
Author 
G. Polya 
ISBN10 
9781400828678 
Year 
20141026 
Pages 
288 
Language 
en 
Publisher 
Princeton University Press 
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A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out—from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft—indeed, brilliant—instructions on stripping away irrelevancies and going straight to the heart of the problem.

Author 
G. Polya 
ISBN10 
9780691119663 
Year 
20040425 
Pages 
253 
Language 
en 
Publisher 
Princeton University Press 
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Outlines a method of solving mathematical problems for teachers and students based upon the four steps of understanding the problem, devising a plan, carrying out the plan, and checking the results.
Professor Polya explains the history, techniques, and applications of heuristic reasoning for students and teachers

Author 
G. Polya 
ISBN10 
9780486318325 
Year 
20130409 
Pages 
80 
Language 
en 
Publisher 
Courier Corporation 
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Based on Stanford University's wellknown competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Author 
Terence Tao 
ISBN10 
9780199205615 
Year 
2006 
Pages 
103 
Language 
en 
Publisher 
OUP Oxford 
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Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the tactics involved in solving mathematical problems at the Mathematical Olympiad level. With numerous exercises and assuming only basic mathematics, this text is ideal for students of14 years and above in pure mathematics.

Author 
Daniel J. Velleman 
ISBN10 
9781139450973 
Year 
20060116 
Pages 

Language 
en 
Publisher 
Cambridge University Press 
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Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a stepbystep breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Author 
Kevin Houston 
ISBN10 
1139477056 
Year 
20090212 
Pages 

Language 
en 
Publisher 
Cambridge University Press 
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Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof  direct method, cases, induction, contradiction and contrapositive  are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

Author 
Razvan Gelca 
ISBN10 
9780387684451 
Year 
20070811 
Pages 
798 
Language 
en 
Publisher 
Springer Science & Business Media 
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Putnam and Beyond takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problemsolving at the high school level to the university and beyond, that is, to mathematical research.

Author 
ALAN H. SCHOENFELD 
ISBN10 
9781483295480 
Year 
20140628 
Pages 
409 
Language 
en 
Publisher 
Elsevier 
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This book is addressed to people with research interests in the nature of mathematical thinking at any level, to people with an interest in "higherorder thinking skills" in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problemsolving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, "rules of thumb" for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problemsolving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior.

Author 
Sanjoy Mahajan 
ISBN10 
9780262265591 
Year 
20100305 
Pages 
152 
Language 
en 
Publisher 
MIT Press 
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In problem solving, as in street fighting, rules are for fools: do whatever works  don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In StreetFighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and downanddirty, opportunistic problem solving across diverse fields of knowledge  from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool  the general principle  from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. StreetFighting Mathematics grew out of a short course taught by the author at MIT for students ranging from firstyear undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.StreetFighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Author 
Zbigniew Michalewicz 
ISBN10 
3540224947 
Year 
20040921 
Pages 
554 
Language 
en 
Publisher 
Springer Science & Business Media 
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No pleasure lasts long unless there is variety in it. Publilius Syrus, Moral Sayings We've been very fortunate to receive fantastic feedback from our readers during the last four years, since the first edition of How to Solve It: Modern Heuristics was published in 1999. It's heartening to know that so many people appreciated the book and, even more importantly, were using the book to help them solve their problems. One professor, who published a review of the book, said that his students had given the best course reviews he'd seen in 15 years when using our text. There can be hardly any better praise, except to add that one of the book reviews published in a SIAM journal received the best review award as well. We greatly appreciate your kind words and personal comments that you sent, including the few cases where you found some typographical or other errors. Thank you all for this wonderful support.

Author 
Imre Lakatos 
ISBN10 
0521290384 
Year 
19760101 
Pages 
174 
Language 
en 
Publisher 
Cambridge University Press 
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Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.
George Polya was a Hungarian mathematician. Born in Budapest on 13 December 1887, his original name was Polya Gyorg. He wrote perhaps the most famous book of mathematics ever written, namely "How to Solve It." However, "How to Solve It" is not strictly speaking a math book. It is a book about how to solve problems of any kind, of which math is just one type of problem. The same techniques could in principle be used to solve any problem one encounters in life (such as how to choose the best wife ). Therefore, Polya wrote the current volume to explain how the techniques set forth in "How to Solve It" can be applied to specific areas such as geometry.

Author 
Bonnie Averbach 
ISBN10 
9780486131740 
Year 
20120315 
Pages 
480 
Language 
en 
Publisher 
Courier Corporation 
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Fascinating approach to mathematical teaching stresses use of recreational problems, puzzles, and games to teach critical thinking. Logic, number and graph theory, games of strategy, much more. Includes answers to selected problems. Free solutions manual available for download at the Dover website.