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Related lectures (27)
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Introduction to Analysis
Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.
Sets and Functions
Introduces sets and functions, covering union, intersection, complement, functions terminology, and set operations analogies.
Sparsest Cut: ARV Theorem
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.
Sets, Functions and Relations: Q&A
Covers examples of relation composition, Cartesian product, and injective functions.
Linear Algebra: Sets and Operations
Introduces fundamental concepts of linear algebra, focusing on sets and operations.
Properties of Real Numbers
Covers countability and bijections between sets, demonstrating the uncountability of real numbers.
Conditional Expectation
Covers conditional expectation, Fubini's theorem, and their applications in probability theory.
Approximation Algorithms
Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.
Set Cover: Integrality Gap
Explores the integrality gap concept in set cover and multiplicative weights algorithms.
Mathematical Induction: Basics and Applications
Introduces mathematical induction principles and applications, including inequalities, divisibility, subsets, and strong induction.