Mathematics as Problem Solving

Authors: Soifer, Alexander

  • -Introduces various elementary techniques for solving problems in algebra, geometry, and combinatorics
  • -Each self-contained chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems
  • -Roughly 200 different problems and multiple proofs for each
  • -Aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving
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eBook $29.99
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  • ISBN 978-0-387-74647-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA
  • ISBN 978-0-387-74646-3
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  • Usually dispatched within 3 to 5 business days.
About this Textbook

Retelling the best solutions and sharing the secrets of discovery are part of the process of teaching problem solving. Ideally, this process is characterized by mathematical skill, good taste, and wit. It is a characteristically personal process and the best such teachers have surely left their personal marks on students and readers. Alexander Soifer is a teacher of problem solving and his book, Mathematics as Problem Solving, is designed to introduce problem solving to the next generation.

--Cecil Rousseau

The American Mathematical Monthly

The problems faithfully reflect the world famous Russian school of mathematics, whose folklore is carefully interwoven with more traditional topics. Many of the problems are drawn from the author's rich repertoire of personal experiences, dating back to his younger days as an outstanding competitor in his native Russia, and spanning decades and continents as an organizer of competitions at the highest level.

--George Bersenyi

The book contains a very nice collection of problems of various difficulty. I particularly liked the problems on combinatorics and geometry.

--Paul Erdos

Professor Soifer has put together a splendid collection of elementary problems designed to lead students into significant mathematical concepts and techniques. Highly recommended.

--Martin Gardner

To assemble so much material of the type used in Mathematical Olympiads, which has been tried and tested there, is unusual. To then present it in a form which develops themes, supported by relevant examples and problems for the reader, does the author great credit.

--R. W. Whitworth

The Mathematical Gazette

Reviews

From the reviews:

“How does one describe a mathematician? I know no better way than to read this delightful book. For Alexander Soifer has not just written another book about mathematics. He has opened up his heart---and in the process his great love for mathematics, his creative ability, his respect for and skill in teaching, his joy in living all shine through. I invite you to come meet a dear friend and share his exhilaration and insight.”  --- PHILIP L. ENGEL

From the reviews of the second edition:

“...this book can be the portal that leads the reader into the world of mathematics.”
  --- Cristinel Mortici (Targoviste)ür Mathematik, Zentralblatt f 

“This is a very readable collection of interesting problems of varying levels of difficulty. … It is so delightfully written that anyone who simply likes working on challenging problems could read it independently. … More than 150 problems are included in this collection. … helpful for an instructor who is looking for ways of integrating problem solving into a particular course, and might be useful for coaching a mathematics competition team. This … book would be a good resource for an instructor or coach." ---Sr. Barbara E. Reynolds, The Mathematical Association of America

“The author grew up in the problem solving atmosphere in Moscow and collected about 200 problems from his experience in mathematical clubs, schools, and Olympiads. … Many problems … are discussed in detail and in a way that can be followed easily. So the book can also be recommended to young students.” (H. Humenberger, Monatshefte für Mathematik, Vol. 159 (1-2), January, 2010)

“Clearly attractiveness of problems and beauty of solution have been major criteria in the selection for this book. The author devised many of the problems, and his enthusiasm is evident. … I am confident that readers will find this book to be a valuable showcase for ‘what (pure) mathematics is really like’.” (John Baylis, The Mathematical Gazette, Vol. 95 (532), March, 2011)


Table of contents (7 chapters)

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-0-387-74647-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA
  • ISBN 978-0-387-74646-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mathematics as Problem Solving
Authors
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-387-74647-0
DOI
10.1007/978-0-387-74647-0
Softcover ISBN
978-0-387-74646-3
Edition Number
2
Number of Pages
XVIII, 106
Additional Information
Originally published by Soifer, Alexander, 1987
Topics