## Rose-Hulman - Department of Mathematics - Course Syllabus MA275 - Discrete and Combinatorial Algebra I - 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 275 Discrete and Combinatorial Algebra I 4R-0L-4C F
An introduction to enumeration and discrete structures. Permutations, combinations and the pigeonhole principle. Elementary mathematical logic and proof techniques, including mathematical induction. Properties of the integers. Set theory. Introduction to functions.

Prerequisite: None, though it is normal that a student has completed part of the calculus sequence first.

### Course Goals

1. Introduce students to discrete mathematics, covering especially the topics noted below .
2. Improve mathematical modeling and analytical problem solving skills, especially with discrete mathematics topics.
3. Develop ability to communicate mathematically.
4. Introduce applications of discrete mathematics, especially to science and engineering.

### Textbook and other required materials

Textbook: Discrete and Combinatorial Mathematics, an Applied Introduction 5'th edition. Ralph Grimaldi, Addison-Wesley

### Course Topics

1. Logic
2. Set Theory
3. Proof Techniques
• Induction
• Proof by contrapositive
4. Counting Techniques
• Permutations
• Combinations
• Pigeonhole principle
5. Properties of integers
6. Functions

### Course Requirements and Policies

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

#### Final Exam Policy

The final exam will contain a large common part (approx 80%) with individual instructors adding additional questions. Students shall be restricted to the use of calculators and note cards, in the same way in all sections.