Biographical Memoirs Volume 59 (1990) / Chapter Skim
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George Pólya
George Pólya
Pages 338-355
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ones. Although his main mathematical interest was in analysis, at the peak of his career he was contributing not only to real and complex analysis, but also to probability, combinatorics, occasionally to algebra and number theory, and to the theory of proportional representation and voting.
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Polya's papers were published in four volumes: the first two devoted to complex analysis, the third to other branches of analysis including mathematical physics, the fourth to probability, combinatorics, and teaching and learning in mathematics.] ORIGINS AND CAREER Polya was born in Budapest on December 13, 1887, and died in Palo Alto, California, September 7, 1985.
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These include limit laws (Polya also named the central limit theorem) , the continuity theorem for moments, stable distributions, the theory of contagion and exchangeable sequences of random variables, and the roots of random polynomials.
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According to Fabry's famous gap theorem, the circle of convergence of a power series is a natural boundary if the density of zero coefficients is I P6lya proved that no weaker condition will suffice for the same conclusion.
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The whole subject originatect with P6lya's discovery (1915, 2) that 2Z is the "smallest" entire function, not a polynomial, that has integral values at the positive integers.
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, the zeros of its successive derivatives become concentrated near the polygon whose points are equidistant from the two nearest poles. The situation for entire functions is much more complex, ant!
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COMBINATORICS Combinatorics aciciresses questions about the number of ways there are to clo something that is too complicated to be analyzed intuitively. Polya's chief discovery was the enumeration of the isomers of a chemical compound, that is, the chemical compounds with different properties but the same numbers of each of their constituent elements.
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P6lya was interested in estimating quantities of physical interest connected with particular domains, as, for example, electrostatic capacitance, torsional rigidity, and the lowest vibration frequency. Usually one wants an estimate for some property of a domain in terms of another.
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TEACHING AND LEARNING MATHEMATICS Polya believed that one should learn mathematics by solving problems. This led him to write, with G
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Whether heuristics can really be successful on a large scale as a teaching technique has not yet been established. Some researchers in artificial intelligence have not found it elective for teaching mathematics.
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Uber einen Zusammenhang zwischen der Konvergenz von Polynomfolgen und der Verteilung ihrer Wurzeln.
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.. Uber den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem.
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Ann., 88: 169-83. Uber die Existenz unendlich vieler singularer Punkte auf der Konvergenzgeraden gewisser Dirichletscher Reihen.
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Mech., 13: 125-28. Untersuchungen uber Lucken und Singularitaten von Potenzreihen.
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Acta Math., 68: 145-254. Uber die Realitat der Nullstellen fast alter Ableitungen gewisser ganzer Funktionen.
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Princeton: Princeton University Press. 1952 Sur une interpretation de la methode des differences finies qui pent fournir des bornes superieures ou inferieures.
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Revised and enlarged English language version of 1925,1.
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