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Proofs: Contraposition vs. Contradiction
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Related lectures (47)
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Graph Sketching: Connected Components
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Covers the concept of graph sketching with a focus on connected components.
Fundamental Solutions
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Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.
Hermite Normal Form: Computation & Properties
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Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.
Optimal Transport: Heat Equation and Metric Spaces
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Explores optimal transport in heat equations and metric spaces.
Newtonian Potential: Bounded Domains
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Explores Newtonian potential in bounded domains, discussing its conditions and properties.
Number Theory: Operations and Equivalence
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Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.
Integers and Rings
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Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.
Markov Chains Decomposition
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Covers Markov chains decomposition, LLN proof, Inventory Model application, and average costs.
Proof of Sylow Subgroup Properties
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Explores the properties of p-subgroups of Sylow in a group.
Functional Analysis I: November 18, 2021
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Covers partially ordered sets, maximal elements, upper bounds, and the Zorn lemma in functional analysis.
Orthogonality and Least Squares Methods
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Explores orthogonality, norms, and distances in vector spaces for solving linear systems.
Harmonic Forms and Riemann Surfaces
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Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.
Arithmetic Fundamentals: Equivalence and Irreducibility
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Covers the fundamental theorem of arithmetic, focusing on equivalence and irreducibility of integers.
Convex Optimization: Gradient Descent
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Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.
Sparsest Cut: Bourgain's Theorem
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Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.
Sparsest Cut: (log n) Approximation Algorithm
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Covers the (log n) approximation algorithm for the sparsest cut problem, presenting the mathematical theorems and proofs.
Math-101(en) / Min/Max, Inf/Sup
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Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.
Fixed Point Proof: Exam Blanc
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Covers the definition and proof of fixed point methods, emphasizing the importance of continuity.
Semi-Definite Programming
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Covers semi-definite programming and optimization over positive semidefinite cones.
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