Product Description
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. ... Read more

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"Solving problems", wrote 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." ... Read more

Customer Reviews (41)

Kindle edition poorly formatted
Good content, but reading it in the Kindle app for iPad is almost impossible.Holding the iPad in portrait orientation produces text in landscape layout; holding it in landscape orientation produces a portrait text layout.

As I have no issue with dozens of other Kindle edition books read on my iPad, I attribute this to the book being ~66 years old and so probably scanned into Kindle.

Very poorly done IMHO.

Not just math
I agree totally with other reviewers that the title is far too narrow. This book is useful to anyone who ever has to solve any problem--does that exclude anyone? My fridge broke while I was mid-read and I decided to try out some of Polya's main strategies. Amazingly applicable. (And the fridge works great now.)

One word of caution, after a brief structured section, the remainder of the book is arranged by alphabetical topics. After skimming the first few, I assumed that they were just obvious definitions and "notes" about the "body" of the book. That was a big mistake. Much as I hate alphabetical arrangement (particularly with seemingly randomly generated titles), the alphabetical section is where the best stuff is. And the "title" of the section is no help in finding the good ones. The best way for me to think about it was to just imagine it as a blog: some days he wrote a little nothing, other days he wrote something awesome. The crossreferences within the blog entries are helpful for finding the best entries.

Help, Insightful, A Great Resource
Joseph R. Dell'Aquila, Ph.D.
My first exposure to this book was probably as a young college student. When I started teaching physics and mathematics at the college and university level, I recommended this book to all of my students. Why? The table-like pages xvi - xvii are an excellent reminder of fruitful ways to understand, think about, attack and solve problems. Although I am a PhD in theoretical physics, I still dip into it occasionally when I need some insight or want to recall what I knew about approaching a problem. Is the book at that high a level? Of course not. It is a basic introduction to the fundamentals of problem solving. But remember that Michael Jordan, in "I Can't Accept Not Trying," always thanked Dean Smith, his famous college coach - who would bench Jordan if he got sloppy, for teaching him the fundamentals and Jordan said within a page of that: "fundamentals, that's what made Larry Bird such a great player." That is all this book is trying to give, fundamentals, and it does so brilliantly. To those whose reviews said it was not helpful and wanted to know where was the graduate level analysis, if you want to stick with Polya try Inequalities by G. H. Hardy, J. E. Littlewood, G. Pólya, all great to exceptional mathematicians with plenty of analysis to share and, for more specialized work, Isoperimetric Inequalities in Mathematical Physics by Polya and Szego. Note that one computer scientist/programmer disliked the book but another lauded it. I would never want to restrict dialogue on review but please check out the appropriateness and level of any book you buy. I have rarely written negative reviews on Amazon or elsewhere because I do my homework: using the Internet to find information on the work and even going to a library to see whether I like what their copy offers (I'm phrasing it this way because different editions, perhaps the library's edition vs. the one you're considering purchasing, can be quite different). Buy and use Polya appropriately.

One of the best Math books ever written
I first read this book some 35 yrs ago and the knowledge I acquired by studying itremained in my memory ever since, not because I have a great memory but because I have used this knowledge and heuristics again and again, first in the high school, then at the University, and later on in my career as a professional engineer. From D student in elementary school Math I first became A student in High School, then Math champion of the high school, then Math champion of the district and even went on to state championships competing with the best. I am not saying that only this book helped me in this transformation, but this book alone empowered me to be able to study other math books and solve all sorts of problems in math, and even science and engineering.
I highly recommend this book to any elementary, middle, high school, and even University student. The wisdom you will gain from this book will remain with you forever.

Not Worth the Time
Bought the book because it had great reviews and looked beneficial.Once I got it I read through the first couple of chapters and did not find it useful at all.I am an engineer and the the basic skills he presents are taught early on in the undergraduate curriculum.Needless to say I was very disappointed.This may be a good book for someone that is in high school to sharpen critical thinking skills. ... Read more

Product Description
A classic of this century that has had a lot of influence on teaching, & research in several branches of hard analysis, particularly complex function theory. An essential source book for mathematicians. Paper. DLC: Series, integral calculus, theory of functions. ... Read more

Customer Reviews (3)

WELL KNOWN BOOK,NO NEED OF INTRODUCTION BUT
IF YOU HAVE MORE AMBITION: TRY THE KING OF ALL MATHEMATICAL PROBLEMS!!!!!!!!!

Problems in Mathematical Analysis (Hardcover)
by g. yankovsky (Translator), B. Demidovich (Author
Publisher: mir publisher; 4th Printing edition (1976)
ASIN: B000GTC2GA

A Beautiful Classic
This book by Polya and Szego contains many wonderful gems of mathematics.The exercises are very interesting, and sometimes I pick the book up just for fun.I wish I had been able to purchase a hardcover copy. Unfortunately, it's only available in paperback.

This book is suitable for mathematics graduate students.

Excellent. A good way to start researches
The selected problems aren't the typical ones. The great beauty of manyresults are marvellous and, disposed in dificulty ascendent, are teh bestway to start researches. I teach in the University of Málaga and I'minterested in the second vol. ... Read more

Product Description
"Mathematics, taught and learned appropriately, improves the mind and implants good habits of thought. " This tenet underlies all of Professor Polya's works on teaching and problem-solving. The distinctive feature of the present book 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. ... Read more

Customer Reviews (1)

page turner
This book describes plausible arguments for different laws of physics, like how levers work.There is the right amount of causual prose, mathematics, history, and cleverness blended together.I was able to think of fluid dynamics with his style of approaching things.The principle of insufficient reason he describes led me to develop my own test to see whether cars on the other side of the road were going faster or slower than me, which is practicle for when you don't know the speed limit. ... Read more

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Developed from the authors’ introductory combinatorics course, this book focuses on a branch of mathematics which plays a crucial role in computer science. Combinatorial methods provide many analytical tools used for determining the expected performance of computer algorithms. Elementary subjects such as combinations and permutations, and mathematical tools such as generating functions and Pólya’s Theory of Counting, are covered, as are analyses of specific problems such as Ramsey Theory, matchings, and Hamiltonian and Eulerian paths.

This introduction will provide students with a solid foundation in the subject.

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"This is a delightful little paperback which presents a day-by-day transcription of a course taught jointly by Pólya and Tarjan at Stanford University. Woods, the teaching assistant for the class, did a very good job of merging class notes into an interesting mini-textbook; he also included the exercises, homework, and tests assigned in the class (a very helpful addition for other instructors in the field). The notes are very well illustrated throughout and Woods and the Birkhäuser publishers produced a very pleasant text.

One can count on [Pólya and Tarjan] for new insights and a fresh outlook. Both instructors taught by presenting a succession of examples rather than by presenting a body of theory…[The book] is very well suited as supplementary material for any introductory class on combinatorics; as such, it is very highly recommended. Finally, for all of us who like the topic and delight in observing skilled professionals at work, this book is entertaining and, yes, instructive, reading."

—Mathematical Reviews (Review of the original hardcover edition)

"The mathematical community welcomes this book as a final contribution to honour the teacher G. Pólya."

—Zentralblatt MATH (Review of the original hardcover edition)

Product Description
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. ... Read more

Customer Reviews (1)

As good as "How to Solve it"
If you enjoy the golden classic "How to solve it", this is the right next step.
"Mathematical Discovery" gives more concrete picture and Polya shows the edge of the wisdom.We have many logical mathematician but he is exceptional because every single problem and explanation is based on the real classroom and even the little advice gives a big help to the real math class.

... Read more

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From the reviews: "... In the past, more of the leading mathematicians proposed and solved problems than today, and there were problem departments in many journals. Pólya and Szego must have combed all of the large problem literature from about 1850 to 1925 for their material, and their collection of the best in analysis is a heritage of lasting value. The work is unashamedly dated. With few exceptions, all of its material comes from before 1925. We can judge its vintage by a brief look at the author indices (combined). Let's start on the C's: Cantor, Carathéodory, Carleman, Carlson, Catalan, Cauchy, Cayley, Cesàro,... Or the L's: Lacour, Lagrange, Laguerre, Laisant, Lambert, Landau, Laplace, Lasker, Laurent, Lebesgue, Legendre,... Omission is also information: Carlitz, Erdös, Moser, etc." - -Bull.Americ.Math.Soc. ... Read more

Customer Reviews (1)

THE BOOK OF PROBLEMS
Polya and Szego's 1923 two volumes of mathematics problems are still the best collections ofproblems for people who want to learn advanced undergraduate and graduate level mathematics.When I want to know something about zeros of polynomials, about inequalities for polynomials ortrigonometric polynomials, or determinants and quadratic forms, the firstplace I look is volume 2 of Polya and Szego.It is a great source ofproblems to give to students if you are a teacher, and the best set ofproblems to work through if you are learning mathematics at the advancedundergraduate level or higher. Volume 2 contains long chapters on complexvariables and number theory and some problems in geometry.Both volumesbelong on a shelf close to the desk of anyone who teaches college levelmathematics.They are also very useful for those who use mathematics.These two volumes are gems, and would be rated above 5 stars if possible. The German original is available here in a nice English translation. Somenew material was added when the translation was first published. ... Read more

Product Description
George Pólya was one of the giants of classical analysis in the 20th century, and the influence of his work can be seen far beyond analysis, into number theory, geometry, probability and combinatorics. This book serves both as a biography of Pólya's life, and a review of his many mathematical achievements by experts from a wide range of different fields. Last but not least the book finishes with two essays by Pólya himself which focus on how to learn to solve problems, a subject with which he was fascinated throughout his life. ... Read more

Customer Reviews (2)

George Polya and his times.
Even if you aren't in math, I think you are likely to be caught up in the drama of George Polya and the various lives, the times, and the events that he touched. The writing is fast paced and engaging, much like that of Constance Reid's books: "Hilbert", or "Courant"... Through its appendices [by K.L. Chung, R. P. Boas, M. M. Schiffer...], this lovely book further gives you some insight into the math that underlies the stories. Other characters in the book: G. Szego, L. Fejer, J von Neumann, G. H. Hardy, H. Weyl, E. Landau, ...Through the book, the reader gets to experience the tumultous historical period that spans the long career of G. Polya: His life includes the main centers of science and math in Europe in the Golden period between the two World Wars.The second part is Polya's life of teaching and research in the US, at Stanford University. I was a guest at Polya's ninetieths birthday. It has been said that mathematicians have been more likely than others to have been uprooted in the upheavals of history, perhaps because they are concerned with theories and ideas that are more universal.

A prolific, versatile man who was also a mathematician
While George Polya is credited with coining the phrase "random walk", his journey through life was anything but random. Extremely influential in many areas of mathematics, his book, "How to Solve It" alone would have made a career. Like so many mathematical heavyweights of this century, his nationality was Hungarian. Given the number of mathematicians and their collective prolific output, Hungary must lead the world in per capita production of mathematical papers. Polya's first papers were published in 1912 and his last in 1987.
The range of the work is just as impressive. Many concepts now considered standard mathematical fare were products of his genius. When reading this biography, you are struck by the features of human nature that he projects. Who else would talk about the list of the three nicest mathematicians that they ever met? Would anyone else dare to also talk about the three most unpleasant mathematicians that they ever encountered? His honesty when admitting that he was intimidated by John von Neumann show a level of humility that few people of his stature would ever acknowledge.
In an era when being a lackluster to pathetic teacher is considered a prerequisite for a position as a research mathematician it is extremely refreshing to read about his qualities as a teacher and his concern for the profession. He was an existence proof of the reality that it is possible to be both. His contributions to the field of teaching are as strong as those in any other area of his expertise.
Biographies of mathematicians sometimes degenerate into lists of life accomplishments emphasizing the major formulas and proofs of their lives. In others, the person comes across as a solid professional, but there seems to be little else to their life. In writing about Polya, the author is describing a person that you would no doubt find to be pleasant company.
One of those amazing Hungarian mathematical exports that graced the United States with their presence, George Polya was truly a credit to the professions of being a mathematician and a human. This is one of the most enjoyable biographies of a mathematician that I have ever read. ... Read more

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For many years the mathematicians visiting Stanford enjoyed guided tours through pages of the Polya photograph album, led by Polya himself. This is a selection of the photographs accompanied by remarks taken from tapes of Polya's conversations with his visitors. ... Read more

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“How to Solve It” is not strictly speaking a math book. It is a book about how to solve problems of any kind, of which math is just one type of problem. The same techniques could in principle be used to solve any problem one encounters in life (such as how to choose the best wife??).Therefore, Polya wrote the current volume to explain how the techniques set forth in "How to Solve It" can be applied to specific areas such as geometry.The method of solving problems he provides and explains in his books was developed as a way to teach mathematics to students. The steps seem simple but yet are often not followed.For example, the first step to solving a problem is: Understand the problem.As he points out, this seems so obvious that it is often not even mentioned. Yet, would-be problem solvers often do not understand the problem fully.This step too can be broken down into smaller steps. ... Read more

Customer Reviews (1)

What a biography are for
This life history helped me get a whole picture of G.Polya.

Usual mathematician prefer generalization and has little interest in education.But Polya prefer specialization and has much interest in education.That's why I wondered why.This book gave some ideas of his thought.

... Read more