Exam 1 review, due on September 22

I think that some of the most important topics to study would be those concerning rings and modular arithmetic. Having clear how to show something is a ring, subring, field, integral domain, isomorphism, homomorphism, etc. seem like topics that will be important to know. So basically all of the theorems and definitions that relate to these topics are areas that I think will be important. I also think knowing modular arithmetic properties will be especially important because it applies to divisibility, primes, and rings. Modular arithmetic seems like something that connects together everything that we have learned.

On the exam I expect to see lots of definitions and about 2 theorems out of the list provided that we will have to prove. I also expect 1 or 2 other proofs that will be very similar to previous homework problems that we have had. I expect something about how to show that a particular set is a subring, isomorphism, and homomorphism whether it be a proof or just giving the definition.