MA 301 - Mathematical Structures and Proofs
- Techniques of Proof
b) Mathematical induction
c) Proof by contradiction
- Elementary Set Theory
a) Sets and subsets
b) Combining sets
- Relations and Functions
a) Definition and basic properties
b) Injective and surjective functions
c) Composition and invertible functions
d) Equivalence relations
- The Integers
a) Axioms and basic properties
b) Greatest common divisor, Euclidean Algorithm
c) Prime numbers, unique factorization
- 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.