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.
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
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