MTH 232 Discrete Mathematics 2

Lecture Hours: 4
Credits: 4

A second course in discrete mathematics. Builds on the topics of MTH 231 including topics in combinatorics, mathematical proofs, probability, graph theory and number theory. Applications include cryptography and analysis of algorithms.

Prerequisite: Placement into WR 115 (or higher), or completion of WR 090 (or higher); and completion of MTH 231 or equivalent course as determined by instructor; or consent of instructor. (All prerequisite courses must be completed by a grade of C or better.)
Student Learning Outcomes:

Model and solve counting problems by applying properties of functions and techniques of combinatorics including problems involving indistinguishable items, repetition, and the principle of inclusion/exclusion.
Apply mathematical proof techniques in settings of number theory, graph theory, analysis of algorithms, and probability.
Calculate and interpret probabilities by applying principles of discrete probability, techniques of combinatorics and set theory.
Analyze graphs and apply techniques for identifying Euler and Hamiltonian paths, shortest paths, chromatic numbers, and isomorphic graphs.
Classify the growth of functions and the run-time of algorithms using Big O notation.
Apply principles of number theory including divisibility, modular arithmetic, modular congruences, and their applications to cryptography.

Statewide General Education Outcomes

Use appropriate mathematics to solve problems.
Recognize which mathematical concepts are applicable to a scenario, apply appropriate mathematics and technology in its analysis, and then accurately interpret, validate, and communicate the results.

Content Outline

Foundational Topics in Discrete Mathematics
- Proofs (direct, contraposition, contradiction, induction)
- Sets
- Basic Combinatorics
Advanced Combinatorics
- Permutations with non-distinct objects
- Repetition allowed combinations
- Inclusion/Exclusion
- Applications
Discrete Probability
- Basics of Discrete Probability
- Methods for Calculating Probability (probability theory)
- Conditional Probability and Bayes Theorem
- Expected Value
Algorithms
- Number Theory
- Divisibility
- Modular arithmetic
- Primes and GCD’s
- Representations of Integers and related Algorithms
- Modular Congruences
- Applications in Cryptography
Graph Theory
- Basics of Graph Theory
- Graph Isomorphisms
- Euler Paths
- Hamiltonian Paths
- Shortest Paths
- Planar Graphs
- Graph Coloring