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Product Review Summary: Following the footsteps of a giant After more than 50 years, Polya's advice on tackling problems is still worth reading. But be warned, this is not the latest, brightest, trendiest, best-selling "problem solving book" out there that target MBAs or a kind of personal self-development book. Its author had contributed to important fields of mathematics and he had been through many problems, many difficulties, many students and many different questions by those students.
If you're a young but eager student who faces problems in math (or in natural sciences), a person trying to solve some puzzles or practical problems, or a researcher about to start a long and unguaranteed journey in order to solve a big problem then you owe yourself to have this classic on your bookshelf, or better on your table.
I'd like to quote some important passages from the book but last time I checked my notes they are about as long as the book. So maybe it is better to let Polya do the talking...
Product Review Summary: Overrated and too simplistic. Hey, Have a problem in Real Analysis? Simple...run away! Heavily recommended by many, I decided to give How to Solve It a go, and real analysis, or should I say the science and art of proofing, is my worst nightmare. Although I do understand and appreciate the concept of proofs and consider it to be the most fundamental and mathematical aspect of mathematics, trying to prove already proven theorems, postulates, propositions, lemmas, and whatever else is a very tedious and mind-numbing task that robs the fun out of mathematics for the sake of learning. At least that's how I felt when I took the upper level college courses and amazingly survived them. In my opinion, it's the professors that needlessly made the experience of many students' to be harrowingly miserable due to their stilted, ad verbatim pedagogy with no real connection between prior knowledge and real analysis being taught. With that in mind, I've seen my math classes turned into the American Gladiators race, watching the large number of students from the beginning of the semester to dwindle down to a paltry few, and have essentially become the survival of the fittest. Why? Real Analysis, or should I say, "The science of proving without the art involved?" So, I decided to read How to Solve It to see if it could help me out while I was in one of those classes, and it amazingly did not. In fact, the book is so obscenely basic that even I could have written the same thing myself, and the knowledge contained in the book could not even guide me through whatsoever the material in the advanced classes. Maybe at just the very, very beginning of the whole journey, the book might work, and by that time, an ordinary mathematics student, falsely lured by the feeling of having fun while doing algebra, would be persuaded greatly to skip away from majoring in mathematics and find something else that is more realistic and not so painful. For me, anytime I got a problem with a proof, How to Solve It is a place I would never go to. All in all, How to Solve It is a vastly overrated book that is too simplistic and unhelpful.
Product Review Summary: Useful book for LSAT preparation As a professional LSAT tutor/blogger in NYC, I found this book to offer simple advice on problem solving and logical thinking. It's useful because it gives you a framework to identify and analyze the relationship between evidence and conclusion.
The book gives you some questions to ask yourself about any Logic Game or Logical Reasoning stimulus.
When to read it: Before you begin studying or when you need a break.
Product Review Summary: Shows you how to adjust your mental grip on your problem-solving golf club I had had this book for some time and never read it except for a glance or two. A few days ago I sat down after a successful stint at a pure maths problem and applied myself fully to this book. Wonderful! I was particularly taken by the claim in the introduction, by Sutherland, that Polya is concerned with helping show how to think. Just as a golf coach shows you how to hold the club, the tool of the game, as well as being concerned with getting the ball into the hole, the solution, so Polya shows one how to exactly adjust one's mental grip on the golf club of mathematical and general problem solving. This is a key part that most textbooks on maths omit.
An example of the kind of thing that is very useful in this book is the following short quote from Polya: "Even fairly good students, when they have obtained the solution of their problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. By looking back at the completed solution, by reconsidering and reexamining the result and the path that led to it, they could consolidate their knowledge and develop their ability to solve problems.... There remains always something to do; with sufficient study and penetration we could improve any solution, and, in any case, we can always improve our understanding of the solution."
Highly recommended. If you are serious about either learning maths or solving problems of any kind, this book is worth buying (and reading.)
Product Review Summary: Excellent book and recommended reading for anybody If you are a student, this book is for you. If you are into self-betterment, then this book is for you. Basically, if you want to learn how to think about problems and potential solutions, then this is for you.
Clearly written albeit math-oriented.
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