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Mathematics - Algebra | Mathematics as Problem Solving

Mathematics as Problem Solving

Soifer, Alexander

Originally published by Soifer, Alexander, 1987

2nd ed. 2009, XVIII, 106p. 62 illus..

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  • -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

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

Content Level » Lower undergraduate

Keywords » Algebra - Problem-solving - combinatorial problems - geometry - induction - mathematics - pigeonhole principle - proof - proof writing

Related subjects » Algebra - Geometry & Topology - Mathematics

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