MA 245 - Discrete Mathematical Structures
Description
MA 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.
Credit Hours: 4
Contact Hours: 4
School: School of STEM
Department: Mathematics
Discipline: MA
Major Course Revisions: N/A
Last Revision Date Effective: 20220213T19:35:32
Course Review & Revision Year: 2026-2027
Course Type:
Elective- Offering designed to expand learning opportunities for degree seeking students. May or may not be required for students in a specific GRCC program.
Course Format:
Lecture - 1:1
General Education Requirement: None
General Education Learner Outcomes (GELO):
None
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.
Approved for Online Delivery?: Yes
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
Mandatory CLO Competency Assessment Measures:
None
Name of Industry Recognize Credentials: None
Instructional Strategies:
Lecture: 10-50%
Facilitated discussion: 10-50%
Mediated instruction: 0-20%
Collaborative work: 10-30%
Mandatory Course Components:
None
Academic Program Prerequisite: None
Prerequisites/Other Requirements: C or Higher in one of the following courses: MA 131 or MA 133 or MA 134 or MA 255 or MA 257 or ALEKS score of 76 or Higher
English Prerequisite(s): None
Math Prerequisite(s): None
Course Corerequisite(s): None
Course-Specific Placement Test: None
Course Aligned with IRW: NA
Consent to Enroll in Course: No Department Consent Required
Total Lecture Hours Per Week: 4
Faculty Credential Requirements:
18 graduate credit hours in discipline being taught (HLC Requirement), Master’s Degree (GRCC general requirement)
Faculty Credential Requirement Details: Standard requirements for the Mathematics department apply.
Maximum Course Enrollment: 30
Equivalent Courses: None
Dual Enrollment Allowed?: Yes
Advanced Placement (AP) Exam Credit Accepted: None
AP Min. Score: NA
Number of Times Course can be taken for credit: 1
Programs Where This Courses is a Requirement:
None
Course Fees: $19.00
People Soft Course ID Number: 101088
Course CIP Code: 27.01
High School Articulation Agreements exist?: No
If yes, with which high schools?: NA
Non-Credit GRCC Agreement exist?: No
If yes, with which Departments?: NA
Corporate Articulation Agreement exist?: No
If yes, with which Companies?: NA
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