MTH 2310 - Discrete Mathematics

• Convert logical statements from informal language to propositional and predicate logic expressions
• Apply formal methods of symbolic propositional and predicate logic, such as calculating validity of formulae
• Use the rules of inference to construct proofs in propositional and predicate logic
• Use propositional and predicate logic to model, analyze, and interpret real-life situations
• Outline the basic structure of direct proof and proof by contradiction
• Apply direct proof or proof by contradiction, where appropriate, in the construction of a sound argument
• Use the basic terminology of sets, functions, and relations
• Perform common operations associated with sets, functions, and relations
• Use sets, functions, and relations to model, analyze, and interpret real-life situations
• Recognize and construct arithmetic and geometric progressions
• Perform computations involving modular arithmetic, including solving linear congruences
• Construct proofs using weak and strong induction
• Solve a variety of basic recurrence relations
• Analyze a problem to determine an underlying recurrence relation
• Apply counting arguments, including sum and product rules, inclusion-exclusion principle, and the pigeonhole principle.
• Compute permutations and combinations of a set, and interpret the meaning in the context of the particular application
• Identify whether a relation is reflexive, symmetric, antisymmetric, or transitive and if it is an equivalence relation
• Use basic terminology of graph theory
• Identify the type and special properties of a graph
• Demonstrate different traversal methods for trees and graphs, including pre-, post-, and in-order traversal of trees

• Precalculus mathematics

• Propositional logic
• Predicate logic 
• Universal and existential quantifiers
• Modus ponens and modus tollens
• Direct proofs
• Proof by contradiction
• Sets
• Functions
• Arithmetic and geometric progressions
• Cardinality, countability, and inclusion-exclusion principle   
• Basic modular arithmetic
• Greatest common divisor and Euclidean algorithm (time permitting)
• The Chinese Remainder Theorem
• Mathematical induction and well ordering principle
• Recursive definition
• Sum and product rules
• The pigeonhole principle
• Permutations and combinations
• The binomial theorem
• Recurrence relations
• Solving recurrence relations
• Relations (reflexivity, symmetry, antisymmetry, transitivity)              
• Equivalence relations and partial ordering       
• Fundamental terminology of graphs
• Directed, undirected, and weighted graphs
• Graph isomorphism (time permitting)
• Trees, traversal strategies