Course Description
A rigorous introduction to discrete mathematical structures, proof techniques, and programming. Topics include sets, functions, sequences, relations, induction, propositional and predicate logic, modular arithmetic, and mathematical programming. Notes: Only one of MAT 253 or MAT 295 can count toward degree requirements for MATH major.
Syllabus
Student Learning Outcomes, Goals, Objectives:
Students successfully completing this course will be able to:
SLO 1
- translate statements between the English language and first order logical statements using quantifiers and logical operations
- draw Venn diagrams to illustrate relationships between categories
- give truth tables for logical statements
- give definitions of the fundamental discrete mathematical structures
- identify and describe various types of relations between objects
- translate the instructions for a procedure between English and Python computer code
SLO 2
- prove logical statements are tautologies via truth tables
- analyze simple algorithms and identify values of variables at various stages of completion
- compute the number of solutions to problems or arrangements
- evaluate an argument for logical validity
SLO 3
- combine the definitions and methods learned in class to create rigorous proofs of basic statements about discrete mathematical structures, more specifically:
- prove statements are true directly, by contrapositive, or by contradiction
- prove statements are false by giving counterexamples
- prove statements are true via induction
- prove given functions have mathematical properties such as injectivity
- prove given relations have mathematical properties such as transitivity
- prove statements about divisibility
Course Grading Information:
| Activity/Performance Measure | Percentage/Points |
|---|---|
| Homework Assignments | 20% |
| Programming Assignments | 10% |
| Attendance | 10% |
| Tests 1-3 | 45% |
| Final Exam | 15% |
Attendance/Participation:
Attendance/participation is a graded component included in the student's final grade for this course.
Course Materials Purchased by the Students:
No course materials are required.
Scholarly Perspectives
This course engages diverse scholarly perspectives to develop critical thinking, analysis, and debate and inclusion of a reading does not imply endorsement.