Examples of books giving problems that require more than one branch of mathematics

Question

I want to know if there are books that give problem sets requiring knowledge of two or more branches of mathematics. For example, there could be a problem requiring geometry, set theory, and number theory, and another problem requiring ring theory and calculus. All the problems should be solvable with merely an undergraduate background.

Answer 1

You should take a look at the William Lowell Putnam Mathematics Competition 1985-2000: Problems, Solutions and Commentary, by Kedlaya, Poonene and Vakil.

The very focus of the Putnam Competition is to test undergraduates knowledge of large fields of mathematics, with a focus on synthesizing ideas in interesting ways. Many of the problems are quite hard, and require a good deal of breadth of knowledge, but they are not unaccessible, and the book gives hints as well as solutions, so that you can practice many types of problems.

Answer 2

Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach by John and Barbara Hubbard offer many problems that tie together analysis and linear algebra. The problem sets however do not require as diverse of a knowledge as competition level problems (as stated by Alfred).