MTH 288 Discrete Mathematics
Course Title: MTH 288: Discrete Mathematics
Course Description
Presents topics in sets, counting, graphs, logic, proofs, functions, relations, mathematical induction, Boolean Algebra, and recurrence relations. Lecture 3 hours per week. 3 credits.
General Course Purpose
The goal is to give the student a solid grasp of the methods and applications of discrete mathematics to prepare the student for higher level study in mathematics, engineering, computer science, and the sciences.
Course Prerequisites/Corequisites
Prerequisite: Completion of MTH 263 Calculus I with a grade of C or better or equivalent.
Course Objectives
Upon completing the course, the student will be able to:
Note: Methods of proofs and applications of proofs are emphasized throughout the course.
Logic  Propositional Calculus

Use statements, variables, and logical connectives to translate between English and formal logic.

Use a truth table to prove the logical equivalence of statements.

Identify conditional statements and their variations.

Identify common argument forms.

Use truth tables to prove the validity of arguments.
Logic  Predicate Calculus

Use predicates and quantifiers to translate between English and formal logic.

Use Euler diagrams to prove the validity of arguments with quantifiers.
Logic  Proofs

Construct proofs of mathematical statements  including number theoretic statements  using counterexamples, direct arguments, division into cases, and indirect arguments.

Use mathematical induction to prove propositions over the positive integers.
Set Theory

Exhibit proper use of set notation, abbreviations for common sets, Cartesian products, and ordered ntuples.

Combine sets using set operations.

List the elements of a power set.

Lists the elements of a cross product.

Draw Venn diagrams that represent set operations and set relations.

Apply concepts of sets or Venn Diagrams to prove the equality or inequality of infinite or finite sets.

Create bijective mappings to prove that two sets do or do not have the same cardinality.
Functions and Relations

Identify a function's rule, domain, codomain, and range.

Draw and interpret arrow diagrams.

Prove that a function is welldefined, onetoone, or onto.

Given a binary relation on a set, determine if two elements of the set are related.

Prove that a relation is an equivalence relation and determine its equivalence classes.

Determine if a relation is a partial ordering.
Counting Theory

Use the multiplication rule, permutations, combinations, and the pigeonhole principle to count the number of elements in a set.

Apply the Binomial Theorem to counting problems.
Graph Theory

Identify the features of a graph using definitions and proper graph terminology.

Prove statements using the Handshake Theorem.

Prove that a graph has an Euler circuit.

Identify a minimum spanning tree.
Boolean Algebra

Define Boolean Algebra.

Apply its concepts to other areas of discrete math.

Apply partial orderings to Boolean algebra.
Recurrence Relations

Give explicit and recursive descriptions of sequences.

Solve recurrence relations.
Major Topics to be Included
Logic – Propositional Calculus
Logic  Predicate Calculus
Logic  Proofs
Set Theory
Functions and Relations
Counting Theory
Graph Theory
Boolean Algebra
Recurrence Relations