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Can anybody please recommend a list of Advanced Mathematics Books for physics that can be used for self study. Most importantly they must have answers for odd or even problems. I have a big list of really good Math Books, but they are not convenient for self study -specially they don't have answers for the problems, so how would I know I am on the right path!-

For example: Div, Grad, Curl, and All That by H. M. Schey, is a good book, it has many problems and provides the final answer -not the entire solution- to all of its problems at the end of the book. so I am looking for more books like that one.

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Here is what I would do to find those books:

  1. Search the internet by typing the names of the topics that the books may discuss about.
  2. Search publishers for new books with answers.
  3. Search authors who just wrote new books with answers in physics.
  4. Search new problem-books or old qualifying exams from universities.
  5. Join Physics SE site and ask experts there for books you want to buy.
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After a certain point, it is actively bad for books to give answers to problems. The temptation to go look up the answer is too great.

The best skill you will learn, as a self-studier, is to be very careful and doubtful of your own work. After that, you will be building the solutions manual as you solve the problems!

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I have to disagree with this. There is more to an answer than a solution. You can learn a lot about how to approach problems and how to think about math by seeing how an expert in the field solves problem, even after writing up your own solutions. For example Don Passman used to write solutions to the algebra qualifying exams at Wisconsin. I learned more about algebra by solving old problems then looking at how he did it than I ever did by taking a class or reading a book. Most of my solutions were correct, but they were the wrong answer. –  Chris Janjigian Jun 10 at 16:53
    
@ChrisJanjigian I don't disagree at all! But these should not be part of a text itself (IMO), and perhaps more importantly, rarely are - one should become accustomed to being satisfied with one's own work. (And certainly one can google the vast majority of textbook questions in just about any text and find a solution to that question written by someone who knows what they're on about.) –  Mike Miller Jun 10 at 17:23

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