MATH 176 Discrete Mathematics*

This course is designed to prepare the student for computer science and upper-division mathematics courses. Material covered will include sets, propositions, proofs, functions and relations, equivalence relations, quantifiers, Boolean algebras, graphs, and difference equations.

Credits

4 Credits

Semester Contact Hours Lecture

60

Prerequisite

MATH 170

MATH 176Discrete Mathematics*

Please note: This is not a course syllabus. A course syllabus is unique to a particular section of a course by instructor. This curriculum guide provides general information about a course.

I. General Information

Department

Mathematics & Engineering

II. Course Specification

Course Type

Program Requirement

Credit Hours Narrative

4 Credits

Semester Contact Hours Lecture

60

Prerequisite Narrative

MATH 170

Grading Method

Letter grade

Repeatable

N

III. Catalog Course Description

This course is designed to prepare the student for computer science and upper-division mathematics courses. Material covered will include sets, propositions, proofs, functions and relations, equivalence relations, quantifiers, Boolean algebras, graphs, and difference equations.

IV. Student Learning Outcomes

Upon completion of this course, a student will be able to:

• Understand the rules of logic, and use these to construct arguments and write formal mathematical proofs.
• Identify and classify functions, sequences, and relations, and explore mathematical and practical examples of these.
• Understand pseudocode and use it to write and analyze algorithms.
• Work with various aspects of number theory (including divisors and the Euclidean Algorithm), and graph theory (including paths and cycles).
• Understand counting methods, including permutations, combinations, the Binomial Theorem, and apply these to real-world situations.

V. Topical Outline (Course Content)

Basic set notations, Venn diagrams, and set operations. Propositional logic Simplifying negations Techniques for completing proofs and finding counterexamples Mathematical induction and strong mathematical induction Basic definitions for functions Compositions and inverses of functions Sequences and strings Binary relations Reflexive, symmetric, antisymmetric, and transitive relations Equivalence relations and class Partial orders Algorithms Analyzing the complexity of algorithms Integers, divisibility, and congruence mod p Multiplication and addition principles for counting Counting permutations and combinations Principle of inclusion-exclusion The pigeon-hole principle Solving first- and second-order recurrence relations Paths and cycles Hamiltonian Cycles Basic definitions of graphs Isomorphisms of graphs Boolean algebras

VI. Delivery Methodologies