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ISBN: 9782701147376 2701147379 Year: 2008 Publisher: Paris: Belin,
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Mathematics --- Mathematicians --- Mathématiques --- Mathématiciens --- Research --- Recherche --- Psychology --- Mathématiques --- Mathématiciens --- Mathematicians - Psychology --- Mathematics - Research
ISBN: 9780801885877 0801885876 9780801896897 0801896894 Year: 2007 Publisher: Baltimore: Johns Hopkins University press,
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ISBN: 0691150915 0691145997 1400833957 128253145X 9786612531453 0691127387 9780691127385 9781400833955 6612531452 9781282531451 9780691145990 Year: 2007 Publisher: Princeton Princeton University Press
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To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
Mathematicians --- Mathematics --- Psychology --- Social Sciences --- Psychological aspects --- Philosophy --- Logic of mathematics --- Mathematics, Logic of --- Math --- Science --- Scientists --- Psychology. --- Psychological aspects. --- Philosophy. --- Mathematicians - Psychology --- Mathematics - Psychological aspects --- Mathematics - Philosophy
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ISBN: 1461470331 146147034X Year: 2014 Publisher: New York : Birkhauser,
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Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi.
Mathematical analysis. --- Numerical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Gautschi, Walter. --- Mathematicians -- Psychology. --- Mathematics. --- Computer science --- Approximation theory. --- Differential equations. --- History. --- Numerical Analysis. --- Mathematics of Computing. --- Approximations and Expansions. --- History of Mathematical Sciences. --- Ordinary Differential Equations. --- Computer science. --- Differential Equations. --- 517.91 Differential equations --- Differential equations --- Math --- Science --- Informatics --- Computer science—Mathematics. --- Annals --- Auxiliary sciences of history --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Computer mathematics --- Electronic data processing --- Mathematics --- Functions, Special. --- Interpolation. --- Mathematicians.
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