This is the third volume of the collected papers of George Pólya, one of the most influential mathematicians and teachers of our time. Volumes I (Singularities of Analytic Functions) and II (Location of Zeros) were published in 1974. Volume III contains 58 papers spanning Pólya's career (the earliest is from 1913, the latest from 1976) and covering a wide range of subjects in mathematical analysis and mathematical physics. The commentaries on these papers attest to the fertility and continued importance of Pólya's ideas in current mathematics. This volume is the twenty-second in the series Mathematicians of Our Time, edited by Gian-Carlo Rota.

George Pólya: Collected Papers, Vol. 3: Analysis (Mathematicians of Our Time)

Science & Math

Pólya, George

Rota, Gian-Carlo

Hersh, Joseph

Mathematics

Mit Pr

This volume completes the publication of the collected papers of George Pólya, one of the most influential mathematicians and teachers of our time. Volumes I (Singularities of Analytic Functions) and II (Location of Zeros) were published in 1974.  Volume IV presents 20 papers on probability, 17 on combinatorics, and 18 on the teaching and learning of mathematics. Pólya has made a number of fundamental contributions to the first two fields, including perhaps the first use of the term "central limit theorem," but his major influence on mathematics has clearly been his approach to pedagogy. Many of the papers throughout these volumes have a strongly pedagogical flavor, but the papers in the third section of this volume focus squarely on the real business of how to do mathematics—how to formulate a problem and then create a solution.  This volume is the twenty-third in the series Mathematicians of Our Time, edited by Gian-Carlo Rota.

Collected Papers, Vol. 4: Probability / Combinatorics / Teaching and Learning in Mathematics (George Polya, Collected Papers, Vol. 4) (English, French and German Edition)

Papers on the location and behavior of zeros, including some of Polya's most influential work.

George Pólya: Collected Papers, Volume 2: Location of Zeros (Mathematicians of Our Time)

Evolution

MIT Press]

The first volume of Polya's papers deals with singular points of analytic functions and with other broadly related topics, such as conformal mappings, entire functions, and the rate of growth of analytic functions. The papers are arranged in chronological order, but the editor, in his introduction, shows that they fall into four main sets of topics.The first is concerned with properties of a function (in particular, the location and nature of its singular points) as deduced from the properties of the coefficients in its power series.A second set deals with a closely related problem: connections between global properties of a function and its values at an isolated set of points. Analytic functions, especially entire functions, are the subject of a third set of papers, and a final set of six investigates problems in conformal mapping.

George Polya: Collected Papers, Singularities of Analytic Functions (Mathematicians of Our Time)

In 1937 there appeared a paper that was to have a profound influence on the progress of combinatorial enumeration, both in its theoretical and applied aspects. Entitled Kombinatorische Anzahlbest immungen jUr Gruppen, Graphen und chemische Verbindungen, it was published in Acta Mathematica, Vol. 68, pp. 145 to 254. Its author, George Polya, was already a mathematician of considerable stature, well-known for outstanding work in many branches of mathematics, particularly analysis. The paper in Question was unusual in that it depended almost entirely on a single theorem -- the "Hauptsatz" of Section 4 -- a theorem which gave a method for solving a general type of enumera tion problem. On the face of it, this is not something that one would expect to run to over 100 pages. Yet the range of the applica tions of the theorem and of its ramifications was enormous, as Polya clearly showed. In the various sections of his paper he explored many applications to the enumeration of graphs, principally trees, and of chemical isomers, using his theorem to present a comprehen sive and unified treatment of problems which had previously been solved, if at all, only by ad hoc methods. In the final section he investigated the asymptotic properties of these enumerational results, bringing to bear his formidable insight as an analyst.

Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds

Read, R.C.

Springer

Mathematical Discovery Volume 1

Wiley, John Sons

A unique, heuristic approach to mathematical discovery and problem solving This combined edition of Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving is unique among mathematics texts. Espousing a heuristic approach to mathematical problem solving, the text may be followed sequentially or according to instructors' individualized curricula. Beginning with a discussion of patterns and practical approaches to problem solving, the book then presents examples from various branches of math and science to help students discover how to solve problems on their own – an invaluable skill for the classroom and beyond.

Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving Combined Edition

Business & Money

Management & Leadership

wiley

Complex variables

John Wiley&Sons, Inc.

“Solving problems”, writes Polya, “is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice. This book cannot offer you a magic key that opens all the doors and solves all the problems, but it offers you good examples for imitation and many opportunities for practice: If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.” “In enough cases to allay ... discouragement over not immediately discovering a solution, Professor Polya masterfully leads the reader down several unproductive paths. At the end of each chapter he provides examples for the render to solve. By means of these carefully selected and arranged problems, many of them directly related to others that precede, and guided by just the right suggestions at just the proper time, the reader's own ability is developed and extended. Solutions to the examples and, in many cases, outlines of procedures for discovering solutions. arc given at the back of the book. With striking promise for effectiveness, the  entire book as a unit is one great experience in learning processes for problem solving through participation. The author has captured with great success the implication of his basic premise stated in the preface ...”  The Mathematics Teacher  218 pages.

Mathematical Discovery, Volume II, On Understanding, Learning, and Teaching Problem Solving

Here the author of How to Solve It explains how to become a "good guesser" Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.

Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics

Humor & Entertainment

Puzzles & Games

Princeton University Press

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