[ugrads] Elective Courses in Spring 2009

Hemanshu Kaul kaul at math.iit.edu
Thu Nov 6 19:35:45 CST 2008

Dear Students,

I wanted to bring your attention to an elective course in number theory 
that is being offered in Spring 2009. This course is offered once every 
two years, and was offered for the first time in Spring 2007. You can find 
the official syllabus at 

Starting with minmal prerquisites, this course builds upto the famous 
classical result of Gauss in quadratic reciprocity that answers the 
fundamental question of when does a quadratic equation have a integer 
solution (modulo prime). Along the way, we will explore many other 
fundamental properties of integers. Finally we will apply our knowledge to 
the study of cryptosystems.

Also, the students who have/ are taking courses in Linear Algebra, Graph 
Theory, and Probabilty, might be interested in a graduate level course in 
Discrete Math that I am offering next semester. Only the students with 
strong performance in these courses will be permitted to take this course. 
Please contact me if you any questions/ need more information.

Here is a description of the course:

Math 554: Discrete Applied Mathematics II

Instructor: Hemanshu Kaul, http://www.math.iit.edu/~kaul

This graduate-level course in Discrete Mathematics will introduce students 
in Applied Mathematics, Computer science, and Engineering, to the use of 
tools and techniques from various fields of mathematics like Probability, 
Linear Algebra, and Geometry, to existential and algorithmic problems 
arising in Graph Theory, Combinatorics, and Computer science. The tools 
considered would include Probabilistic Method, Entropy, Vector Space 
method, Combinatorial Nullstellensatz, Martingales and large deviation 
bounds, Markov Chain Monte Carlo, etc.

The only prerequisites would be standard undergraduate courses in
Probability, in Elementary Linear Algebra, and in Graph Theory or
Combinatorics. Undergarduate students with strong performance in these 
courses will be admitted with the consent of the instructor.

Course grade will be based on 8-10 homeworks, a mid-term and a final exam, 
and a reading project with presentation.

I apologize for any multiple mailings.


Hemanshu Kaul
Assistant Professor of Applied Mathematics
Illinois Institute of Technology, Chicago

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