrical aspects of standard spaces, the eigenvalue problem, and geometrical aspects of abstract spaces.
- Linear Algebra from Math World - With links to various topics, including determinants, general linear algebra, linear independence, linear systems of equations, matrices, permanents and lie theory.
- Linear Algebra by Jim Hefferon - Text available for free download in pdf or postscript. Source in LaTeX and MetaPost.
- Linear Algebra Toolkit - With modules designed to help a linear algebra student learn and practice a basic linear algebra procedure, such as Gauss-Jordan reduction, calculating the determinant, or checking for linear independence.
- Linear and Multilinear Algebra; Matrix Theory (Finite and Infinite) - Includes history, applications and related fields, subfields, textbooks and tutorials, software and tables, and links to related websites and topics.
- Lyryx Interactive Linear Algebra - Self-contained introductory course in linear algebra and its applications, suitable for undergraduate university level.
- Matrix Multiplication - Java-enabled interactive micro-course for beginners.
- Notes on Linear Algebra - Files available in pdf or postscipt. Topics include inverse of a matrix, equivalents statements, equivalent characterizations of basic concepts, grammar lessons in algebra, pivotal role of zero, linear independence, and eigenvalues.
- Professor Strang's Linear Algebra Class Lecture Videos - Videotaped Lectures from MIT's Course 18.06: Linear Algebra.
- Topics in Linear Algebra - Extends the existing one-way connections among the solving linear systems of equations, matrix inversion, and linear programming. With illustrative numerical examples.
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Ring_Theory
- Associative Rings and Algebras - Includes introduction, applications and related fields, references, software, and related links.
- Basic Books on Rings and Modules - Provides description of books on such topics as general theory of rings and modules, classical theory of artinian rings, and commutative rings.
- Pictures from Noncommutative Ring Theory Meetings - Collected by Tim Hodges.
- Nonassociative Rings and Algebras - Widens scope of rings to be studied, with emphasis on special cases of such rings such as Lie algebras and Jordan algebras.
- Lists of Ring Theorists - Mathematicians who study non-commutative, associative rings. With links to Web pages, e-mail addresses, MathSciNet entries, when available.
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Geometry >
Polytopes
- Polyhedra and N-Dimensional Space - Polytopes and optimal packing of p points in n dimensional spheres. With definitions, assumptions, findings and further improvements of the computational model.
- The Geometry Junkyard: Polyhedra and Polytopes - Provides pointers on geometric properties of polygons, polyhedra, and higher dimensional polytopes (particularly convex polytopes).
- Guy's Polyhedra Pages - Includes papers, current research and random resources on such topics as general theory of polytopes and polyhedra, stellation and faceting, and space-filling polyhedra.
- The Mathematical Atlas: Polytopes and Polyhedra - Covers geometric objects made from straight pieces. Discusses applications and related fields, textbooks and references, and related websites.
- Final Answers: Polyhedra and Polytopes - Set of articles on questions about hexahedra and other polyhedra.
- Regular Polygons - Topics include geometric properties, diagonals, graphs, and Euler's formula, and supplements and links.
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Higher_Dimensional
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Polyhedra
- Virtual Polyhedra - Provides a collection of thousands of virtual reality polyhedra. Serves as a free self-contained tutorial, reference work, and object library for people interested in polyhedra.
- Alexander's Polyhedra - Collection of virtual reality polyhedra. By Alex Doskey.
- Circumnavigating a Cube and a tetrahedron - Explores the shortest possible closed route on the surface of the polyhedron.
- Polyhedra Gallery - From books in the Tarquin catalogue. Models can be viewed and manipulated in three dimensions - virtual reality..
- Juno's World - Includes puzzles, gallery of polyhedra and a collection of VRML models.
- Martin's Pretty Polyhedra - Explains principles behind creation of polyhedra using a visual basic program.
- Harold Scott MacDonald Coxeter - Specialized in geometry, particularly on polytopes, non-euclidean geometry, group theory and combinatorics.
- Mathematician's Portrait: Professor Emeritus H.S.M. Coxeter - Biography courtesy of the Mathematics Survival Guide, published by the Department of Mathematics, University of Toronto.
- Mathematical Models - Offers a set of models for purchase. Models made of solid aluminum, precision die-cast, and available in four different painted colors.
- Multiple-Unit Dodecahedral Constructions - By Stephan Werbeck. Features images and VRML models.
- Polyhedra Database - Solids include the regular polyhedra, Archimedean, some prisms and anti-prisms, Archimedean duals, the Johnson solids (all convex polyhedra with regular faces) and some weird solids.
- Paper Models of Polyhedra - With over eighty paper models available for free.
- Pavilion of Polyhedreality - Practical polyhedra constructions by George W. Hart.
- Platonic Solids - Explores the question on why there can only be five Platonic solids.
- The Platonic Solids by Peter Alfeld - Provides general explanation, with java applets for illustration.
- Platonic Spheres - Presents a systematic approach to generating the Platonic bodies and discusses the symmetry of the Platonic spheres.
- Polyedergarten - Collection of constructions and VRML models. Also available in German or French versions.
- Polyhedra by Jim McNeill - Provides some form of ordered access to VRML models of polyhedra made using HEDRON. Software available for purchase.
- Polyhedra by Peter Cromwell - Book aimed at searching and presenting in a readable fashion the mathematics of polyhedra. With reviews, details, errata.
- Polyhedra Models by Douglas Zongker - Provides templates, available in pdf format, for making paper models for the 5 Platonic solids and the 13 Archimedean semi-regular polyhedra.
- Puzzling World of Polyhedral Dissections - Book by Stewart T. Coffin. Intended to be a puzzle designerb.
- Stellated Icosahedra - Excerpt of an article published in Mathematica in Education, discussing 59 stellations of the icosahedron.
- Studies into Polyhedra - Written by Anthony Thyssen. Topics include regular and semi-regular polyhedra, prisms, deltahedra, Johnston solids, and known polyhedral mathematical formula.
- Superliminal Geometry Page - Includes regular polyhedra, infinite polyhedra, flexible polyhedra, and hyperbolic tessellations. With images and links to 3D images and Tyler applets.
- Symmetry, Crystals and Polyhedra - By Steven Dutch. Discusses symmetry concepts, crystallography, tilings, and different types of polyhedra.
- Uniform Polyhedra - Provides an excerpt of Chapter 9 of R. Maeder's book, The Mathematica Programmer II. With images and animation of 80 polyhedra.
- Zvi Harb - Senior lecturer at the Department of Mathematics at the Technion, Israel Institute of Technology. With links to papers available in ps or dvi, and software packages.
- Polyhedra by Bob - Describes the Platonic Solids, Archimedian Solids and Catalan Solids. With download links to Poly, a dos program to study the truncations and transformations of the Platonic Solids.
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Software
- Peek - Program for N-dimensional polytope visualization by cross-section and projection.
- Poly - Shareware program for exploring and constructing polyhedra. Fully-functional evaluation version available for download.
- PPL: The Parma Polyhedra Library - C library providing numerical abstractions especially targeted at applications in the field of analysis and verification of complex systems.
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