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What Is Mathematics

Author: Richard Courant
Publisher: Oxford University Press, USA
ISBN: 9780195105193
Size: 61.86 MB
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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

What Is Mathematics

Author: the late Richard Courant
Publisher: Oxford University Press
ISBN: 9780199754878
Size: 39.42 MB
Format: PDF
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For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.

What Is Mathematics

Author: Richard Courant
Publisher: Oxford University Press, USA
ISBN: 0195105192
Size: 69.61 MB
Format: PDF, Mobi
View: 3035
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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

What Is Mathematics

Author: Richard Courant
Publisher: Oxford University Press, USA
ISBN:
Size: 61.61 MB
Format: PDF, ePub, Docs
View: 5357
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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning

Concepts Of Modern Mathematics

Author: Ian Stewart
Publisher: Courier Corporation
ISBN: 0486134954
Size: 77.55 MB
Format: PDF, ePub, Mobi
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In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

What Is Mathematics Really

Author: Reuben Hersh
Publisher: Oxford University Press, USA
ISBN: 9780195130874
Size: 34.12 MB
Format: PDF, Mobi
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Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

Mathematics

Author: A. D. Aleksandrov
Publisher: Courier Corporation
ISBN: 0486157873
Size: 71.62 MB
Format: PDF, Kindle
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Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

Mathematics And The Physical World

Author: Morris Kline
Publisher: Courier Corporation
ISBN: 0486136310
Size: 36.17 MB
Format: PDF, Kindle
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Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

Mathematics

Author: Morris Kline
Publisher: Oxford University Press, USA
ISBN: 9780195030853
Size: 33.61 MB
Format: PDF, ePub
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Refuting the accepted belief that mathematics is exact and infallible, the author examines the development of conflicting concepts of mathematics and their implications for the physical, applied, social, and computer sciences