Assignment 10: Preparing for Exam 1

Most Important Topics and Theorems: I think that among the most important topics we have learned are the division algorithm, the greatest common divisor of two numbers, properties of prime numbers, modular arithmetic, congruence classes, properties of Z(n) and Z(p) when p is prime, rings (their definitions and properties), and isomorphisms and homomorphisms. Some of the most important theorems are the fundamental theorem of arithmetic, the division algorithm, theorem 2.8, theorem 2.7, Corollary 2.5, theorem 2.1, theorem 1.8, and theorem 1.5.

Expected Questions: I expect to see questions about definitions on the exam. I also expect to have to prove major theorems we have learned in class. I know that we will have to prove other theorems using the definitions and theorems that we have studied, but it is hard to know what theorems to focus on. I want to thoroughly understand all of them, but I know that some are more important than others when considering proving new theorems. I expect the questions to be focused on the definitions and theorems. I expect that if I know the definitions really well, I will be able to prove the theorems.