MATH 3325 Intro to Proofs

MATH 3325 Intro to Proofs, Fall 2024

Syllabus

Class meeting

Hall 305 MW 12:30pm – 1:45 pm

Office hours

Hall 314U Mon, 4:45 pm– 5:30 pm; Anytime by appointment (please email me)

Textbook

Proofs: A Long-Form Mathematics Textbook by J. Cummings

Mathematical Proofs: A Transition to Advanced Mathematics by Gary Chartrand, Albert D. Polimeni, Ping Zhang

Notes

Intuitive Proofs

- Chessboard problems
- The pigeonhole principle

Direct proofs

- If...then and proof by cases
- Divisibility and Modular Arithmetic
- Exercises class direct proofs

Sets and Logic

- Sets
- Exercise class - Sets

Induction

- Examples of induction
- ** Extra Credit and group work**

Logic

- Exercises class
- The contrapositive

Homeworks

There will be a homework each week. These assessed questions will collectively count for 20% of your overall grade.

HW 1: Exercises 1.3, 1.4, 1.7, 1.8, 1.15, 1.17 Deadline: Sep 4 (Solutions .tex template I use TexShop(local) or overleaf(online) to edit latex files)
HW 2:Exercises 2.2(a),2.5(a),2.6,2.7(a,b),2.11 Deadline: Sep 11
No Homework this week due to the Exam next week.
HW 3: Choose 5 exercises from chapter 3 that we didn't do in class. Deadline: Sep 30
HW 4: Exercises 4.19,4.22,4.25,4.27,4.30. Deadline: Oct 9
HW 5: Exercises 5.15,5.19,5.23(b), 5.24(f), 5.25(g). Deadline: Oct 21
No homework this week due to the group work we did.
HW 6: Exercises 7.2(c),7.3(a), 7.6(a), 7.12, 7.14 of chapter 7 exercises Deadline: Nov 11
HW 7: Exercises 9.63,9.64, 9.65, 9.74, 9.79 of chapter 9 exercises Deadline: Dec 2

Exams