Thinking in Problems : How Mathematicians Find Creative Solutions This concise self contained textbook gives an in depth look at problem solving from a mathematician’s point of view. 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 real life problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a self study guide. Prerequisites include linear algebra and analysis. Preface Using the Stars on Problems Understanding the Advanced Skill Requirements Acknowledgements Jacobi Identities and Related Combinatorial Formulas A Property of Recursive Sequences A Combinatorial Algorithm in Multiexponential Analysis A Frequently Encountered Determinant. A Dynamical System with a Strange Attractor Polar and Singular Value Decomposition Theorems 2x2 Matrices Which Are Roots of Unity A Property of Orthogonal Matrices Convexity and Related Classical Inequalities One Parameter Groups of Linear Transformations. Some Problems in Combinatorics and Analysis that can be Explored using Generating Functions Least Squares and Chebyshev Systems References Index of Terms.