How to Solve It

How to Solve It Author G. Polya
ISBN-10 9781400828678
Year 2014-10-26
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.

How to Think Like a Mathematician

How to Think Like a Mathematician Author Kevin Houston
ISBN-10 1139477056
Year 2009-02-12
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.

How to Solve it

How to Solve it Author George Pólya
ISBN-10 0691023565
Year 1971
Pages 253
Language en
Publisher
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Professor Polya explains the history, techniques, and applications of heuristic reasoning for students and teachers

The Stanford Mathematics Problem Book

The Stanford Mathematics Problem Book Author G. Polya
ISBN-10 9780486318325
Year 2013-04-09
Pages 80
Language en
Publisher Courier Corporation
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Based on Stanford University's well-known 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.

How to Prove It

How to Prove It Author Daniel J. Velleman
ISBN-10 9781139450973
Year 2006-01-16
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 step-by-step 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.

Mining of Massive Datasets

Mining of Massive Datasets Author Jure Leskovec
ISBN-10 9781107077232
Year 2014-11-13
Pages 476
Language en
Publisher Cambridge University Press
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Now in its second edition, this book focuses on practical algorithms for mining data from even the largest datasets.

How to Solve It Modern Heuristics

How to Solve It  Modern Heuristics Author Zbigniew Michalewicz
ISBN-10 3540224947
Year 2004-09-21
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.

Mathematical Problem Solving

Mathematical Problem Solving Author ALAN H. SCHOENFELD
ISBN-10 9781483295480
Year 2014-06-28
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 "higher-order thinking skills" in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving 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 problem-solving 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.

Street Fighting Mathematics

Street Fighting Mathematics Author Sanjoy Mahajan
ISBN-10 9780262265591
Year 2010-03-05
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 Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, 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. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year 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.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Solving Mathematical Problems

Solving Mathematical Problems Author Terence Tao
ISBN-10 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.

Infinity and the Mind

Infinity and the Mind Author Rudy Rucker
ISBN-10 9785885010894
Year
Pages
Language en
Publisher Рипол Классик
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The book contains popular expositions (accessible to readers with no more than a high school mathematics background) on the mathematical theory of infinity, and a number of related topics. These include G?del's incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt G?del.An appendix contains one of the few popular expositions on set theory research on what are known as "strong axioms of infinity."

Mathematical Discovery on Understanding Learning and Teaching Problem Solving

Mathematical Discovery on Understanding  Learning  and Teaching Problem Solving Author George Pólya
ISBN-10 4871878317
Year 2009
Pages 236
Language en
Publisher
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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.

Problem Solving Through Problems

Problem Solving Through Problems Author Loren C. Larson
ISBN-10 9781461254980
Year 2012-12-06
Pages 352
Language en
Publisher Springer Science & Business Media
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This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

A Mathematical Mosaic

A Mathematical Mosaic Author Ravi Vakil
ISBN-10 1895997046
Year 1996-01
Pages 254
Language en
Publisher Brendan Kelly Publishing Inc.
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Excerpt from a review in the "Mathematics Teacher." A Mathematical Mosaic is a collection of wonderful topics from nmber theory through combinatorics to game theory, presented in a fashion that seventh- and eighth- grade students can handle yet high school students will find challenging." John Cocharo, Saint Mark's School of Texas, Dallas, TX