# Discrete Mathematics

MTH 260## Course Description

Prerequisite: MTH 161 with a grade of "C" or better. Introduces discrete mathematics topics for applied mathematics and computer science. Includes Boolean algebra, predicate logic, sets, relations, induction and recursion, counting theory, graphs and trees. (45-0)

## Outcomes and Objectives

### The student will learn the fundamental terms and vocabulary of mathematical discourse.

#### Objectives:

- Use functions, sequences and summations.
- Use the fundamental properties of the integers.
- Use matrices in a variety of contexts.
- Use the basic principles of mathematical logic.
- Define, identify, and apply sets and set operations.
- Use the concepts of algorithm, recursion, and iteration.
- Use the concept of mathematical induction.

### The student will learn the fundamental principles of counting.

#### Objectives:

- Set-up and solve problems related to permutations and combinations.
- Use generalized permutations and combinations.
- Apply the basic rules of probability in solving problems.
- Define, identify, and apply recurrence relations.
- Use the principle of inclusion-exclusion.

### The student will learn about relations and their representations.

#### Objectives:

- Identify several fundamental properties of relations.
- Use tables, graphs, and matrices.
- Identify and define constructions of fundamental closures of relations.
- Define and identify equivalence relation and partition.
- Use various examples of partial orderings.

### The student will learn the fundamental properties and applications of graphs and trees.

#### Objectives:

- Use fundamental graph and tree terminology.
- Identify several graphs.
- Define, identify, and apply Euler and Hamilton paths.
- Define, identify, and apply weighted graphs and shortest path problems.
- Define and solve problems related to homeomorphism and isomorphism of graphs.
- Define and solve problems related to tree traversal, spanning trees and minimal spanning trees.

### The student will learn the fundamental properties and applications of Boolean algebra.

#### Objectives:

- Define and represent Boolean functions.
- Recognize various examples of Boolean algebras.
- Identify and define logic gates and combinatorial circuits.
- Apply algorithms for minimization of circuits.