Thinking in Problems

How Mathematicians Find Creative Solutions

Authors: Roytvarf, Alexander A.

  • Introduces key problem-solving techniques in depth
  • Provides the reader with a range of methods that are used in numerous mathematical fields
  • Each self-contained chapter builds on the previous one, allowing the reader to uncover new approaches and prepare creative solutions
  • Corresponding hints, explanations, and full solutions are supplied for each problem
  • The difficulty level for all examples are indicated throughout the book
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eBook $59.99
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  • ISBN 978-0-8176-8406-8
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  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-8176-8405-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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.

Reviews

From the reviews:

“The problems are enhanced by introductory summaries, overviews of notations and definitions, historical comments, and bibliographic references. The text’s sequential approach will help developing mathematicians both expand their understanding of advanced mathematics and improve their problem-solving abilities … . Summing Up: Recommended. Upper-division undergraduates, graduate students, and researchers/faculty.” (J. Johnson, Choice, Vol. 51 (2), October, 2013)

“This marvelous collection of problems represents an interesting and valuable resource for students who prepare various types of mathematics contests. … very strongly recommends this book to all undergraduate and graduate students curious about elementary mathematics. Teachers would find this book to be a welcome resource, as will contest organizers.” (Teodora-Liliana Rădulescu, zbMATH, Vol. 1270, 2013)

Table of contents (12 chapters)

  • Jacobi Identities and Related Combinatorial Formulas

    Roytvarf, Alexander A.

    Pages 1-23

  • A Property of Recursive Sequences

    Roytvarf, Alexander A.

    Pages 25-28

  • A Combinatorial Algorithm in Multiexponential Analysis

    Roytvarf, Alexander A.

    Pages 29-35

  • A Frequently Encountered Determinant

    Roytvarf, Alexander A.

    Pages 37-41

  • A Dynamical System with a Strange Attractor

    Roytvarf, Alexander A.

    Pages 43-53

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-8406-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-8176-8405-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Thinking in Problems
Book Subtitle
How Mathematicians Find Creative Solutions
Authors
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-8176-8406-8
DOI
10.1007/978-0-8176-8406-8
Hardcover ISBN
978-0-8176-8405-1
Edition Number
1
Number of Pages
XXXVII, 405
Number of Illustrations and Tables
14 b/w illustrations
Topics