Search Results for "what-is-mathematics-an-elementary-approach-to-ideas-and-methods"

What is Mathematics?

What is Mathematics?

An Elementary Approach to Ideas and Methods

  • Author: Richard Courant,Herbert Robbins,Ian Stewart
  • Publisher: Oxford University Press, USA
  • ISBN: 9780195105193
  • Category: Mathematics
  • Page: 566
  • View: 4634
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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

What is Mathematics?

What is Mathematics?

An Elementary Approach to Ideas and Methods

  • Author: Richard Courant,Herbert Robbins
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: 521
  • View: 3027
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Perfect Rigor

Perfect Rigor

A Genius and the Mathematical Breakthrough of the Century

  • Author: Masha Gessen
  • Publisher: Houghton Mifflin Harcourt
  • ISBN: 0547427565
  • Category: Biography & Autobiography
  • Page: 256
  • View: 7697
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A gripping and tragic tale that sheds rare light on the unique burden of genius In 2006, an eccentric Russian mathematician named Grigori Perelman solved the Poincare Conjecture, an extremely complex topological problem that had eluded the best minds for over a century. A prize of one million dollars was offered to anyone who could unravel it, but Perelman declined the winnings, and in doing so inspired journalist Masha Gessen to tell his story. Drawing on interviews with Perelman’s teachers, classmates, coaches, teammates, and colleagues in Russia and the United States—and informed by her own background as a math whiz raised in Russia—Gessen uncovered a mind of unrivaled computational power, one that enabled Perelman to pursue mathematical concepts to their logical (sometimes distant) end. But she also discovered that this very strength turned out to be Perelman's undoing and the reason for his withdrawal, first from the world of mathematics and then, increasingly, from the world in general.

Computable Foundations for Economics

Computable Foundations for Economics

  • Author: K. Vela Velupillai
  • Publisher: Routledge
  • ISBN: 1134253362
  • Category: Business & Economics
  • Page: 512
  • View: 8449
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Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode completely non-algorithmic, which means it is numerically meaningless. The book provides a systematic attempt to dissect and expose the non-algorithmic content of orthodox mathematical economics and game theory and suggests a reformalization on the basis of a strictly rigorous algorithmic mathematics. This removes the current schizophrenia in mathematical economics and game theory, where theory is entirely divorced from algorithmic applicability – for experimental and computational exercises. The chapters demonstrate the uncomputability and non-constructivity of core areas of general equilibrium theory, game theory and recursive macroeconomics. The book also provides a fresh look at the kind of behavioural economics that lies behind Herbert Simon’s work, and resurrects a role for the noble classical traditions of induction and verification, viewed and formalised, now, algorithmically. It will therefore be of particular interest to postgraduate students and researchers in algorithmic economics, game theory and classical behavioural economics.

Approaching Infinity

Approaching Infinity

  • Author: M. Huemer
  • Publisher: Springer
  • ISBN: 1137560878
  • Category: Philosophy
  • Page: 275
  • View: 9781
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Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes.

Math Teacher's Survival Guide: Practical Strategies, Management Techniques, and Reproducibles for New and Experienced Teachers, Grades 5-12

Math Teacher's Survival Guide: Practical Strategies, Management Techniques, and Reproducibles for New and Experienced Teachers, Grades 5-12

  • Author: Judith A. Muschla,Gary Robert Muschla,Erin Muschla
  • Publisher: John Wiley & Sons
  • ISBN: 9780470574997
  • Category: Education
  • Page: 368
  • View: 796
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Classroom-tested strategies to help new and experienced math teachers thrive Math teachers must not only instruct their students in basic mathematical skills and concepts, they must also prepare them for standardized tests, provide instruction in the use of technology, and teach problem-solving and critical-thinking skills. At the same time, they must also manage their other responsibilities – taking attendance, planning, grading, record-keeping, disciplining, and communicating with parents and administrators. This book provides efficient and practical information on the management skills necessary to succeed in this most challenging profession. Offers realistic suggestions and strategies for planning and delivering effective math instruction Helps math teachers achieve excellence and continue to be enthusiastic and successful in their teaching careers Includes reproducible forms to help math teachers stay on top of everything they need to do The Math Teacher's Survival Guide contains a wealth of useful tools and strategies that can help any math teacher succeed in the classroom.

Journey Into Geometries

Journey Into Geometries

  • Author: Marta Sved
  • Publisher: Cambridge University Press
  • ISBN: 9780883855003
  • Category: Mathematics
  • Page: 182
  • View: 3337
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Informal introduction into the non-Euclidean geometries through a series of dialogues involving Alice in Wonderland.

Elliptic Tales

Elliptic Tales

Curves, Counting, and Number Theory

  • Author: Avner Ash,Robert Gross
  • Publisher: Princeton University Press
  • ISBN: 1400841712
  • Category: Mathematics
  • Page: 280
  • View: 9317
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Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics—the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which may appear simple, but arise from some very deep—and often very mystifying—mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics.

Pythagoras

Pythagoras

Pioneering Mathematician and Musical Theorist of Ancient Greece

  • Author: Dimitra Karamanides
  • Publisher: The Rosen Publishing Group, Inc
  • ISBN: 9781404205000
  • Category: Juvenile Nonfiction
  • Page: 112
  • View: 5350
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Biography of the Greek philosopher Pythagoras and his lasting contributions on the fields of mathematics and philosophy.