Mathematics and Plausible Reasoning: Vol. II: Patterns of Plausible Inference

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9784871878340: Mathematics and Plausible Reasoning: Vol. II: Patterns of Plausible Inference

This is a guide to the practical art of plausible reasoning, particularly in mathematics but also in every field of human activity. Using mathematics as the example par excellence, Professor Polya shows how even that most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can even begin, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but not proved until much later. In the same way, solutions to problems can be guessed, and a good guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser." Professor Polya's deep understanding of the psychology of creative mathematics enables him to show the reader how to attack a new problem, how to get at the heart of it, what trains of thought may lead to a solution. There is no magic formula here, but there is much practical wisdom. Volumes I and II together make a coherent work on Mathematics and Plausible Reasoning. Volume I on Induction and Analogy stands by itself as an essential book for anyone interested in mathematical reasoning. Volume II on Patterns o f Plausible Inference builds on the examples of Volume I but is not otherwise dependent on it. A more sophisticated reader with some mathematical experience will have no difficulty in reading Volume II independently, though he will probably want to read Volume I afterward. Professor Polya's earlier more elementary book How to Solve It was closely related to Mathematics and Plausible Reasoning and furnished some background for it.

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About the Author:

George Polya was a Hungarian mathematician. Born in Budapest on 13 December 1887, his original name was Pólya Györg. He wrote “How to Solve It”, perhaps the most famous book of mathematics ever written, second only to Euclid's “Elements”. George Polya continued to work on mathematics, even past age 90. He died in Palo Alto, California on September 7, 1985, at age 97.


Thanks so much for all you have done to honor your Uncle Matty and the great paratroopers of the 82nd Airborne Division in the liberation of France. He died to make others free -- there is no higher honor.

--Airborne All the Way! General Mark Milley, U.S. Army*

Your Uncle Martin Teahan's rifle is a special piece of history. He must be smiling from Paratroopers' Heaven.

--Brigadier General Patrick Collet, Commanding Officer, 11th Parachute Brigade, French Army (Armee de Terre)

I was in the same company as Private Martin Teahan when we both jumped into Normandy on June 6, 1944. He ran around with one of the commo [communication] platoon Sergeants, O.B. Hill, and sang a lot of country songs. Being from Oklahoma, I was always there, listening. If I could say one word to Teahan, it would be this: "The bond that existed when you left the 508th PIR still exists today, some 73 years later, due to your friend Sergeant O.B. Hill and the officers and members of the Family and Friends of the 508th PIR Association.

--Retired Command Sergeant Major Kenneth J. "Rock" Merritt, HQ Co., 1st BN 508TH PIR (1942-1946)

Jim Farrell has brought his hero Uncle Matty back to life as he traces the fascinating journey of Matty's rifle from the battlefield where he was slain to its display in the office of 39th Army Chief of Staff General Mark A. Milley more than 70 years after Matty's death. It is an incredible, one-of-a-kind story, written with eloquence and emotion.

--Dick O'Donnell, National Chairman, Family and Friends of the 508th PIR Association

The story of Matty Teahan's rifle, and the determination of his nephew to honor a fallen family hero, is one of the most inspiring and poignant stories I have ever reported on in my 50 years as a journalist. Jim Farrell's Uncle Matty Comes Home is a fitting tribute and epitaph to one man's sacrifice for the cause of freedom.

--Andrew Smart, Features Department, Nottingham Post, England

* Disclaimer: The above quote is my own and does not necessarily reflect the views of the Department of Defense or its components.

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