MAT 299 - Mathematical Proof and Problem Solving
Syllabus (Fall 2022)
Course Description: This course introduces students to the language and methods used to create and write mathematical proofs and solve problems. Methods of proof will include: direct, contrapositive, contradiction, and induction. Students will learn about and utilize the many functions of proof including: verification, explanation, communication, discovery, justification, and inquiry. The course will also explore the relationship between problem solving and the process of proving. Students will explore fundamental abstract concepts in mathematics including: functions and relations, set theory, number theory, and logic.
Course Timeline and Notebooks
Below is a tentative timeline for our course. It includes preparatory work that should be done prior to each class meeting, a detailed set of notes corresponding to each class meeting, and assignments following each class meeting.
| Class Meeting | Before Class | During Class | After Class |
|---|---|---|---|
| 1 | Review Syllabus Setup Google Colab |
Introduction and What to Expect Sets, Part I |
HW 1: Intro to Colab and LaTeX |
| 2 | Sets, Part II | HW 2 | |
| 3 | Logic for Proof, Part I | ||
| 4 | Logic for Proof, Part II | ||
| 5 | Direct Proof, Part I | HW 3 | |
| 6 | Direct Proof, Part II | ||
| 7 | Proof by Contrapositive, Part I | HW 4 | |
| 8 | Proof by Contrapositive, Part II | ||
| 9 | Catch-Up Day | ||
| 10 | Proof by Contradiction, Part I | HW 5 | |
| 11 | Proof by Contradiction, Part II | ||
| 12 | Biconditionals | HW 6 | |
| 13 | Existence and Uniqueness | ||
| 14 | Proofs About Sets, Part I | HW 7 | |
| 15 | Proofs About Sets, Part II | ||
| 16 | Disproof | ||
| 17 | Exam I, Part I | ||
| 18 | Exam I, Part II | ||
| 19 | Proof by Induction, Part I | HW 8 | |
| 20 | Proof by Induction, Part II | ||
| 21 | Relations, Part I | HW 9 | |
| 22 | Relations, Part II | ||
| 23 | Functions, Part I | HW 10 | |
| 24 | Functions, Part II | ||
| 25 | Functions, Part III | ||
| 26 | Exam II, Part I | ||
| 27 | Exam II, Part II | ||
| 28+ | Oral Proof Defenses |