دانلود کتاب Thinking in Problems: How Mathematicians Find Creative Solutions

Introduces key problem-solving techniques in depthProvides the reader with a range of methods that are used in numerous mathematical fieldsEach self-contained chapter builds on the previous one, allowing the reader to uncover new approaches and prepare creative solutionsCorresponding hints, explanations, and full solutions are supplied for each problemThe difficulty level for all examples are indicated throughout the bookThis 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.Content Level » GraduateKeywords » Analysis - Chebyshev systems - Combinatorial theory - Dynamical systems - Jacobi identities - Multiexponential analysis - Singular value decomposition theorems