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Topics in Combinatorics

 

The current course handouts can be found here: handout.pdf (in farsi) which contains all neccessary information about the course (syllabus, office hours, grading system, references, etc).

Homeworks will be handed out and in through IUT web course.

This is a secondary course in combinatorics which aims to explore a number of significant topics in combinatorics and graph theory. It is suitable for graduate students after passing one of the courses combinatorics (19-14-564) or graph theory (19-14-563). The basic topics which are covered in this course are a discussion in enumerative combinatorics (counting the structures of a given kind and size) and extremal combinatorics (finding largest or smallest combinatorial objects). The mutual interactions of combinatorics and probability (including random graphs) as well as set systems (including hypergraphs) are also studied.

Textbooks: 

1- Jukna S., Extremal Combinatorics With Applications in Computer Science, Second Edition, 2011.

2- Cameron P.J., Combinatorics, Topics, Techniques, Algorithms, 1994.

 
Outline of the course:
 
1- Enumerative combinatorics
Double counting
Pigeon-hole principle
 
2- Extremal combinatorics
Extremal set theory
Extremal graph theory
Ramsey theory
Partially ordered sets: chains and anti-chains
Set systems and hypergraphs
 
3- Probabilistic methods
 
4- Algebraic methods
 
Prerequisites: 

Discrete Mathematics

Grading Policy: 

15% Homeworks

85% Midterm and Final Exams

There is a number of optional self-reading subjects. For the list check this link.

Time: 

Mondays and Wednesday 13:00-15:00

Term: 
Fall 2013
Grade: 
Graduate