MTH 232 Discrete Mathematics 2

Lecture Hours: 4
Credits: 4

Applies fundamentals from MTH 231 to tree theory, advanced counting techniques, relations, and Boolean algebra. Offers a second course for computer science and mathematics majors.

Prerequisite: Placement into WR 115 (or higher), or completion of WR 090 (or higher); and completion of MTH 231 (or higher) 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:

Use properties of functions to model and solve counting problems
Write a permutation in disjoint cycle notation
Evaluate inverses and composites of permutations
Use Euclid’s algorithm to evaluate the GCD of two integers
Use the Chinese remainder theorem to solve a system of congruencies
Identify properties that an operation does or does not have on a given set
Determine whether two groups are isomorphic
Encrypt and Decrypt messages using RSA and Rabin’s method
Create viable public and private keys for RSA and Rabin’s method

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

Functions
- Function Properties
- Pigeonhole Principle
- Composition
- Permutations
- Symmetry
- Asymptotics
Number theory
- Division algorithm
- GCD
- Modular Arithmetic
- Chinese Remainder Theorem
- Factoring
Group Theory
- Groups
- Isomorphism
- Subgroups
- Fermat’s Little Theorem
Cryptography
- Public Key Cryptography
- Rabin’s Method
- RSA