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How to Solve It: A New Aspect of Mathematical Method
by
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
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Paperback, 288 pages
Published
September 25th 2015
by Princeton University Press
(first published November 30th 1944)
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(showing 1-30)
This book contains no magic, no tricks. It's not one of those "esoteric knowledge revealed" books nor a book which promises you'll get an Abel prize or a Fields Medal someday.
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
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
George Polya's classic How to Solve It is a seminal work in mathematics education. Written in 1945 and referenced in almost every math education text related to problem solving I've ever read, this book is a short exploration of the general heuristic for solving mathematical problems. While the writing is a bit clunky (Polya was a mathematician and English was not his first language), the ideas are so deeply useful that they continue to have relevance not just for solving mathematical problems,
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Polya tries to explain how to become a better 'problem solver', and how to guide others to better solve problems themselves. The core of the content is terrific, and gets you thinking about 'how to best think'.
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).
The ...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).
The ...more
I recently finished reading How To Solve It - A New Aspect Of Mathematical Method - by George Polya.
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
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
Oct 26, 2008
Louis
rated it
it was amazing
·
review of another edition
Recommends it for:
Anyone who has to analyze situations not seen before
Shelves:
math-stats
This is a book I wish I had read at the beginning of grad school. How to Solve It is not as much about methods of solving mathematical problems as it is about various approaches to solving problems in general. The method he uses to teach problem solving is to apply the approaches to problems of geometry. This is actually in line with the ancient greek (Aristotle) opinion that the young should learn geometry first, then when they have learned logic and how to prove things with physical reality, t
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This is one of those mathematical "classics" that those of us with a training in math are supposed to love. Fact of the matter is that it is poorly written and pedestrian in nature. If you are seeking insight into how mathematicians think and approach problem-solving, give this one a miss. You'd be far better off to read Hardy's "A Mathematician's Apology" (dated, but still charming), or Ian Stewart's recent "Letters to a Mathematician" (charming and not dated at all).
Dec 21, 2009
Pasparto
rated it
really liked it
·
review of another edition
Shelves:
problem-solving,
math
این کتاب ترجمه کار کلاسیک جرج پولیا: How to solve it هست.
به نظرم شاید برای خوانندهای که هنوز چندان با مسئلههای ریاضی کلنجار نرفته خیلی جالب نباشه، اما برای معلمان ریاضی و کسانی به صورت جدیتر درگیر حل مسائل ریاضی هستند کتاب تامل برانگیز و آموزندهای هست که کمک میکنه با دید بازتر راهی که در حل مسائل میرند رو بازبینی کنند و نسبت به فرآیند حل مسئله خودآگاهتر بشند. این خودآگاهی و توصیههای راهیابانه کتاب میتونه به بهتر شدن مهارت حل مسئله افراد کمک کنه. ...more
به نظرم شاید برای خوانندهای که هنوز چندان با مسئلههای ریاضی کلنجار نرفته خیلی جالب نباشه، اما برای معلمان ریاضی و کسانی به صورت جدیتر درگیر حل مسائل ریاضی هستند کتاب تامل برانگیز و آموزندهای هست که کمک میکنه با دید بازتر راهی که در حل مسائل میرند رو بازبینی کنند و نسبت به فرآیند حل مسئله خودآگاهتر بشند. این خودآگاهی و توصیههای راهیابانه کتاب میتونه به بهتر شدن مهارت حل مسئله افراد کمک کنه. ...more
This is a great book.
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 :)
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 such a great book. Polya lays out the different approaches you can take to solve a problem. He primarily uses Euclidean geometry to explain the possible ways to approach different problems.
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
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
Pólya is the teacher I never had.
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".
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".
Elegance in solving problems is not strictly a mathematical skill set. Polya wisely formats word problems, critical thinking problems, and yes mathematical problems that occasionally are intimidating.
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
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
Jun 13, 2012
Jessica
added it
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I picked this up by happenstance in a college bookstore over the summer. I'm always looking for educational texts on analytical methods, so this one caught my eye. What an amazing find! Pólya presents the reader with a list of steps to use when analyzing a problem and breaks each one down comprehensively. The entire book references back upon itself repeatedly, so you can always circle back to important, related points.
The writing style is quirky, yet approachable, and very direct. The author's r ...more
The writing style is quirky, yet approachable, and very direct. The author's r ...more
Aug 09, 2007
Ari
rated it
it was amazing
·
review of another edition
Recommends it for:
everyone
Shelves:
owned
I don't remember when I first encountered this book -- I think it was early in my time at Cornell. It's had a great deal of influence on how I approach math. It's one of the best math books I've ever read, and quite possibly the best book on mathematical problem solving ever written.
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
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
Hailed as the classic guide to problem solving, this book did quite a good job at categorizing the ways of looking at a problem, and some general methods of solving and treating them. However, I think I read this at the wrong time - it could have fascinated me much more had I read it in the early 2000s (then again, there was not any translation to Vietnamese back then, and I suspect my mediocre English back then would not let me finish it).
Still, the way I went at the book is that I skimmed thro ...more
Still, the way I went at the book is that I skimmed thro ...more
This book was used as a reference in several of the other books I have read, and I understood it to be more of a general methodology of problem solving when I decided to read it. It is written in a somewhat awkward style, to an audience that is difficult to discern, and with enough repetition that I had to skip pages at a time to get to the next topic. This was frustrating as I really wanted to like this book. When Polya does focus on the generalized concepts of problem solving, he has wonderful
...more
This book may not necessarily make you a better problem solver—that comes only from practice—but it is a useful first step in examining the types of creativity that go into problem-solving. Thus it's almost more a philosophical or psychological work than a how-to guide. The examples are all at middle-school or high-school level; the real point of the book is the enumeration of problem-solving strategies. It may even help you get unstuck when you're overlooking some trick you've used in the past.
This book is not only for math teachers, but anyone who has problems to solve. It gives very simple and precise suggestion to solve a problem; such as 'understand the problem'. It is obvious but often people forget those principals when they face a hard problem, particularly long time.
Reading this book is fun and will be useful once I hit a tough problem to solve.
Reading this book is fun and will be useful once I hit a tough problem to solve.
TODO:
+ 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
+ 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 book is written in an ‘easy to read’ manner, I had thought when I read the introduction that it is made for mathematical teachers only, but when I read further, i understood that it’s made for anyone who can ‘think’ and want to ‘solve’ any sort of problem, this book can be read by people in the mathematics field or anyone who just reads book to kill the time. This book, needless to say teaches how to solve any sort of problems, not only pure mathematical but also physical, crossword puzzles
...more
Nice introduction to heuristics and problem solving techniques. The math is very accessible, as it does not require any higher level maths to understand the examples. A familiarity with geometry and algebra would suffice. The book has historical significance as being a pioneer in attempting to address problem solving techniques in a organized and rigorous way. The organization of his techniques is alphabetical by title and Polya does not attempt to offer any over arching structure to his techniq
...more
Some of my favorite quotes from the book:
The worst may happen if the student embarks upon computations or constructions without having understood the problem.
It is foolish to answer a question that you do not understand.
Simplex sigillum veri.
Human superiority consists in going around an obstacle that cannot be overcome directly, in devising a suitable auxiliary problem when the original problem appears insoluble..
Respice finem.
And if yuou are inclined to be a pedant and must rely upon some rule...more
I don't understand why this is considered to be a good book. The author seems to have picked a few obvious points and had an endless amount of commentary addressed to them. Mathematical examples for some advice were few or nonexistent which made it hard to imagine how he envisioned the reader to apply his advice.
Some problems in the end practice problems were also worded so poorly that I didn't even understand what some questions were asking. For example the problem about the book using 2898 di ...more
Some problems in the end practice problems were also worded so poorly that I didn't even understand what some questions were asking. For example the problem about the book using 2898 di ...more
[5 out of 5] My only regret is that I must return this book to the library. This is one of those rare books I recommend to pretty much anyone who has to deal with problem solving.
Not just mathematical problems, though. Polya writes an excellent case for the way we all should approach problems. It's not a formula, rather a scaffolding for thought, strategies for learning and teaching, reflections on successful solving and common pitfalls. If you want to think like a scientist, this is an excellen ...more
Not just mathematical problems, though. Polya writes an excellent case for the way we all should approach problems. It's not a formula, rather a scaffolding for thought, strategies for learning and teaching, reflections on successful solving and common pitfalls. If you want to think like a scientist, this is an excellen ...more
Good book by Polya, he explains the process used in solving and proving problems.
My biggest problem with this book is that it's way to dense and also he should have used more mathematical equations and figures in some cases instead of a wall of text where you get easily lost.
Some nice tables would also be good.
I read it all and stopped in part IV which is where the book ends, and he gives you some problems with hints and solutions for you to solve.
Overall nice book, but not for casuals, more if ...more
My biggest problem with this book is that it's way to dense and also he should have used more mathematical equations and figures in some cases instead of a wall of text where you get easily lost.
Some nice tables would also be good.
I read it all and stopped in part IV which is where the book ends, and he gives you some problems with hints and solutions for you to solve.
Overall nice book, but not for casuals, more if ...more
A quick pamphlet distilling a heuristic-based approach to solving math and practical problems (but mostly math) by asking/answering a series of general questions ("what is unknown? does this problem look like something else I know how to solve? does my plan / answer make use of all the data provided?" etc) useful for both teachers to guide students to finding solutions themselves and for self-directed validation. In part a defense (in 1944) of using heuristic / encouraging validated guesses at a
...more
An interesting book which briefly describes an approach to solving problems separated into four stages. The whole process is described in less than 20 pages and it is what we do, mostly not thinking about the steps — so it's compelling to make them more explicit and helpful, and i think it's the biggest benefit. The big part of the book has a "glossary" where problem solving-related terms are explained in various details.
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Goodreads Librari...: Could you please fix the page number of this book? | 7 | 24 | Feb 20, 2018 07:30AM |
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