MAT-160 Introduction to Discrete Mathematics

An introduction to many of the principal topics of discrete mathematics, including number systems, sets, logic, relations, combinatorial methods, graph theory, regular sets, vectors and matrices. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.

Credits

4

Prerequisite

MAT-152

Department

• Mathematics

Semesters Course Will Be Offered

• Spring

Course Rotation Schedule

• Spring: In Person

For more detailed course information view the Course Outline

MAT 160: Introduction to Discrete Mathematics

Department

Mathematics

Course Description

An introduction to many of the principal topics of discrete mathematics, including number systems, sets, logic, relations, combinatorial methods, graph theory, regular sets, vectors and matrices. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.

Credit Hours

4

Contact Hours

Lecture	4
Lab	0
Other	0

Grading Scheme

Letter

Semester(s) Course Will Be Offered

Spring

Prerequisites

MAT-152

SUNY General Education Course

• Mathematics and Quantitative Reasoning

Course Learning Outcomes

1. Apply precise mathematical reasoning in the use and analysis of course content.
2. Justify conclusions supported by appropriate evidence, presented with proper terminology and notation.
3. Articulate clear solutions to problems by applying definitions, properties, techniques and logical structure included within course concepts.

Topic Outline

1. 1. Number systems
2.     a. Binary, octal, and hexadecimal systems
3.     b. Properties of the integers
4.     c. Modular arithmetic
5. 2. Sets
6.     a. Sets, subsets, and power sets
7.     b. Set representations and Venn diagrams
8.     c. Set operations: intersection, union, and complement
9.     d. Cartesian product
10. 3. Logic
11.     a. Logical operators: conjunction, disjunction, negation, and implication
12.     b. Tautologies and contradictions
13.     c. Truth tables and logical equivalence
14.     d. Valid and invalid arguments
15.     e. Decision tables
16.     f. Quantifiers: universal, existential, and uniqueness
17. 4. Proof techniques
18.     a. The rationale of mathematical proof
19.     b. Understanding the reasoning behind and evaluating the validity of proposed direct proofs
20.     c. Understanding the reasoning behind and evaluating the validity of proposed proofs by contradiction
21.     d. Understanding the reasoning behind and producing basic proofs by mathematical induction
22. 5. Functions
23.     a. Relations as subsets of the Cartesian product
24.     b. Partial orders and equivalence relations
25.     c. Functions: one-to-one, onto, and inverses
26.     d. Recursively defined functions
27. 6. Combinatorics
28.     a. Permutations and combinations
29.     b. The binomial theorem
30.     c. The pigeonhole principle
31. 7. Graph theory
32.     a. Types of graphs, including Kₙ, Cₙ, trees, digraphs, and weighted graphs