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Advances in computer technology have had a tremendous impact on mathematics in the last two decades. In June of 1989, an international conference was held at MIT, bringing together mathematicians and computer scientists, to survey the work that has been done in computational mathematics, to report recent results in this field, and to discuss research directions as well as educational issues. This book presents a fascinating collection of contributions on topics ranging from computational algebra, and parallel computing, to mathematics education. Mathematicians interested in the computational aspects of their discipline as well as computer scientists interested in mathematical applications will enjoy the integrative view provided by this book.
Front Matter
A Completion Procedure for Computing a Canonical Basis for a k -Subalgebra
Summation of Harmonic Numbers
Algorithm and Implementation for Computation of Jordan Form over A [ x 1 ,..., x m ]
Fast Group Membership Using a Strong Generating Test for Permutation Groups
Finite-Basis Theorems and a Computation-Integrated Approach to Obstruction Set Isolation
Practical Determination of the Dimension of an Algebraic Variety
A Computer Generated Census of Cusped Hyperbolic 3-Manifolds
Classicality of Trigonal Curves of Genus Five
Symmetric Matrices with Alternating Blocks
Cohomology to Compute
Use of symbolic methods in analyzing an integral operator
Computer Algebraic Methods for Investigating Plane Differential Systems of Center and Focus Type
An Example of Computer Enhanced Analysis
An Algorithm for Symbolic Computation of Hopf Bifurcation
Application of the REDUCE Computer Algebra System to Stability Analysis of Difference Schemes
Signs of Algebraic Numbers
Efficient Reduction of Quadratic Forms
A Story About Computing with Roots of Unity
Exact Algorithms for the Matrix-Triangularization Subresultant PRS Method
Computation of Fourier Transforms on the Symmetric Group
Integration in Finite Terms and Simplification with Dilogarithms: A Progress Report
Why Integration is Hard
Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients
Recipes for Classes of Definite Integrals Involving Exponentials and Logarithms
Logic and Computation in MATHPERT: An Expert System for Learning Mathematics
Representation of Inference in Computer Algebra Systems with Applications to Intelligent Tutoring
Bunny Numerics
Advanced Mathematics from an Elementary Viewpoint: Chaos, Fractal Geometry, and Nonlinear Systems
Iterated Function Systems and the Inverse Problem of Fractal Construction Using Moments
Working with ruled surfaces in solid modeling
Using MACSyma to Calculate the Extrinsic Geometry of a Tube in a Riemannian Manifold
Computer Algebra in the Theory of Ordinary Differential Equations of Halphen Type
Symbolic Derivation of Equations for Mixed Formulation in Finite Element Analysis
Semantics in Algebraic Computation
Symbolic Computation with Symmetric Polynomials an Extension to MACSYMA
Simultaneous Computations in Fields of Different Characteristics