MA 301 - Mathematical Structures and Proofs

1. Techniques of Proof
   a) Statements
   b) Mathematical induction
   c) Proof by contradiction
   
   
2. Elementary Set Theory
   a) Sets and subsets
   b) Combining sets
   
   
3. Relations and Functions
   a) Definition and basic properties
   b) Injective and surjective functions
   c) Composition and invertible functions
   d) Equivalence relations
   
   
4. The Integers
   a) Axioms and basic properties
   b) Greatest common divisor, Euclidean Algorithm
   c) Prime numbers, unique factorization
   d) Congruences
   
   
5. Infinite Sets
   a) Countable sets
   b) Uncountable sets, Cantor's Theorem
   c) Collections of sets
   
   

Learning Outcome 1: The student will demonstrate a knowledge of set theory and logic.

Learning Outcome 2: The student will be able to construct mathematical proofs.

Learning Outcome 3: The student will be able to demonstrate an understanding of functions and proofs involving relations and functions.