Students should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor. For more detailed information visit the Math 587 Wiki page.
- Arithmetic functions
- Elementary theorems on distribution of prime numbers
- Finite abelian groups and their characters
- Dirichlet series and Euler product
- The zeta function and the Dirichlet L-functions