Mathematics 4801/5609 Topics in Combinatorics

Fall 2017, 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 16:05-17:25 and Thursdays 16:05-17:25. Room: HP 4369
Office hours: Tuesdays and Thursdays 17:30-18:00, or by appointment (send me mail or talk with me).


General Information


Tentative lecture schedule - subject to change

WEEK 

DATES 

CHAPTER 

TOPICS

1

Sep. 6-8

1

Introduction to the course. Six proofs of the infinitude of primes.

2

Sep. 11-15

1

More on six proofs of the infinitude of primes and proofs that the sum of the reciprocal of the primes diverges.

3

Sep. 18-22

2

Bertrand's postulate. [A1 out]

4

Sep. 25-29

6

Every finite division ring is a field.

5

Oct. 2-6

8

Some irrational numbers.

6

Oct. 10-13

9

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

7

Oct. 16-20

9

Three times pi^2/6 (cont).

~

Oct. 23-27

READING WEEK

8

Oct. 30 - November 3

27

Pigeonhole principle and double counting.

9

Nov. 6-10

27

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

10

Nov. 13-17

29

Three famous theorems in finite sets.

11

Nov. 20-24

30

Shuffling cards.

12

Nov. 27 - December 1

30; 34

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

13

Dec. 4-7

Student presentations (lectures from textbook).

The above weekly outline is subject to change depending on the progress of the course. Student presentations could be early in November. The chapters are from the textbook.