## Rose-Hulman - Department of Mathematics - Course Syllabus

MA375 - **Discrete and Combinatorial Algebra II** - 2010-11

**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

- Continue to introduce students to discrete mathematics, covering especially
the topics noted in the course topics below.
- Improve mathematical modeling and analytical problem solving skills,
especially with generating functions and recurrence relations.
- Develop an ability to communicate mathematically.
- 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**

- Relations
- Equivalence relations
- Modular arithmetic

- Principle of Inclusion-Exclusion
- Generating functions
- Recurrence relations
- Finite State Machines
- 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

- Under Relations:
- Graph theory
- Relation matrices
- Partial orders

- Minimization of finite state machines
- Modular arithmetic : Multiplicative inverses
- Permutation groups
- 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.

**Individual Instructor Policies**

Your instructor will determine the following for your class:
- the grading scheme, based on the various course components.
- the number and format of hour exams, quizzes, homework
assignments, in class assignments, and projects,
- the policies governing the work items above, e.g.,
whether the computer will be used, what collaboration is allowed, and the
format of assignments.
- all policies for classroom procedure, including group
work, class participation, laptop use and attendance*.

*Note that most instructors will enforce some type of grade
penalty for students with more than four unexcused absences.
###

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