MATH 3060 - Discrete Mathematics

• Athens: Irregular

• Students will be able to demonstrate facility with the terminology and notation of logical statements constructed using logical connectives and quantifiers.
• Students will be able to apply the methods of Direct Proof, Disproof by Counterexample, Proving the Contrapositive, and Proof by Contradiction to prove and disprove statements about Integers.
• Students will be able to describe sequences as functions with domain a subset of the integers, describe how sequences can be described recursively, & solve problems involving important sequences such as the arithmetic, geometric, and Fibonnacci sequences.
• Students will be able to use the Method of Induction to prove propositions.
• Students will be able to perform operations on sets, use Venn diagrams to illustrate simple set identities, and use more rigorous methods such as element proofs and algebraic proofs to prove statements about sets.
• Students will be able to determine the injective and surjective properties of functions and compositions of functions, and find the inverse of bijective functions.
• Students will be able to determine the reflexive, symmetric, and transitive properties of relations, and identify equivalence relations, equivalence classes, and partitions.
• Students will be able to solve counting problems involving the Multiplication Rule, the Addition Rule, Permutations and Combinations, and the Principle of Inclusion and Exclusion.
• Students will be able to investigate Pascal’s Triangle and apply the Binominal Theorem.
• Students will be able to organize and communicate mathematical reasoning both orally and in writing to prove theorems and describe solutions to problems in a variety of contexts.