## Rose-Hulman - Department of Mathematics - Course Syllabus MA375 - Discrete and Combinatorial Algebra II - 2010-11

 Description & Prerequisites Course Goals Texts and Other Materials Course Topics Course Policies Links last posted to site: 08/19/10

Parts of the web page to be completed or determined by the instructor are in green.

### Catalogue Description and Prerequisites

MA 375 Discrete and Combinatorial Algebra II 4R-0L-4C W Pre: MA 275
A continuation of MA 275. Relations. An introduction to finite state machines. More advanced enumeration techniques including recurrence relations, generating functions and the principle of inclusion and exclusion.

Prerequisite: MA 275

### Course Goals

1. Continue to introduce students to discrete mathematics, covering especially the topics noted in the course topics below.
2. Improve mathematical modeling and analytical problem solving skills, especially with generating functions and recurrence relations.
3. Develop an ability to communicate mathematically.
4. Introduce applications of discrete mathematics, especially in science and engineering.

### Textbook and other required materials

Textbook: Discrete and Combinatorial Mathematics, an Applied Introduction

### Course Topics

1. Relations
• Equivalence relations
• Modular arithmetic
2. Principle of Inclusion-Exclusion
3. Generating functions
4. Recurrence relations
5. Finite State Machines
6. The following topics are to be included as examples of the above topics:
• Introduction to group theory
• Introduction to graph theory

The following list of topics are those that, while not required, are suggested topics used to supplement the above required topics. Those who teach MA 375 in a given year are to decide which of these topics are to be included. The specific course topics to be covered will be listed in the companion file MA375TopicsFromText.php

1. Under Relations:
• Graph theory
• Relation matrices
• Partial orders
2. Minimization of finite state machines
3. Modular arithmetic : Multiplicative inverses
4. Permutation groups
5. Spanning trees

### Course Requirements and Policies

The following policies and requirements will apply to all sections and classes:

Final Exam Policy There will be final exam common to all sections.