Topics in Combinatorics - the Probabilistic Method (MAT577 and MAT478)

Noga Alon (first name initial followed by last name at math dot princeton dot edu)
Spring 2022, Tuesday and Thursday 9:30-10:50, Room:

The main webpage of the course appears in Canvas.

Procedural Matters:

Prerequisites: Basic knowledge of Discrete Mathematics and Probability.

Text books:
Most of the topics covered in the course appear in the books listed below (especially the first one). Other topics appear in recent papers, many of which can be found in the journal Random Structures and Algorithms.
N. Alon and J. H. Spencer, The Probabilistic Method, Fourth Edition, Wiley, 2016.
B. Bollobas, Random Graphs, Second Edition, Cambridge University Press, 2001.
S. Janson, T. Luczak and A. Rucinski, Random Graphs, Wiley, 2000.
M. Molloy and B. Reed, Graph Colouring and the Probabilistic Method, Springer, 2002.

Course syllabus:

Probabilistic methods in Combinatorics and their applications in theoretical Computer Science. The topics include linearity of expectation, the second moment method, the local lemma, correlation inequalities, martingales, large deviation inequalities, geometry and possibly more as time permits.


For undergrads who need to receive a grade, there will be a few problem sets over the semester. There will be no final exam.