# Introduction to Mathematical Proofs

Lectures: W 11:10–13:00 in HW 204

Office hours: W 10:30–11:00 in HE 924 or email me at miha.habic@hunter.cuny.edu for a different time

Course syllabus

Here is the midterm. It is due in class on April 5 by 11:30am. If you cannot make it to class that day, please drop it off in advance in my mailbox in the office, or scan your exam and email it to me. If you would like me to post your results before Apr 19, please add your EMPLID to the exam.

Here are the midterm results. Well done, everyone!

Here are the solutions for the midterm.

Here are some extra problems to practice for the final. I also strongly recommend that you redo all of the homework problems. Here are the solutions.

The in-class final will be on **May 17**. Here is the front page of the final, with a fact sheet.

I will be holding extended office hours on Tuesday, May 16, between 2pm and 4pm. I will also be in the office on Wednesday, before the final.

## Homework sets and practice problems

May 3: Cardinalities of infinite sets, Cantor’s theorem. (Similar to Sections 9.3, 9.4, 10.1–10.3)

- Find the review problems for the final above.

April 26: The fundamental theorem of arithmetic and applications. (Similar to Section 11.6)

April 19: Euclid’s theorem on the infinitude of primes, Bézout’s lemma, equivalent definitions of primes. (I didn’t follow the book here, but much of this is in Sections 11.3 and 11.6)

- No homework today.

April 5: Sections 6.2, 6.4

- No homework today.
- Suggested practice problems (don’t hand these in): 6.21, 6.42, 6.45

March 29: Class cancelled

March 22: Sections 5.1, 5.5, 6.1

- Homework set #7
- Suggested practice problems (don’t hand these in): 5.1, 5.3, 6.5, 6.9, 6.11, 6.16

March 15: Sections 4.1, 5.2, 5.4

- Homework set #6
- Here is a guided “fill in the gaps” outline of a proof of the irrationality of
*e*. Have a look if you like. It needs a bit of familiarity with infinite series and is outside the scope of this course, but is a fun proof nonetheless. - Suggested practice problems (don’t hand these in): 5.14, 5.17, 5.26, 5.28, 5.31

March 8: Sections 3.3, 3.4

- Homework set #5
- Suggested practice problems (don’t hand these in): 3.16, 3.17, 3.20, 3.21, 3.29, 3.31, 3.35

March 1: Sections 3.2, 3.4 (partly), and 4.4

- Homework set #4
- Suggested practice problems (don’t hand these in): 3.8, 3.9, 3.10, 3.11, 3.13, 3.15, 4.40, 4.44, 4.46, 4.49

February 22: Sections 2.10 and 3.2 (partly)

- Homework set #3
- Suggested practice problems (don’t hand these in): 2.68, 2.69, 2.70, 2.71, 2.88, 2.99

February 15: No class today

February 8: Sections 1.4, 1.6, 2.1–2.8

- Homework set #2 (due on Feb 22)
- Suggested practice problems (don’t hand these in): 1.41, 1.45, 2.3, 2.6, 2.13, 2.17, 2.21, 2.24, 2.29, 2.45, 2.48, 2.49, 2.54

February 1: Sections 1.1–1.3

- Homework set #1
- Please read Chapter 0 in the textbook when you have some free time.
- Suggested practice problems (don’t hand these in): 1.6, 1.10, 1.20, 1.21, 1.25, 1.29