Thinking in problems : how mathematicians find creative solutions
 Author/Creator
 Roytvarf, Alexander A.
 Language
 English.
 Imprint
 New York : Birkhäuser, c2013.
 Physical description
 xxxvii, 405 p. : ill. ; 25 cm.
Access
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 389401) and index.
 Contents

 Section I. Problems. 1. Jacobi Identities and Related Combinatorial Formulas. 2. A Property of Recurrent Sequences. 3. A Combinatorial Algorithm in Multiexponential Analysis. 4. A Frequently Encountered Determinant. 5. A Dynamical System with a Strange Attractor. 6. Polar and Singular Value Decomposition Theorems. 7. 2X2 Matrices Which Are Roots of 1. 8. A Property of Orthogonal Matrices. 9. Convexity and Related Classical Inequalities. 10. OneParameter Groups of Linear Transformations. 11. Examples of Generating Functions in Combinatorial Theory and Analysis. 12. Least Squares and Chebyshev Systems. Section II. Hints. 1. Jacobi Identities and Related Combinatorial Formulas. 2. A Property of Recurrent Sequences. 3. A Combinatorial Algorithm in Multiexponential Analysis. 4. A Frequently Encountered Determinant. 5. A Dynamical System with a Strange Attractor. 6. Polar and Singular Value Decomposition Theorems. 7. 2X2 Matrices Which Are Roots of 1. 8. A Property of Orthogonal Matrices. 9. Convexity and Related Classical Inequalities. 10. OneParameter Groups of Linear Transformations. 11. Examples of Generating Functions in Combinatorial Theory and Analysis. 12. Least Squares and Chebyshev Systems. Section III. Explanations.1. Jacobi Identities and Related Combinatorial Formulas. 2. A Property of Recurrent Sequences. 3. A Combinatorial Algorithm in Multiexponential Analysis. 4. A Frequently Encountered Determinant. 5. A Dynamical System with a Strange Attractor. 6. Polar and Singular Value Decomposition Theorems. 7. 2X2 Matrices Which Are Roots of 1. 8. A Property of Orthogonal Matrices. 9. Convexity and Related Classical Inequalities. 10. OneParameter Groups of Linear Transformations. 11. Examples of Generating Functions in Combinatorial Theory and Analysis. 12. Least Squares and Chebyshev Systems. Section IV. Full Solutions. 1. Jacobi Identities and Related Combinatorial Formulas. 2. A Property of Recurrent Sequences. 3. A Combinatorial Algorithm in Multiexponential Analysis. 4. A Frequently Encountered Determinant. 5. A Dynamical System with a Strange Attractor. 6. Polar and Singular Value Decomposition Theorems. 7. 2X2 Matrices Which Are Roots of 1. 8. A Property of Orthogonal Matrices. 9. Convexity and Related Classical Inequalities. 10. OneParameter Groups of Linear Transformations. 11. Examples of Generating Functions in Combinatorial Theory and Analysis. 12. Least Squares and Chebyshev Systems.
 (source: Nielsen Book Data)
 Publisher's Summary
 This concise, selfcontained textbook gives an indepth look at problemsolving from a mathematician's pointofview. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to solving mathematical problems, and this book outlines the tools necessary to improve the reader's technique. The text is divided into twelve chapters, each providing corresponding hints, explanations, and finalization of solutions for the problems in the given chapter. For the reader's convenience, each exercise is marked with the required background level. This book implements a variety of strategies that can be used to solve mathematical problems in fields such as analysis, calculus, linear and multilinear algebra and combinatorics. It includes applications to mathematical physics, geometry, and other branches of mathematics. Also provided within the text are reallife problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a selfstudy guide. Prerequisites include linear algebra and analysis.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Alexander A. Roytvarf.
 ISBN
 9780817684051
 0817684050
 9780817684068
 0817684069