Thinking in Problems

How Mathematicians Find Creative Solutions

  • Alexander A. Roytvarf

Table of contents

  1. Front Matter
    Pages i-xxxvii
  2. Alexander A. Roytvarf
    Pages 1-23
  3. Alexander A. Roytvarf
    Pages 25-28
  4. Alexander A. Roytvarf
    Pages 29-35
  5. Alexander A. Roytvarf
    Pages 37-41
  6. Alexander A. Roytvarf
    Pages 43-53
  7. Alexander A. Roytvarf
    Pages 55-84
  8. Alexander A. Roytvarf
    Pages 85-105
  9. Alexander A. Roytvarf
    Pages 107-137
  10. Alexander A. Roytvarf
    Pages 139-195
  11. Alexander A. Roytvarf
    Pages 197-290
  12. Alexander A. Roytvarf
    Pages 319-387
  13. Back Matter
    Pages 389-405

About this book


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.


Analysis Chebyshev systems Combinatorial theory Dynamical systems Jacobi identities Multiexponential analysis Singular value decomposition theorems

Authors and affiliations

  • Alexander A. Roytvarf
    • 1
  1. 1.Rishon LeZionIsrael

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