How to Solve Mathematical Problems (Dover Books on Mathematics)

Title Page; Copyright Page; Dedication; Table of Contents; Preface; 1 - Introduction; SCOPE OF THE BOOK; GENERAL VERSUS SPECIAL METHODS; RELATION TO ARTIFICIAL INTELLIGENCE; APPLYING METHODS TO PROBLEMS; 2 - Problem Theory; FOUR SAMPLE PROBLEMS; Instant Insanity; Chess Problem; Find Problem from Mechanics; Proof Problem from Modern Algebra; WHAT IS A PROBLEM?; Givens; Operations; Goals; Implicit Specification of Givens, Operations, and Goals; Incomplete Specification of Givens, Operations and Goals; WHAT IS A PROBLEM STATE?; WHAT IS A SOLUTION?; STATE-ACTION TREE; 3 - Inference; GIVENS. Numerical PropertiesTopological Properties; Operations; GOALS; 4 - Classification of Action Sequences; RANDOM TRIAL AND ERROR; SYSTEMATIC TRIAL AND ERROR; CLASSIFICATORY TRIAL AND ERROR; MACROACTIONS; GETTING OUT OF LOOPS; INCUBATION; 5 - State Evaluation and Hill Climbing; THEORY; APPLICATIONS; DIFFICULTIES WITH HILL CLIMBING; 6 - Subgoals; THEORY; APPLICATIONS; 7 - Contradiction; INDIRECT PROOF; MULTIPLE CHOICE-SMALL SEARCH SPACE; CLASSIFICATORY CONTRADICTION-LARGE SEARCH SPACE; ITERATIVE CONTRADICTION IN INFINITE SEARCH SPACES; 8 - Working Backward; THEORY; APPLICATIONS. 9 - Relations Between ProblemsEQUIVALENT PROBLEMS; SIMILAR PROBLEMS; SPECIAL CASE; GENERALIZATION; 10 - Topics in Mathematical Representation; REPRESENTATION ON PAPER OR IN THE HEAD; DIAGRAMMATIC REPRESENTATION; SYMBOLIC REPRESENTATION; SOME IMPORTANT MATHEMATICAL CONCEPTS; 11 - Problems from Mathematics, Science, and Engineering; ALGEBRA; TRIGONOMETRY; ANALYTIC GEOMETRY; CALCULUS; DIFFERENTIAL EQUATIONS; PROBABILITY AND STATISTICS; COMBINATORIAL ANALYSIS; NUMBER THEORY; MODERN ALGEBRA; MECHANICS; HEAT; ELECTRICITY; ELECTRICAL ENGINEERING; COMPUTER PROGRAMMING; References; Index. If you've ever tried to solve mathematical problems without any idea how to go about it, this book is for you. It will improve your ability to solve all kinds of mathematical problems whether in mathematics, science, engineering, business, or purely recreational mathematical problems (puzzles, games, etc.). In the pages of this book you'll discover seven indispensable problem-solving techniques: inference, classification of action sequences, state evaluation and hill climbing, subgoals, contradiction, working backward and relations between problems. Based on modern advances in the fields of ar. If you've ever tried to solve mathematical problems without any idea how to go about it, this book is for you. It will improve your ability to solve all kinds of mathematical problems whether in mathematics, science, engineering, business, or purely recreational mathematical problems (puzzles, games, etc.). In the pages of this book you'll discover seven indispensable problem-solving techniques: inference, classification of action sequences, state evaluation and hill climbing, subgoals, contradiction, working backward and relations between problems. Based on modern advances in the fields of artificial intelligence and computer simulation of thought, the techniques are taught here by an effective problem-solving methodology. Dr. Wickelgren, formerly a Professor of Psychology at MIT and the University of Oregon, first defines a problem-solving method, then illustrates its application to simple recreational mathematics problems that require no more background than a year of high school algebra and a year of plane geometry. By devoting the majority of the book to such "puzzle" problems, which require less background and information than more advanced mathematics and science problems, the author reaches the widest possible audience. In the final chapter, however, Dr. Wickelgren deals with specific problems from mathematics, science, and engineering. Throughout the book, sample problems illustrate each method and the author has supplied hints and complete solutions. Carefully and clearly written, this indispensable guide will help students in every discipline avoid countless hours of frustration and wasted effort. It is an ideal book for early undergraduate courses in mathematics, physical science, engineering, computer science, economics and other fields that require problem solving. Preface. Introduction. References.Index. 73 line illustrations. Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.