Course Overview:
The Probabilistic Method is a powerful tool in tackling many problems in discrete mathematics. It belongs to those areas of mathematics which have experienced a most impressive growth in the past few decades. Roughly speaking, its basic idea can be described as follows. In order to prove existence of a combinatorial structure with certain properties, we construct an appropriate probability space, and show that a randomly chosen element of this space has the desired property, with positive probability. This course provides a gentle introduction to the Probabilistic Method, with emphasis on methodology. We will try to illustrate the main ideas by showing the application of probabilistic reasoning to various combinatorial problems.
MAIN TEXTBOOK:
- The Probabilistic Method, Third Edition, 2008, by N. Alon and J.H. Spencer
Class time and Location:
Saturday and Monday 10:00-12:00 AM (Fall 2018), Room 204/1.
Prerequisites:
General mathematical sophistication; and a solid understanding of Algorithms, Linear Algebra, and Probability Theory, at the advanced undergraduate or beginning graduate level, or equivalent.
Grading:
- Homework – 10%
- Midterm – 40%
- Endterm – 50%
Midterm Examination 1: Monday, 95/02/06, 10:00-12:00 AM
Midterm Examination 2: Saturday, 95/03/01, 10:00-12:00 AM
Final Examination: Monday, 95/03/10, 08:00-12:00 AM
Questions?
I’ll be having office hours for this course on Saturday and Monday 08:30–10:00 AM. If this isn’t convenient, email me at hhaji@sbu.ac.ir or talk to me after class.
Grades:
Stu. Num. Midterm 1 Midterm 2 Homework Final
94422052 26.3/30 26/30 3.9/5 9.9/12
93422001 3.8/50 18.5/30 2/5 4/12
94420000 19.2/30 17.5/30 2/5 6.9/12
M. M. 26.7/30 28.5/30 5/5 9/12