Maths 215: Discrete Systems

Syllabus

1. Prerequisite: MATHS 162 or 165 or permission of the department chairperson.

 

2. Course Description: Topics from discrete mathematics, including formal logic, methods of proof, set theory, relations, recursion, combinatorics, and graph theory. A systematic development of number systems via equivalence classes is included as an application of these topics.

 

3. Course Objectives: Students will be introduced to a variety of topics in discrete mathematics, and will gain experience in using definitions, making logical arguments, and constructing correct proofs in the context of topics in discrete mathematics.

 

4. Course Rationale: This is an important course in developing the mathematical maturity of students, since it expressly treats the most important foundational ideas in mathematics: logic, proof, set, and function.The specific topics in discrete mathematics introduced in this course find important application in such fields as probability theory, computer science, number theory, and abstract algebra.

 

5. Course Content: Formal logic, sets, and functions. The integers: factorization, the Euclidean algorithm, and modular arithmetic. Proof techniques. Recursive definitions and algorithms. Counting arguments. Recurrence relations. Relations in set theory, including equivalence relations and orders. Graph theory.

 

6. Course Format:lecture/discussion.

 

7. Methods of Evaluating Student Performance: Typical components are homework assignments, projects, and take-home exams (possibly involving group work); in-class exams; and student presentations. The evaluation and weight of these components are at the discretion of the instructor. Students may be evaluated on their understanding of the content material of the course, their ability to solve problems related to the course material, and on their ability to communicate mathematically to others orally and/or in writing.

 

8.  Evaluation of the Course: The instruction of the course is evaluated by departmental student evaluations and peer evaluation. The course is reviewed and revised periodically by the Departmental Undergraduate Programs Committee.

 

Revised M. Karls Fall 2006