Mathematics As Problem Solving [Paperback]

Alexander Soifer (Author)

Book Description

ISBN-10: 0940263009 | ISBN-13: 978-0940263000 | Publication Date: June 1987 | Edition: 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.

Editorial Reviews

Review

Aus den Rezensionen zur 2. Auflage:

 

“... zweifellos die internationale fachliche Anerkennung des Autors herauslesbar ist. ... Zu einem Teil der vorgestellten Problemstellungen finden sich Lösungen bzw. unterschiedliche Lösungsansätze. Insgesamt wird dieses Buch das Interesse an der Beschäftigung mit Mathematik und die Freude an der Eleganz mathematischer Argumentation sicher fordern.“ (P. Paukowitsch, in: IMN Internationale Mathematische Nachrichten, August/2010, Issue 214, S. 63) --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: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,835,091 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:

http://www.springer.com/math/numbers/book/978-0-387-74640-1

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 :-).

Customer Reviews

Most Helpful Customer Reviews

5 of 12 people found the following review helpful:

5.0 out of 5 stars Judge for yourself!, September 24, 2004

By 

Alexander Soifer (Colorado Springs, CO USA) - See all my reviews
(REAL NAME)   

This review is from: Mathematics As Problem Solving (Paperback)

Best information comes from objective extended journal reviews. See
them for yourself at

http://www.uccs.edu/~asoifer/

I hope you would enjoy reading this book as much as I enjoyed writing it!

(This is all I meant to say, but amazon.com required a "rating in stars" in order to receive these lines -- I am not a judge, you are! So read and enter your verdict.)