How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight.
In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generat...more
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What this books is, is a systematic and incredibly instructive overview of guidelines in mathematical problem solving, which are, as the author put it - "natural, simple, obvious, and proceed from plain common sense."
If you've ever put yourself against a serious problem which you really, really, really wanted to have solved ...more
Unfortunately, almost everything gets repeated numerous times, and as a whole the books ends up being thoroughly redundant. You don't really need to read beyond the first 36 pages (the rest of the book consists of a 'problem solving dictionary', and here's where the redundancy begins).
Below are key excerpts from this book that I found particularly insightful:
A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. ...more
Majority of the people who are aware of the Mathematics Events around the world have heard of George Polya even if they are not that much into mathematics themselves, for his name is on a par with legends like Gauss and Leibnitz now. Okay so we are all more or less familiar with his genius, but how many with his meant-to-be-simple-yet-intuitive works?
As a matter o ...more
Now you might get scared with the word "Mathematical" in the title - don't be. It is a general guide to how to solve a problem. Starting from establishing the question, gathering the known and to find the unknown. The method you are using to find the minimum distance between two points can also be used to find the most convenient road to your nearest grocery store. This book shows you -"How to Solve it".
It's an authentic treasure to everyone interested in problem-solving (and every one of us has enough problems to be interested in with problem-solving).
I think this should be one of the obligatory lectures for high-school or college education because it states clearly the steps one intuitively follows when trying to solve a problem mathematical or not.
The key takeaways for me are:
1. If you conceive a plan to solve the problem you're almost done. ...more
This bo ...more
It teaches solving mathematical problems. It is mostly focused on high-school problems, but it is applicable to most types of mathematical problems out there. The author has developed a nice heuristic framework for tackling problems and has done a wonderful job of explaining it. It's not just the methods – exposition is also a great takeaway from this read.
On the downside, the book was written in 1945 and sometime it shows. It's more cute than a nuisance, though :)
This is especially great when you have to analyze a problem that you haven't seen before - where and how to begin? He goes through the problem-solving process in detail, beginning with the detailed analysis of the question and then the systematic synthesis of the answer.
This book really changed how I ...more
Polya G (1945) How to Solve It - A New Aspect of Mathematical Method
From the Preface to the First Printing (1944)
From the Preface to the Seventh Printing (1954)
Preface to the Second Edition (1956)
“How to Solve It” list
• Understanding the problem
• Devising a plan
• Carrying out the plan
• Looking back
Foreword (by John H. Conway)
Part I: In the Classroom
• 01. Helping the student
• 02. Questions, recommendations, mental operations
• 03. Generality
• 04. Com ...more
You have to understand the problem.
UNDERSTANDING THE PROBLEM
What is the unknown? What are the data? What is the condition?
Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?
Draw a figure. Introduce suitable notation.
Separate the various parts of the condition. Can you write them down?
Find the connection between the data and the unknown.
You may be obliged to consi
The book is divided into four parts "In The Classroom" - tips for the educator on guiding a student, "How To Solve It" - presenting the main questions you should ask yourself while solving problems, "Short Dictionary of Heuris ...more
But one of the big takeaways is that problems are only as hard as they are unresolved. Not only does Polya give excellent ideas for solving problems: creating auxiliary problems, using heuristics, working backwards.
Each example that Polya gives takes concentration and critical analysis. But when yo ...more
+ Good ideas on how to teach average math students a process for solving problems in mathematics. Overall, useful concept, but limited and ill-aged approach.
+/- (Heuristic) Process based on four stages: 1. Understanding the problem. 2. Use related work = Finding related (solved) problems and decide on a plan to solve the current problem based prior solutions and/or their principles. 3. Solve = Show the plan works. 4. Check carefully the result and ask related questions about it. Process in ...more
The thing that makes this book unusual is that it's about the ...more
There are two copies of it floating around my lab at Berkeley, evidence, i think, that I'm not the only one who appreciates it.
Polya was a first rate mathematician, and his book is devoted to explaining simply and u ...more
Still, the way I went at the book is that I skimmed thro ...more
The writing style is quirky, yet approachable, and very direct. The author's r ...more
This book helped open my e ...more
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