"Solving problems", writes Polya, "is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice. This book cannot offer you a magic key that opens all the doors and solves all the problems, but it offers you good examples for imitation and many opportunities for practice: If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems." "In enough cases to allay . . . discouragement over not immediately discovering a solution, Professor Polya masterfully leads the reader down several unproductive paths. At the end of each chapter he provides examples for the render to solve. By means of these carefully selected and arranged problems, many of them directly related to others that precede, and guided by just the right suggestions at just the proper time, the reader's own ability is developed and extended. Solutions to the examples and, in many cases, outlines of procedures for discovering solutions. arc given at the back of the book. With striking promise for effectiveness, the entire book as a unit is one great experience in learning processes for problem solving through participation. The author has captured with great success the implication of his basic premise stated in the preface ..." The Mathematics Teacher

Can one learn linear algebra solely by solving problems? Paul Halmos thinks so, and you will too once you read this book. The Linear Algebra Problem Book is an ideal text for a course in linear algebra. It takes the student step by step from the basic axioms of a field through the notion of vector spaces, on to advanced concepts such as inner product spaces and normality. All of this occurs by way of a series of 164 problems, each with hints and, at the back of the book, full solutions. This book is a marvelous example of how to teach and learn mathematics by 'doing' mathematics. It will work well for classes taught in small groups and can also be used for self-study. After working their way through the book, students will understand not only the theorems of linear algebra, but also some of the questions which were asked which enabled the theorems to be discovered in the first place. They will gain confidence in their problem solving abilities and be better prepared to understand more advanced courses. As the author explains, 'I don't think I understand a subject until I know the questions ... I wrote this book to organize those questions, problems, in my own mind.' Try this book with your students and they too will be able to organize and understand the questions of linear algebra.

" A comic, bittersweet tale of family evocative of The Yiddish Policemen's Union and Everything Is Illuminated Alexander "Sasha" Karnokovitch and his family would like to mourn the passing of his mother, Rachela, with modesty and dignity. But Rachela, a famous Polish e;migre; mathematician and professor at the University of Wisconsin, is rumored to have solved the million-dollar, Navier-Stokes Millennium Prize Problem. Rumor also has it that she spitefully took the solution to her grave. To Sasha's chagrin, a ragtag group of socially challenged mathematicians arrives in Madison and crashes the shiva, vowing to do whatever it takes to find the solution-even if it means prying up the floorboards for Rachela's notes. Written by a trained geophysicist, this hilarious and multi-layered debut novel brims with colorful characters and brilliantly captures humanity's drive not just to survive, but to solve the impossible"--

A stimulating collection of one hundred problems, complete with instructive solutions, on numbers, equations, polygons, polyhedra and many other topics. Extremely challenging for anyone with a fair knowledge of mathematics up to calculus. Includes an additional 13 problems without solutions.

"So goes the legend of the tricky knot of Gordius, king of Phrygia. Many had tried, many had failed, but Alexander the Great simply cut the knot with his sword. He went on to conquer most of Asia, eventually reaching as far east as Northern India. This book of probability riddles curated to challenge the mind and expand mathematical and logical thinking skills. First housed on cut-the-knot.org, these puzzles and their solutions represent the efforts of great minds around the world. Follow along as Alexander Bogomolny presents these selected riddles by topical progression. Try them for yourself before reading their solutions. Just like it was for Alexander the Great, the non-trivial, unexpected solution might be exactly the one you need." -- from amazon.com

Book by Paul R. Halmos