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A HYPERTEXT ON LINEAR ALGEBRA Prototype of a large-scale system of mathematical text Robert Mayans DEPARTMENT OF MATHEMATICS, FAIRLEIGH DICKINSON UNIVERSITY, MADISON, NJ A MAP OF THE TEXT ABOUT THE PROJECT DESIGN PRINCIPLES A primary source for learning mathematics Simplest formal structure Editorial policy shapes the text, not formalisms Public tools and technology Sparing use of links Repetition preferred to disjointed text Modern, standard notation Goal of the Mathematics Hypertext Project: To create large-scale integrated structures of mathematical text. What is a hypertext? A collection of linked Web pages with a common structure, design, and editorial conventions. Why a hypertext? A dynamic text is a natural organization for mathematics Advancing, improving, correcting, and reorganizing text all part of mathematical work Embraces the intellectual unity of mathematics as well as its diversity of subjects Why linear algebra? Linear algebra holds a central position in mathematics, with strong ties to abstract algebra, functional analysis, multivariate calculus, differential equations, and with an enormous range of applications. Linear algebra presents both a rich area for a linked text and a serious challenge to represent a variety of viewpoints into a coherent whole. Where is it on the Web? Systems of Linear Equations Systems of linear equations Solution by Gaussian elimination Vectors and matrices LU factorizations Continuity and condition number Iterative solutions Orthogonal projections Inconsistent systems Linear equations in integers Linear inequalities Vectors in Rn Subspaces of Rn When will it be done? Systems of linear equations Matrices and linear transformations Fundamental subspaces Invertibility of matrices Orthonormal bases Determinants Eigenvalues and eigenvectors Applications Symmetric matrices Not enough people! We earnestly seek collaborators, designers, experts, students, Web whizzes, and mathematicians of every persuasion to design and develop the text. Contact [email protected] Least squares Linear equations in integers Discussion of a single theme Associative linking Title Book Text Title Chapter 1 Chapter 2 Introduction to Linear Programming Linear Algebra in Rn Google on "Mathematics Hypertext Project". Start at the page: "Setting up your browser". Who's working on it? Core Text Progression of ideas Linear, tree-like linking Inner product and norm Linear independence, basis Geometry in Rn The portion on the map will be completed by the end of 2006. PAGE AND LINK TYPES Matrix factorizations Inner Link Multiplication of vectors Topology of Rn Cauchy-Schwarz inequality Basis of a vector space Outer Link Noncommutative matrix multiplication No return to start point Polynomial interpolation Matrix factorizations Geometric Approach to Determinants Determinants Markov chains Linear Differential Equations Spectral Theory Introduction Axioms of a vector space Linear independence, bases Linear transformations and duality Direct products Quotient spaces TECHNOLOGIES Use of WWW standards: MathML for mathematics. SVG for graphics Easy, free setup for Internet Explorer and Netscape Use of Javascript tools, ASCIIMathML amd ASCIIsvg, designed by Prof. Peter Jipsen, Chapman University Easy to write mathematical text. Example: `e^x = 1 + x + x^2/2 + cdots` prints as expected. Introduction to Vector Spaces Examples of a vector space Subspaces and spans Returns to start point Basis and Isomorphism Theorem Bases for Infinite-Dimensional Spaces Duality Topological Vector Spaces BIBLIOGRAPHY Paul Halmos, Finite Dimensional Vector Spaces Peter Lax, Linear Algebra David Lay, Linear Algebra and Its Applications Robert Mayans, “The future of mathematical text”, Journal of Digital Information, 2004. printed by www.postersession.com