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Knowing and Teaching Elementary Mathematics

Liping Ma, Liping Ma • Routledge eBooks (1999)

Chinese students typically outperform U.S. students on international comparisons of mathematics competency. Paradoxically, Chinese teachers receive far less education than U.S. teachers--11 to 12 years of schooling versus 16 to 18 years of ...

OPENALEX DOI: https://doi.org/10.4324/9781410602589

Mathematical Logic

Willard Van Orman Quine • Harvard University Press eBooks (1951)

W. V. Quine’s systematic development of mathematical logic has been widely praised for the new material presented and for the clarity of its exposition. This revised edition, in which the minor inconsistencies observed since its first publi...

OPENALEX DOI: https://doi.org/10.4159/9780674042469

Mathematical Analysis

Vladimir Igorevich Arnol'd • Birkhäuser Basel eBooks (1990)

Newton remarked that the laws of nature are expressed by the differential equations that he devised. Individual, and at times very important, differential equations had been considered and solved even earlier, but Newton turned them into an...

OPENALEX DOI: https://doi.org/10.1007/978-3-0348-9129-5_3

Mathematics and Reality

Mary Leng • Oxford University Press eBooks (2010)

Mary Leng defends a philosophical account of the nature of mathematics which views it as a kind of fiction (albeit an extremely useful fiction)....

OPENALEX DOI: https://doi.org/10.1093/acprof:oso/9780199280797.001.0001

“Theoretical mathematics”: toward a cultural synthesis of mathematics and theoretical physics

Arthur M. Jaffe, Frank Quinn • Bulletin of the American Mathematical Society (1993)

Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice the...

OPENALEX Open Access DOI: https://doi.org/10.1090/s0273-0979-1993-00413-0

Philosophy of Mathematics

• Cambridge University Press eBooks (1984)

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematic...

OPENALEX DOI: https://doi.org/10.1017/cbo9781139171519

Mathematics for Physics

Michael Stone, Paul M. Goldbart • Cambridge University Press eBooks (2009)

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of ph...

OPENALEX DOI: https://doi.org/10.1017/cbo9780511627040

Mathematical and Physical Papers

WILLIAM J. THOMSON • Cambridge University Press eBooks (2011)

William Thomson, first Baron Kelvin (1824–1907), is best known for devising the Kelvin scale of absolute temperature and for his work on the first and second laws of thermodynamics, though throughout his 53-year career as a mathematical phy...

OPENALEX DOI: https://doi.org/10.1017/cbo9780511996016

Varieties of Constructive Mathematics

Douglas Bridges, Fred Richman • Cambridge University Press eBooks (1987)

This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, wit...

OPENALEX DOI: https://doi.org/10.1017/cbo9780511565663

The Philosophy of Mathematical Practice

Paolo Mancosu • Oxford University Press eBooks (2008)

Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, ...

OPENALEX DOI: https://doi.org/10.1093/acprof:oso/9780199296453.001.0001

What is mathematics, really?

• Choice Reviews Online (1998)

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 evolv...

OPENALEX DOI: https://doi.org/10.5860/choice.35-5132