What Is Mathematics

What is Mathematics  PDF
Author: Herbert Robbins Richard Courant (Ian Stewart)
Publisher: Oxford University Press, USA
ISBN: 9780195105193
Size: 62.62 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 566
View: 1546

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A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.

What Is Mathematics Really

What is Mathematics  Really  PDF
Author: Reuben Hersh
Publisher: Oxford University Press, USA
ISBN: 9780195130874
Size: 24.58 MB
Format: PDF, Docs
Category : Medical
Languages : en
Pages : 343
View: 6086

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Tries to refine the philosophy of mathematics to reflect what mathematicians really do, and argues that mathematics must be understood in a social context.

Mathematics A Very Short Introduction

Mathematics  A Very Short Introduction PDF
Author: Timothy Gowers
Publisher: Oxford Paperbacks
ISBN: 9780192853615
Size: 30.67 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 143
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The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought.

Hearings On Mathematics And Science Education

Hearings on Mathematics and Science Education PDF
Author: United States. Congress. House. Committee on Education and Labor. Subcommittee on Elementary, Secondary, and Vocational Education
Size: 68.67 MB
Format: PDF, ePub
Category : Federal aid to education
Languages : en
Pages :
View: 4179

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Mathematics PDF
Author: Morris Kline
Publisher: Oxford University Press, USA
ISBN: 9780195030853
Size: 60.16 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 366
View: 3992

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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

Cultural Foundations Of Mathematics

Cultural Foundations of Mathematics PDF
Author: C. K. Raju
Publisher: Pearson Education India
ISBN: 9788131708712
Size: 55.24 MB
Format: PDF, ePub, Docs
Category : Calculus
Languages : en
Pages : 477
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The Volume Examines, In Depth, The Implications Of Indian History And Philosophy For Contemporary Mathematics And Science. The Conclusions Challenge Current Formal Mathematics And Its Basis In The Western Dogma That Deduction Is Infallible (Or That It Is Less Fallible Than Induction). The Development Of The Calculus In India, Over A Thousand Years, Is Exhaustively Documented In This Volume, Along With Novel Insights, And Is Related To The Key Sources Of Wealth-Monsoon-Dependent Agriculture And Navigation Required For Overseas Trade - And The Corresponding Requirement Of Timekeeping. Refecting The Usual Double Standard Of Evidence Used To Construct Eurocentric History, A Single, New Standard Of Evidence For Transmissions Is Proposed. Using This, It Is Pointed Out That Jesuits In Cochin, Following The Toledo Model Of Translation, Had Long-Term Opportunity To Transmit Indian Calculus Texts To Europe. The European Navigational Problem Of Determining Latitude, Longitude, And Loxodromes, And The 1582 Gregorian Calendar-Reform, Provided Ample Motivation. The Mathematics In These Earlier Indian Texts Suddenly Starts Appearing In European Works From The Mid-16Th Century Onwards, Providing Compelling Circumstantial Evidence. While The Calculus In India Had Valid Pramana, This Differed From Western Notions Of Proof, And The Indian (Algorismus) Notion Of Number Differed From The European (Abacus) Notion. Hence, Like Their Earlier Difficulties With The Algorismus, Europeans Had Difficulties In Understanding The Calculus, Which, Like Computer Technology, Enhanced The Ability To Calculate, Albeit In A Way Regarded As Epistemologically Insecure. Present-Day Difficulties In Learning Mathematics Are Related, Via Phylogeny Is Ontogeny , To These Historical Difficulties In Assimilating Imported Mathematics. An Appendix Takes Up Further Contemporary Implications Of The New Philosophy Of Mathematics For The Extension Of The Calculus, Which Is Needed To Handle The Infinities Arising In The Study Of Shock Waves And The Renormalization Problem Of Quantum Field Theory.

A History Of Mathematics

A History of Mathematics PDF
Author: Florian Cajori
Publisher: American Mathematical Soc.
ISBN: 9780821821022
Size: 58.78 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 524
View: 6580

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Originally issued in 1893, this popular Fifth Edition (1991) covers the period from antiquity to the close of World War I, with major emphasis on advanced mathematics and, in particular, the advanced mathematics of the nineteenth and early twentieth centuries. In one concise volume, this unique book presents an interesting and reliable account of mathematics history for those who cannot devote themselves to an intensive study. The book is a must for personal and departmental libraries alike. Cajori has mastered the art of incorporating an enormous amount of specific detail into a smooth-flowing narrative. The Index - for example - contains not just the 300 to 400 names one would expect to find, but over 1,600. And, for example, one will not only find John Pell, but will learn who he was and some specifics of what he did (and that the Pell equation was named erroneously after him).In addition, one will come across Anna J. Pell and learn of her work on biorthogonal systems; one will find not only H. Lebesgue but the not unimportant (even if not major) V.A. Lebesgue. Of the Bernoullis one will find not three or four but all eight. One will find R. Sturm as well as C. Sturm; M. Ricci as well as G. Ricci; V. Riccati as well as J.F. Riccati; Wolfgang Bolyai as well as J. Bolyai; the mathematician Martin Ohm as well as the physicist G.S. Ohm; M. Riesz as well as F. Riesz; H.G. Grassmann as well as H. Grassmann; H.P. Babbage who continued the work of his father C. Babbage; R. Fuchs as well as the more famous L. Fuchs; A. Quetelet as well as L.A.J. Quetelet; P.M. Hahn and Hans Hahn; E. Blaschke and W. Blaschke; J. Picard as well as the more famous C.E. Picard; B. Pascal (of course) and also Ernesto Pascal and Etienne Pascal; and, the historically important V.J. Bouniakovski and W.A. Steklov, seldom mentioned at the time outside the Soviet literature.