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Mathematics As Problem Solving [Paperback]

Alexander Soifer
1.0 out of 5 stars  See all reviews (3 customer reviews)

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Kindle Edition $28.82  
Paperback $30.34  
Paperback, June 1987 --  

Book Description

June 1987 0940263009 978-0940263000 1st

Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Each new chapter builds on the previous one, allowing the reader to uncover new methods for using logic to solve problems.  Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries. With roughly 200 different problems, the reader is challenged to approach problems from different angles.

Mathematics as Problem Solving is aimed at students from high school through undergraduate levels and beyond, educators, and the general reader interested in the methods of mathematical problem solving.

--This text refers to an alternate Paperback edition.

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Editorial 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)

--This text refers to an alternate Paperback edition.

From the Back Cover

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

--This text refers to an alternate Paperback edition.

Product Details

  • Paperback: 117 pages
  • Publisher: Center of Excellence in; 1st edition (June 1987)
  • Language: English
  • ISBN-10: 0940263009
  • ISBN-13: 978-0940263000
  • Product Dimensions: 8.3 x 5.5 x 0.5 inches
  • Shipping Weight: 8.8 ounces
  • Average Customer Review: 1.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #5,102,664 in Books (See Top 100 in Books)

More About the Author

I was once born in Moscow to the family of a painter and an actress. There I received my music and math education, became a "Moscow intellectual", and as such I felt a burning desire of freedom - freedom personal, political, and creative.
Half a life ago, I left the familiar landscape in search of freedom. I found it in the United States. In a curious way, I repeated the American history in my personal life. In 1978 I came to Plymouth Rock, by then called Boston. I wintered there, and moved west. I crossed the whole country from Boston to Los Angeles in a covered wagon with "U-Haul" written on its side. It leaked quite authentically! In Los Angeles, I made a U-Turn in my U-Haul, and returned to the picturesque Colorado to take a new job.
I have been a professor at the University of Colorado ever since, for 30 years, with a recent 3-year long excursion to Princeton and Rutgers universities. I have taught courses in math, such as "What is Mathematics?", "Mathematical Coloring Course", "Mathematics: A Human Endeavor". I have also taught "Russian Avant-Garde Art of the Early XX Century" and many European film courses, such as "Andrzej Wajda and Cinema of Poland", "Michelangelo Antonioni and Post W.W.II Cinema of Italy", "Russian Cinema Today."
I write books touching on mathematics, history, biography, and art. All my present and near-future books will be published by Springer. 18-year long investigation into Ramsey Theory and the lives of its creators resulted in what truly could be called the book of my life, "The Mathematical Coloring Book:

Next to come out in Springer are:
*) "Mathematics as Problem Solving"
**) "How Does One Cut a Triangle?"
***) "Geometric Etudes in Combinatorial Mathematics"
****) "Life and Fate: In Search of Van der Waerden"
*****) "Problems of pgom Erdos" - a joint book with my legendary late friend, coauthor and friend Paul Erdos.

I will then write books that do not yet have a publisher:

*) "On Both Sides of the Atlantic: Adventures of a Mathematician."
**) "Memory in Flashback" - a book of maxims in the style of Hugo von Hofmannsthal's 1922 "Buch der Freunde."

The 1-year old collie Pastushok ("Little Sheppard") lives with me. We are musing that one day we will be joined by our Muse :-).

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Most Helpful Customer Reviews
1 of 2 people found the following review helpful
1.0 out of 5 stars Overrated June 29, 2014
By jkorge
Quite frankly, I am disappointed by the book's content. I certainly would not recommend to use this material as a textbook for an undergraduate or graduate students (as the author recommends), maybe for high school students at best. The problem solving solutions presented in the material could have been more sophisticated, given the author's background. The book is not worth the price it is listed for. The great alternative I found is the book by A. M. Yaglom, which offers much wider set of problems and truly challenges the reader to test his/her problem-solving skills.
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1 of 2 people found the following review helpful
1.0 out of 5 stars your money is safer in the dumpster June 28, 2014
The book is apparently mislabeled. Judging by the cover, I would assume it would give me a (hopefully solid) foundation for applying math to solve some real-world problems. Wrong! Instead, you have a bunch of entry-level mathematical concepts randomly assembled together with no clear structure or reasoning behind it. High-school algebra? You got it. Geometry? Go ahead! Combinatorics? Let's throw some in for good measure! And I'd like Chipotle with that, please.

Furthermore, the language is horrendous - it appears that zero editing has been done on this work, which is even more concerning given that the author is not a native English speaker.

I reckon that the only people who could potentially find value in this book are those who had once made skipping their math classes a deliberate, conscientious, and focused effort - but I doubt those are in the market for one.
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0 of 1 people found the following review helpful
I didn't find this book useful and wouldn't recommend it. It definitely needs a lot of editing as well.
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