Mathematics 4801/5609 Topics in Combinatorics

Winter 2019, Math 4801/5609
School of Mathematics and Statistics, Carleton University


Instructor: Daniel Panario
Office: #4372 HP, Tel: (613) 520 2600 (Ext. 2159)
Email: daniel@math.carleton.ca
Lectures: Tuesdays 17:35-20:25. Room: HP 4369
Office hours: Tuesdays 16:35-17:25, or by appointment (send me mail or talk with me).


General Information


Tentative lecture schedule - subject to change

WEEK 

DATES 

CHAPTER 

TOPICS

1

Jan. 7-11

1

Introduction to the course. Six proofs of the infinitude of primes and proofs that the sum of the reciprocal of the primes diverges.

2

Jan. 14-18

2

Bertrand's postulate. [A1 out]

3

Jan. 21-25

6

Every finite division ring is a field.

4

Jan. 28 - Feb.1

8

Some irrational numbers.

5

Feb. 4-8

9

Riemann Zeta function and three times pi^2/6. [A1 in/A2 out]

6

Feb. 11-15

9

Three times pi^2/6 (cont).

~

Feb. 18-22

READING WEEK

7

Feb. 25 - Mar. 1

28

Pigeonhole principle and double counting.

8

Mar. 4-8

28

Double counting and extremal graph theory. [A2 in/A3 out]

9

Mar. 11-15

30

Three famous theorems in finite sets.

10

Mar. 18-22

31

Shuffling cards.

11

Mar. 25-29

31; 35

Shuffling cards (cont.); Kakeya problem. [A3 in] [Deadline to submit project]

12

Apr. 1-5

31; 35

Kakeya problem (cont.).

13

Apr. 8-12

Student presentations (lectures from textbook).

The above weekly outline is subject to change depending on the progress of the course. The chapters are from the textbook.