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Related lectures (53)
Cartesian Product and Induction
Introduces Cartesian product and induction for proofs using integers and sets.
Differential Forms Integration
Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.
Mapping Functions and Surjections
Explores mapping functions, surjections, injective and surjective functions, and bijective functions.
Sets and Proofs
Introduces sets in discrete mathematics and explores proof techniques like direct and indirect proofs.
Sets and Operations: Introduction to Mathematics
Covers the basics of sets and operations in mathematics, from set properties to advanced operations.
Functions: Definitions and Notations
Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.
Set Union: Properties and Operations
Explains the union of sets, its properties, operations, and intersection.
Sets and Functions
Introduces sets and functions, covering union, intersection, complement, functions terminology, and set operations analogies.
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.
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.
Composition of Applications in Mathematics
Explores the composition of applications in mathematics and the importance of understanding their properties.
Introduction to Analysis: Understanding Real Numbers and Proofs
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Covers the basics of analysis, including real numbers, proofs, sets, and operations.
Proofs and Logic: Introduction
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Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.
Analysis IV: Measurable Sets and Properties
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Covers the concept of outer measure and properties of measurable sets.
Sparsest Cut: ARV Theorem
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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.
Properties of Real Numbers
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Covers countability and bijections between sets, demonstrating the uncountability of real numbers.
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