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Spring 2019

Mathematics Courses:

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MAT247 - Discrete Math

Credits: 3

Catalog Description: Provides an introduction to discrete mathematical structures and their applications to computer programming. Topics include logic of compound and quantified statements, elementary number theory, direct & indirect proofs, mathematical induction, sets, discrete probability & counting, functions, and an introduction to graph theory. Spring only. Prerequisite: MAT 140 with a grade of ā€˜Cā€™ or higher or by placement.

Lecture: 3 hrs.

Course Learning Outcomes (CLOs):
Upon completion of the course, the student should be able to:

1.Generate a truth table for at least 5 different sets of propositional statements (and, or, not, if-then, if-and-only-if)
2.Convert between informal English expressions and formal quantified logic.
3.Demonstrate a mathematic proof of a stated algebraic relation using any the following techniques, with 100% accuracy: direct proof, indirect proof, contradiction, mathematical induction
4.Accurately identify the union, intersection, and complements of at least 3 simple sets
5.Prove that one set is a subset of, or is equal to, another set*
6.Use permutations and combinations to perform at least five different (counting) problems
7.Compute probabilities for simple events, accurate to 3 decimal places
8.Identify the domain and range of at least 3 different types of functions
9.Prove that a given relation: is a function, is one-to-one, or is onto*
10.Given any simple function (linear, rational, quadratic, or cubic), evaluate it and find its inverse (or explain why the inverse does not exist)
11.Identify the different components of a graph (vertex, edge, loop, parallel edges, isolated vertex, path, circuit, Euler path, Euler circuit, Hamilton path, and Hamilton Circuit)

* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.

Content Outline:
I. The Logic of Compound Statements
a.Logical Form and Logical Equivalence
b.Conditional Statements
c.Valid and Invalid Arguments

II. The Logic of Quantified Statements
a.Introduction to Predicates and Quantified Statements
b.Statements Containing Multiple Quantifiers
c.Arguments with Quantified Statements

III. Elementary Number Theory and Methods of Proof
a.Methods of Proof (Direct, Indirect, Contradiction)
b.Rational Numbers
c.Divisibility
d.Quotient-Remainder Theorem
e.Algorithms

IV. Mathematical Induction

V. Set Theory
a.Basic Definitions of Set Theory
b.Properties of Sets

VI. Counting
a.Introduction to Discrete Probability
b.Multiplication & Addition Rules
c.Permutations and Combinations, including
d.R-combinations with Repetition Allowed
e.Algebra of Combinations
f.Binomial Theorem

VII. Functions
a.Functions Defined on General Sets
b.One-to-One, Onto, and Inverse Functions
c.The Pigeonhole Principle
d.Compositions
e.Cardinality of Sets

V. Graphs
a.Introduction to Graphs
b.Paths and Circuits
c.Matrix Representation of Graphs
d.Graph Isomorphisms

Effective Term: Fall 2012