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Problems and Theorems in Analysis II

Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry

Few mathematical books are worth translating 50 years after original publication. Polyá-Szegö is one! It was published in German in 1924, and its English edition was widely acclaimed when it appeared in 1972. In the past, more of the leading mathematicians proposed and solved problems than today. Their collection of the best in analysis is a heritage of lasting value.

From the reviews: ".

Mathematics and Plausible Reasoning: Patterns of plausible inference

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. II, on Patterns of Plausible Inference, attempts to develop a logic of plausibility. What makes some evidence stronger and some weaker? How does one seek evidence that will make a suspected truth more probable? These questions involve philosophy and psychology as well as mathematics.

Volume I: Induction and Analogy in Mathematics Volume II: Patterns of Plausible
Inference G. Polya 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 ...

George Pólya - Collected Papers

Location of Zeros

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

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

Mathematics and Plausible Reasoning: Induction and analogy in mathematics

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. I, on Induction and Analogy in Mathematics, covers a wide variety of mathematical problems, revealing the trains of thought that lead to solutions, pointing out false bypaths, discussing techniques of searching for proofs. Problems and examples challenge curiosity, judgment, and power of invention.

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity.

The Stanford Mathematics Problem Book

With Hints and Solutions

Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Problems and Theorems in Analysis I

Series. Integral Calculus. Theory of Functions

From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems." Bulletin of the American Mathematical Society

This picture shows G. Pólya (r.) and G. Szegó (1.) delivering their original
manuscript to Springer in Berlin in 1925 (courtesy of G. Alexanderson). George
Pólya Born in Budapest, December 13, 1887, George Pólya initially studied law,
then ...

Mathematical Methods in Science

This book captures some of Pólya's excitement and vision. Its distinctive feature is the stress on the history of certain elementary chapters of science; these can be a source of enjoyment and deeper understanding of mathematics even for beginners who have little, or perhaps no, knowledge of physics.

' This tenet underlies all of Professor Plya's works on teaching and problem-solving. This book captures some of Plya's excitement and vision.

Mathematical Discovery

Combining standard Volumes I and II into one soft cover edition, this helpful book explains how to solve mathematical problems in a clear, step-by-step progression. It shows how to think about a problem, how to look at special cases, and how to devise an effective strategy to attack and solve the problem. Covers arithemetic, algebra, geometry, and some elementary combinatorics. Includes an updated bibliography and newly expanded index.

Combining standard Volumes I and II into one soft cover edition, this helpful book explains how to solve mathematical problems in a clear, step-by-step progression.

Functional Equations and How to Solve Them

Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.

Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap.