Instructor: Benjamin Schroeter
| Lecture: | Monday | 12:00 - 1:00 | CW 325 |
| Tuesday | 11:40 - 1:05 | OR 100D | |
| Wednesday | 12:00 - 1:00 | CW 325 | |
| Friday | 12:00 - 1:00 | CW 325 |
| Office hours: | Wendnesday | 10:45 - 11:45 | WH 209 |
| Thursday | 11:00 - 12:00 | WH 209 |
This course will focus on enumerative combinatorics and might include basics of algebra, analysis and polyhedral geometry. Basic knowlege in clalculus, linear algebra and writing proofs is assumed.
Mainly we will follow
Principles and techniques in combinatorics
by Chen Chuan-Chong and Koh Khee-Meng.
More about the topics can be found in:
Enumerative Combinatorics, Vol. 1 and Vol. 2. by Richard Stanley,
Catalan Numbers by Richard Stanley,
Triangulations -- Structures for Algorithms and Applications by
Jesús De Loera, Jörg Rambau and Francisco Santos.
There are weekly research talks in the Combinatorics Seminar, and many talks on the AMS Eastern Sectional Meeting (Oct. 12-13) at Binghamton University. I recommend to visit some talks this semester.
You can find the syllabus here.
The first test takes place on Friday, September 25, in CW 325.
The second test takes place on Friday, November 1, in CW 325.
The final exam takes place on Thursday 8am, December 12, in LH 3.
| Week 1 | 21 Aug. -- 23 Aug. | Introduction and Motivation |
| Week 2 | 26 Aug. -- 30 Aug. | Permutations [Sec. 1.1-1.3] |
| Week 3 | 03 Sep. -- 06 Sep. | Combinations and Stirling numbers of the first kind [Sec. 1.4] |
| Week 4 | 09 Sep. -- 13 Sep. | Stirling numbers of the first kind, HW1, injections and bijections [Sec. 1.4-1.5] |
| Week 5 | 16 Sep. -- 20 Sep. | The Injection and Bijection Principle, Repetition and Multisets [Sec. 1.5-1.6] |
| Week 6 | 23 Sep. -- 27 Sep. | Review and Exam |
| Week 7 | 30 Sep. -- 04 Oct. | More about Binomial Coefficients and Practice |
| Week 8 | 07 Oct. -- 11 Oct. | Binomial Coefficients, Lattice Paths in a Rectangular Grid and Multinomial Coefficients [Ch. 2] |
| Week 9 | 14 Oct. -- 18 Oct. | The Pigeonhole Principle [Sec. 3.1-3.3] |
| Week 10 | 21 Oct. -- 25 Oct. | Complete Graphs and Ramsey Numbers [Sec. 3.4-3.5] |
| Week 11 | 28 Oct. -- 01 Nov. | Practice, Review and Exam |
| Week 12 | 04 Nov. -- 08 Nov. | A Brief Introduction of Inclusion-Exclusion [Sec. 4.1-4.3, 4.5] |
| Week 13 | 11 Nov. -- 15 Nov. | Generating Functions [Ch. 5] |
| Week 14 | 18 Nov. -- 22 Nov. | Recurrence Relations, and Jordan Normal Forms |
| Week 15 | 25 Oct. -- 27 Nov. | Solving (inhomogeneous) Linear Recurrence Relations |
| Week 16 | 02 Dec. -- 04 Dec. | Snow and Review |
| Homework Set 1, |
| Homework Set 2, |
| Homework Set 3, |
| Homework Set 4, |
| Homework Set 5, |