| |  | | MA 301 MA 301 -- Mathematical Structures and Proofs
- Techniques of Proof
a) Statements
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
d) Congruences
- Infinite Sets
a) Countable sets
b) Uncountable sets, Cantor's Theorem
c) Collections of sets
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