Course: MCS 582: The Probabilistic Method
Call no: 43767
Time: MWF 12:00-12:50pm
Place: BH 304 (in person)

Professor: Dhruv Mubayi
Office: 620 SEO
Course Web Page:
Office Hours: W 10-12 and by appointment

Grading Policies and Points Breakdown:
Your grade will be based on homework assignments every 2 weeks (80%), and attendance and participation (20%). A grade of 80% on homework (meaning 16/20 for each homework) will usually correlate with an A in the course, assuming good attendance and participation. You can discuss homework with each other but must write it up independently with no help from anyone else. Do not search the web for solutions, but you are permitted to search the web for definitions (or just email me)

Homework *MUST* be typed in Latex and posted on blackboard as a pdf file before class begins on the day it is due.

Accommodations: Disability Policy - Students with disabilities who require accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS). Please contact ODS a 312/413/-2183 (voice) or 312/413-0123 (TTY).

Prerequisite: An undergraduate course in combinatorics or probability and the mathematical maturity of a graduate student.

Course Description: The probabilistic method is a powerful tool for tackling many problems in mathematics, statistics and computer science. The basic idea of the method is as follows: in order to prove that a structure with certain desired properties exists, once defines an appropriate probability space of structure s and then shows that the desired properties hold in this space with positive probability. Introduced by Erdos in the 1940s to solve a basic problem in Ramsey theory, it has since proven useful in many different areas of mathematics (e.g. geometry, number theory, combinatorics) and more recently in computer science and statistics as well. The course should therefore be interesting and useful for students in a variety of fields. This course will be a thorough introduction to the probabilistic method. While we will focus on applicati ons in combinatorics, problems in different areas will often be explored. A sampling of topics: Ramsey numbers, random graphs, Local Lemma, second moment method, correlation inequa lities (the four function theorem and the FKG inequality), martingales, circuit complexity, discrepancy, geometric problems, derandomization.

Course Goals and Learning Objectives: To gain proficiency in applying the probabilistic method to problems in all areas of mathematics and computer science. Recommended Coure Materials: The Probabilistic Method by Alon and Spencer (Fourth edition)

Optional Texts:
Random Graphs by Bollobas (second edition)
Random Graphs by Janson, Luczak, Rucinski
Introduction to Random Graphs by Frieze and Karonski (available for free at

Policy for missed or late work, including acceptance of revised work: Homework turned in late will not be graded unless prior approval of the instructor has been obtained.

Attendance/Participation Policy: Attendance is required and students are expected to actively participate and engage with the material during lectures.

Community Agreement/Classroom Conduct Policy: Community Agreement: Ground Rules for a Safe/Brave Space • Be present (turn off cell phones and remove yourself from other distractions) • Be respectful • Assume good will • Challenge with care - approach discussion as a “think out loud” • Take space/make space 11 • Identities stay, learning leaves • Try not to make assumptions, seek to understand, not to judge • Be open to challenges as an opportunity to learn something new • Be open to different perspectives • Debate the concepts not the person • Be flexible when things don’t work • Share helpful tips • Use preferred names and gender pronouns • No side conversations • Be willing to work together

Homework 1, Due Friday January 19
Homework 2, Due Friday February 2
Homework 3, Due Friday February 16
Homework 4, Due Friday March 1
Homework 5, Due Friday March 15
Homework 6, Due Friday April 5 (extra week due to Spring break)
Homework 7, Due Friday April 19