Book recommendations for Problem Solving

Question

I am looking for book recommendations that will teach me the art of problem solving.

Learning theory is one thing but doing problems in limited time in a test is another.

To increase these skills I am looking for a book that has hard problems of high school level (i.e. pre college level) or maybe undergrad level which will teach me how I should approach a problem / solve it.{From Algebra, Calculus, Coordinate Geometry mainly}[Any books which give extra knowledge of some well known/important theorems , that are a bit above highschool level but not too beyond and can help in problem solving will also be really helpful :)]

Answer 1

Donald J. Newman’s A Problem Seminar is a classic and a delight, and you will certainly benefit from it. It is not a textbook, because it does not teach advanced theorems - it is specifically intended to get your mind aligned to problem-solving.

It has a hundred problems (two or three lines long at the most), then a section with a brief hint as to how to approach each one; and finally the main body of the book gives the answer to each.

The main thing about problem-solving as a specific skill is that it is a question of recognition rather than heavy lifting. The tools in Newman’s book are all within the reach of a high school mathematician. The reason the book is a challenging exercise even for university students is that knowing which tool to use, the key to all advanced mathematics, is a subtle and elusive skill, hard to learn, you might say impossible to teach. But it is a delight.

The book is rather expensive, new, and you might have to sell your grandmother to buy it. But you may be able to find a second-hand copy more reasonably: it came out in 1983.

Answer 2

Beside

$\bullet$ Polya, How to Solve It

Another I can think of is definitely

$\bullet$ Tao, Solving Mathematical Problems: A Personal Perspective

Though not necessarily related, the

$\bullet$ Stein, Mathematics: The Man-Made Universe

Is what kindled my interest in mathematics; the approach is rather unique, and the level is definitely appropriate for high school students.

There must be other resources abundant, but my word is, you think of yourself how you solve the problem. Why so? When you get to the college level, you broaden your perspective and these high school problems, naturally, become no longer important. The thinking process counts more important than whether you succeeded. You may also find some Olympiad problems to think about, but need not be ashamed if you cannot do it.

Answer 3

I think you may like "The Top-Down Approach to Problem Solving", by Eduardo Corpeño (full disclosure: that's me), ISBN 979-8464073296.

It sounds like you described this book in your post, so you may want to look into it. It's on amazon as paperback and ebook.