I will be going for math major this year, and I am hoping to start this book. But after reading some reviews, they say its mostly for teachers. Can it be used by undergrads? If possible include your brief review of it.
Some other questions in my mind regarding the same book:
How to get the most out of it?
What is the structure of the book?
What are the difficulty of problems?
Thank You!
On
I liked Polya's How to Solve It but got much more when I was your age (and still) from his Induction and Analogy in Mathematics, the first volume of Mathematics and Plausible Reasoning.
You can try it out here https://archive.org/details/Induction_And_Analogy_In_Mathematics_1_ . If you like it you'll want your own hard copy, available from Amazon and elsewhere.
I'm surprised to hear that people say its mostly for teachers. It's one of my go-to recommended books for someone who wants to start learning proofs (example). However, reading a book about thinking can only do so much for you. As I stress in that answer, the only way to become a proficient proof writer is to read and write them. If you want to get the most out of the book, make sure to supplement reading that book with a variety of problems and exercises!
I only learned about the book after I had already advanced beyond its intended audience, so I can't personally vouch for its effectiveness or difficulty. That said, I know a number of people who have used it to help them get acquainted with mathematical thinking and have heard nearly uniformly positive things about it.
The answers to this question might also be interesting for you.