I want to know about mathematics books for high school students which focus more towards exposure of a student to different methods or ways of solving problems in Algebra, Calculus , Coordinate Geometry. Most of the books available contain problems based on very similar types of questions or a particular method/methodology being used for the solutions (Maybe because it's the authors style or what he is used to).

I am asking this because I was reading a book by George polya "how to solve it?" in which he says

Do you know a related problem? We can scarcely imagine a problem absolutely new, unlike and unrelated to any formerly solved problem; but, if such a problem could exist, it would be insoluble. In fact, when solving a problem, we always profit from previously solved prob-lems, using their result, or their method, or the experi-ence we acquired solving them. And, of course, the problems from which we profit must be in some way related to our present problem. Hence the question: Do you know a related problem?

And so I'm looking for a book that can increase my exposure towards topics like Algebra, Calculus and Coordinate-Geometry


Here are some resources:

The Art of Problem Solving books, which are intended to help students prepare for mathematics contest.

Four books authored by the great Russian mathematician I. M. Gelfand and assorted co-authors that were originally intended to supplement the Russian mathematics curriculum during the Soviet era. They include:

Algebra by I. M. Gelfand and A. Shen

The Method of Coordinates by I. M. Gelfand, E. G. Glagoleva, and A. A. Kirillov

Functions and Graphs by I. M. Gelfand, E. G. Glagoleva, and E. E. Shnol

Trigonometry by I. M. Gelfand and M. Saul

The Japanese Fields medalist Kunihiko Kodaira edited books for Japanese high school students which contain challenging problems. They include:

Mathematics I: Japanese Grade 10

Algebra and Geometry: Japanese Grade 11

Basic Analysis: Japanese Grade 11

Challenging calculus books tend to be written for college students, rather than high school students. They include:

Calculus: Volume I by Tom M. Apostol

Apostol has a second volume on multi-variable calculus and linear algebra.

Calculus by Michael Spivak


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