MTH 245 - Discrete Mathematical Structures

Description
MTH 245 is a survey of Discrete Mathematics. Topics include mathematical logic, sets, relations, functions, combinatorial mathematics, recurrence relations, proof techniques, mathematical induction, graphs, digraphs, trees and algorithms.

Was previously MA 245.

Credit Hours: 4
Contact Hours: 4
Prerequisites/Other Requirements: C or Higher in one of the following courses: MTH 148 or MTH 178 or MTH 208 or MTH 248 or MTH 252 or Math Placement score of 76 or Higher
English Prerequisite(s): None
Math Prerequisite(s): None
Course Corequisite(s): None
Academic Program Prerequisite: None
Consent to Enroll in Course: No Department Consent Required
Dual Enrollment Allowed?: Yes
Course Fees: $19.00
Number of Times Course can be taken for credit: 1
Programs Where This Course is a Requirement:
None

General Education Requirement:
None
General Education Learner Outcomes (GELO):
NA
Course Learning Outcomes:
1. Construct a truth table to show two compound propositions are logically equivalent.

2. State the definitions and compute various set operations.

3. Determine whether a given function is injective, surjective, bijective, invertible.

4. Identify and apply appropriate proof techniques to prove a theorem.

5. State the principle of mathematical induction and write inductive proofs for mathematical propositions.

6. Distinguish and apply permutations and combinations for counting problems.

7. Compute modular arithmetics and apply them in application problems.

8. Distinguish between graphs, multigraphs, pseudographs, and digraphs.

9. Determine whether two graphs are isomorphic and state the isomorphism.

10. Distinguish and determine Eulerain circuits and Hamiltonian cycles in graphs.

11. Determine chromatic numbers of graphs and apply them in application problems.

12. Distinguish between planar and nonplanar graphs and give graph theoretic justifications.

13. State the definition and characteristics of trees.

14. Effectively organize communications, ensuring there is a clear introduction and conclusion, the content is well sequenced, and there are appropriate transitions.

15. Use creativity and alternative thinking to brainstorm new ideas and possible solutions to problems or issues.
Course Outline:
I. The Foundation

A. Mathematical Logic

B. Sets

C. Relations

D. Functions

II. Algorithms

A. Elementary number theory and the division algorithm

B. The Euclidean Algorithm

C. Dijkstra’s algorithm

III. Mathematical Reasoning

A. Methods of proofs

B. Principle of mathematical induction

C. Recursive definition

IV. Combinatorial Mathematics

A. Basic counting techniques

B. Pigeon-hole principle

C. Permutations and combinations

D. Binomial Theorem

E. Recurrence relation

V. Graph Theory

A. Introduction to Graphs and Digraphs

B. Representation of graphs and isomorphism

C. Connectivity

D. Eulerian and Hamiltonian graphs

E. Graph coloring

F. Planar graphs

G. Trees

Approved for Online and Hybrid Delivery?:
Yes
Instructional Strategies:
Lecture: 10-50%

Facilitated discussion: 10-50%

Mediated instruction: 0-20%

Collaborative work: 10-30%
Mandatory Course Components:
None
Equivalent Courses:
None

Accepted GRCC Advanced Placement (AP) Exam Credit: None
AP Min. Score: NA
Name of Industry Recognize Credentials: None

Course prepares students to seek the following external certification:
No
Course-Specific Placement Test: None
Course Aligned with ARW/IRW Pairing: N/A

Mandatory Department Assessment Measures:
None

GRCC Course Type:
Elective: Expands learning opportunities for degree seeking students. May or may not be required for students in a specific GRCC program.
Course Format:
Lecture - 1:1
Total Lecture Hours Per Week: 4
People Soft Course ID Number: 101088
Course CIP Code: 27.01
Maximum Course Enrollment: 30
High School Articulation Agreements exist?: No
If yes, with which high schools?: NA
Non-Credit GRCC Articulation Agreement With What Area: No
Identify the Non Credit Programs this Course is Accepted: NA

School: School of STEM
Department: Mathematics
Discipline: MA
Faculty Credential Requirements:
Master’s Degree (GRCC general requirement), Other (list below)
Faculty Credential Requirement Details:
Standard requirements for the Mathematics department apply.

Major Course Revisions: Prefix
Last Revision Date Effective: 20260304T10:59:07
Course Review & Revision Year: 2029-2030