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

Semester Contact Hours Lecture

60

General Education Competency

[GE Core type]

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

General Education Competency

[GE Core type]

Credit Hours Narrative

4

Semester Contact Hours Lecture

60

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:

• Engage in substantial mathematical problem solving. Students will learn mathematics through modeling and real-world situations.
• Read, write, listen to, and speak mathematics. Student will have opportunities to be successful in doing meaningful mathematics that fosters self-confidence and persistence.
• Use appropriate technology to enhance their mathematical thinking and understanding. Students will use the technology to solve mathematical problems, and judge the accuracy of their results.
• Expand their mathematical reasoning skills as they develop convincing mathematical arguments. Students will have opportunities to see that mathematics is a growing discipline that is interrelated with human culture, and understand its connections to other disciplines.

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