Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving

Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving PDF Author: George Pólya
Publisher:
ISBN: 9784871878319
Category : Mathematics
Languages : en
Pages : 236

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Book Description
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.

Proofs and Refutations

Proofs and Refutations PDF Author: Imre Lakatos
Publisher: Cambridge University Press
ISBN: 9780521290388
Category : Mathematics
Languages : en
Pages : 190

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Book Description
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.

How Not to Be Wrong

How Not to Be Wrong PDF Author: Jordan Ellenberg
Publisher: Penguin Press
ISBN: 1594205221
Category : Mathematics
Languages : en
Pages : 480

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Book Description
A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

The Stanford Mathematics Problem Book

The Stanford Mathematics Problem Book PDF Author: George Polya
Publisher: Courier Corporation
ISBN: 048631832X
Category : Mathematics
Languages : en
Pages : 82

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Book Description
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.

Geometrical Landscapes

Geometrical Landscapes PDF Author: Amir R. Alexander
Publisher: Stanford University Press
ISBN: 9780804732604
Category : Science
Languages : en
Pages : 318

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Book Description
This challenging book argues that a new way of speaking of mathematics and describing it emerged at the end of the 16th century. Leading mathematicians began referring to their field in terms drawn from the exploration accounts of Columbus and Magellan. Many of those who promoted the vision of mathematics as heroic exploration also played central roles in developing the most important mathematical innovation of the period?the infinitesimal methods, which the author shows was no coincidence.

Science and Method

Science and Method PDF Author: Henri Poincaré
Publisher: Courier Corporation
ISBN: 9780486432694
Category : Mathematics
Languages : en
Pages : 308

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Book Description
Classic account of basic methodology and psychology of scientific discovery explains how scientists analyze and choose their working facts and explores the nature of experimentation, theory, and the mind. 1914 edition.

Pattern Discovery in Bioinformatics

Pattern Discovery in Bioinformatics PDF Author: Laxmi Parida
Publisher: CRC Press
ISBN: 1420010735
Category : Computers
Languages : en
Pages : 542

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Book Description
The computational methods of bioinformatics are being used more and more to process the large volume of current biological data. Promoting an understanding of the underlying biology that produces this data, Pattern Discovery in Bioinformatics: Theory and Algorithms provides the tools to study regularities in biological data. Taking a systema

What's Happening in the Mathematical Sciences

What's Happening in the Mathematical Sciences PDF Author: Barry Cipra
Publisher: American Mathematical Soc.
ISBN: 9780821890431
Category : Science
Languages : en
Pages : 108

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Book Description
Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.

Mathematics and Plausible Reasoning [Two Volumes in One]

Mathematics and Plausible Reasoning [Two Volumes in One] PDF Author: George Polya
Publisher:
ISBN: 9781614275572
Category : Mathematics
Languages : en
Pages : 498

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Book Description
2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket.

Computational Discovery of Scientific Knowledge

Computational Discovery of Scientific Knowledge PDF Author: Saso Dzeroski
Publisher: Springer
ISBN: 3540739203
Category : Language Arts & Disciplines
Languages : en
Pages : 333

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Book Description
This survey provides an introduction to computational approaches to the discovery of communicable scientific knowledge and details recent advances. It is partly inspired by the contributions of the International Symposium on Computational Discovery of Communicable Knowledge, held in Stanford, CA, USA in March 2001, a number of additional invited contributions provide coverage of recent research in computational discovery.