How often have you stared at a math (or physics) problem, unsure of where to begin? Most math books are unusually pedantic and dull – all in an attempt to be more ‘rigorous’. Screw rigor, I say. Students are looking for a deeper understanding – lemmas, theorems are certainly not the way to provide that deep understanding.
These books fill this important gap. By providing the first step (where do I start), these problems bring those abstract theorems to life.
http://www.anujvarma.com/problem-books-for-advanced-math-students/
Here is a list of my favorite books on pure math problems (Algebra, Differential Calculus, Real and Complex Analysis, Linear Algebra and more….) , theoretical (Ph.D. level physics) and mathematical physics problems. Some of the Web Resources also have solutions to common graduate textbook problems ( Goldstein , Jackson , Griffiths , Peskin Schroder , Shankar , Klauber , Merzbacher)
Please comment if I am missing your favorite math problem book (or mathematical physics problem book) ! Also see Rare Finds in Relativity