Math 554: Discrete Applied Math II

Instructor: Hemanshu Kaul

Office: 234B, Engineering 1
Phone: (312) 567-3128
E-mail: kaul [at]

Time: 10am, Tuesday & Thursday.
Place: 106, Engineering 1 Bldg.

Office Hours: 1pm-2pm Tuesday and Thursday, walk-ins, and by appointment. Emailed questions are also encouraged.

|Course Information| |Advice| |Announcements| |Examinations| |Homework| |Class Log & Handouts| |Links|

Course Information:

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, Algebra, and Stochastic processes, to existential and algorithmic problems arising in Graph Theory, Combinatorics, and Computer science.
The tools considered would include Probabilistic Methods, Linear Algebra methods, Combinatorial Nullstellensatz, Entropy, Martingales and large deviation bounds, Markov chain Monte Carlo, etc. These tools will applied to various fundamental problems like - graph and hypergraph coloring, Intersecting families of sets, Ramsey problems, Extremal problems on Graphs and set systems, Optimization problems on discrete structures, Sampling and counting discrete objects, etc.

The Course Information Handout has extensive description of the course - topics, textbooks, student evaluation policy, as well as other relevant information. Read it!

Advice for students:

Excellent advice by Doug West on how to write homework solutions for proof-based problems.

On a more abstract note, here is a discussion of Language and Grammar of Mathematics - which is what you are starting to learn in a course like this.

Excellent advice for math majors and graduate students, by Terry Tao, 2006 Fields medallist. Required reading.

Class Announcements:


Homework Assignments:

  • Homework #1: Due Tuesday, 2/3. Solutions distributed in class on Thursday, 2/5.
  • Homework #2: Due Thursday, 2/12. Solutions distributed in class on Thursday, 2/19.
  • Homework #3: Due Tuesday, 3/3. Solutions distributed in class on Thursday, 3/12.
  • Homework #4: Due Tuesday, 3/24. Solutions distributed in class on Tuesday, 3/24.
  • Homework #5: Due Thursday, 4/23. Solutions distributed in class on Thursday, 5/7.

  • Class Log & Handouts:

    Links for Additional Information:

  • Wikipedia: Combinatorics
  • Mathpages: Combinatorics
  • Glossary of terms in combinatorics
  • Dynamic Surveys in Combinatorics
  • Combinatorics Information Pages
  • Combinatorial Catalogues

  • Mathworld : Graph Theory Dictionary
  • Planet Math : Graph Theory
  • Graph Theory with Applications by Bondy and Murty
  • Graph Theory (3rd ed.) by Diestel

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