Artificial Intelligence in Mathematics
Published on 1. July 1994
Book
Paperback/Softback
338 pages
978-0-19-853686-4 (ISBN)
Description
This book suggests that in future science, social science, engineering and social administration will be based on the complementary interplay of artificial intelligence, mathematics, and statistics. It shows how intelligent computer systems will help pure mathematicians in their work, and how mathematicians may develop as a problem-solving discipline. Artificial intelligence provides profound insights into the nature of complex problems and how computers can be used to solve them; mathematics provides a rich language for presenting systems and methods for investigating them rigorously; while statistics provides the interface between abstract theory and data from observation and experiment. The book is divided into five sections: (1) an introduction to artificial intelligence in mathematics; (2) philosophical and structural issues; (3) automated theorem proving; (4) artificial intelligence in computer algebra and computer systems for mathematics; and (5) artificial intelligence in applied mathematics and statistics. This book is intended for academic and industrial researchers into pure and applied mathematics, artificial intelligence, and statistics.
More details
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Oxford University Press
Target group
College/higher education
Professional and scholarly
Illustrations
bibliography
ISBN-13
978-0-19-853686-4 (9780198536864)
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Schweitzer Classification
Persons
Content
Part I An Introduction to Artificial Intelligence in Mathematics; Jeffrey Johnson, Sean McKee and Alfred Vella: An Introduction to Artificial Intelligence in Mathematics; Part II The Impact of Computers on Mathematics: Philosophical and Structural Issues; James L. Alty: What is Artificial Intelligence and is it Relevant to Mathematics?; Alfred Vella and Carol Vella: Artificial Intelligence and the Mathcycle; Graeme Ritchie: Learning from AM; Ivan Bratko, Stephen Muggleton and Alen Varsek: Learning Qualitative Models of Dynamic Systems; John S.N. Elvey: Varieties of Approximations; Jean-Claude Simon: Uncertainty Versus Computational Complexity; Laurent Siklossy: Representing Ignorance, or Knowing What We Do Not Know; Part III: Logic and Computer Proof; Fausto Giunchiglia and Paolo Traverso: A System for Multi-Level Mathematical Reasoning; Christian Horn and Alan Smaill: From Meta-level Tactics to Object-level Programs; Yang Lu, Zhang Jingzhong: Searching Dependency Between Algebraic Equations: an Algorithm Applied to Automated Reasoning; Part IV Artificial Intelligence in Computer Algebra and Computer Systems for Mathematics; James H. Davenport: The Role of Intelligence in Computer Algebra; J. Calmet and I.A. Tjandra: An Artificial Intelligence Environment for Computer Algebra; Francois Rechenmann: Modelling Mathematical Objects in Knowledge-Based Systems for Scientific Computing; Philippe Laublet: Hybrid Knowledge Representation and Theorem Proving in Mathematics; Edmund Furse: The Mathematics Understander; Thomas Wolf and Andreas Brand: Heuristics for Solving Overdetermined Systems of Partial Differential Equations; Ron Knott: Declarative Programming for Mathematical Exploration; Peter Samuels: Hypertext for Computational Mathematics; Part V Artificial Intelligence in Applied Mathematics and Statistics; David J. Hand: Artificial Intelligence and Statistics: Synergy in Action?; B. Ford, S.J. Hague, R.M.J. Iles, I. Reid: A Framework for Combining Reasoning Components with Mathematical Software; Fergus Daly: An Intelligent Assistant for the Statistical Analysis of Markov Process Data; P. Olioveira, S. McKee, C. Coles: Genetic Algorithms and Optimizing Large Nonlinear Systems; Jeffrey Johnson: Representation, Knowledge Elicitation and Mathematical Science.