Fri, Sep 11 Quiz 1 Quiz Solutions
Topics: Know and be able to use the definitions we have seen: divisibility, congruence modulo $n$, reflexive, symmetric, and transitive relations, equivalence relations, and equivalence classes. Review Theorems 1.1–1.3, 1.6, 1.9–1.14 and the corresponding proofs. Exercise R.5 would also be good practice.

Fri, Sep 25 Quiz 2 Quiz
Topics: Given during the first 15 minutes of class. You should know the statement of every definition and theorem we have encountered since Quiz 1, and be able to use them. This includes the quotient and remainder, common divisor, greatest common divisor, and relatively prime, as well as Theorems 1.26–1.28, 1.32, 1.33, 1.35, 1.38–1.41, and M.1–M.3. You should also know the proof techniques used to establish these results, and be prepared to invoke the theorems in your own proofs. You must know the Euclidean Algorithm as we stated it in the Allowed Results, including what it means for the algorithm to halt in $k$ steps and why the quotient and remainder at each step are unique. Finally, you should know the statements of the Well-Ordering Axiom and the Principle of Mathematical Induction, and be prepared to write a proof by induction. The quiz will not test you on definitions and results from before Quiz 1, but you should still be ready to use them. Material from Homework 10 will not appear on this quiz.

Fri, Oct 30 Quiz 3

Fri, Nov 13 Quiz 4

Fri, Dec 4 Quiz 5