Introduces sets in discrete mathematics and explores proof techniques like direct and indirect proofs.
Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.
Introduces sets and functions, covering union, intersection, complement, functions terminology, and set operations analogies.
Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.
Covers conditional expectation, Fubini's theorem, and their applications in probability theory.
Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.
