Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
Commutative algebra 47: Colimits and exactness
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We discuss the question of when a colimit of exact sequences is exact. We first show that a colimit of right exact sequences i
From playlist Commutative algebra
Danylo Radchenko: Goursat rigid local systems of rank 4
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: I will talk about certain rigid local systems of rank 4 considered by Goursat, with emphasis on explicit constructions and examples. The talk i
From playlist Workshop: "Picard-Fuchs Equations and Hypergeometric Motives"
Math 135 Complex Analysis Lecture 09 021715: Contour Integrals, Path Independence, Cauchy-Goursat
Examples of integration; Path independence theorem; Theorem of Cauchy-Goursat
From playlist Course 8: Complex Analysis
Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - Hélène Gispert - 17/11/17
En partenariat avec le séminaire d’histoire des mathématiques de l’IHP Darboux c’est aussi le nom d’un journal : le Bulletin des sciences mathématiques (1869-1917) Hélène Gispert, GHDSO, Université Paris-Sud 11 À l’occasion du centenaire de la mort de Gaston Darboux, l’Institut Henri Poi
From playlist Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - 17/11/2017
ME565 Lecture 3: Integration in the complex plane (Cauchy-Goursat Integral Theorem)
ME565 Lecture 3 Engineering Mathematics at the University of Washington Integration in the complex plane (Cauchy-Goursat Integral Theorem) Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L03.pdf Course Website: http://faculty.washington.edu/sbrunton/me565/ http://faculty.wash
From playlist Engineering Mathematics (UW ME564 and ME565)
This lecture is part of an online graduate course on Galois theory. We define the discriminant of a finite field extension, ans show that it is essentially the same as the discriminant of a minimal polynomial of a generator. We then give some applications to algebraic number fields. Corr
From playlist Galois theory
Proof & Explanation: Gauss's Lemma in Number Theory
Euler's criterion: https://youtu.be/2IBPOI43jek One common proof of quadratic reciprocity uses Gauss's lemma. To understand Gauss's lemma, here we prove how it works using Euler's criterion and the Legendre symbol. Quadratic Residues playlist: https://www.youtube.com/playlist?list=PLug5Z
From playlist Quadratic Residues
Berge's lemma, an animated proof
Berge's lemma is a mathematical theorem in graph theory which states that a matching in a graph is of maximum cardinality if and only if it has no augmenting paths. But what do those terms even mean? And how do we prove Berge's lemma to be true? == CORRECTION: at 7:50, the red text should
From playlist Summer of Math Exposition Youtube Videos
Complex Analysis - Part 22 - Goursat's Theorem
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From playlist Complex Analysis
Burnside's Lemma (Part 2) - combining math, science and music
Part 1 (previous video): https://youtu.be/6kfbotHL0fs Orbit-stabilizer theorem: https://youtu.be/BfgMdi0OkPU Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be
From playlist Traditional topics, explained in a new way
Lie derivatives of differential forms
Introduces the lie derivative, and its action on differential forms. This is applied to symplectic geometry, with proof that the lie derivative of the symplectic form along a Hamiltonian vector field is zero. This is really an application of the wonderfully named "Cartan's magic formula"
From playlist Symplectic geometry and mechanics
Math 135 Complex Analysis Lecture 10 021915: Cauchy Integral Formula
Extensions of Cauchy-Goursat on a rectangle; rectangle minus finitely many points; curves in an open disk; open disk minus finite number of points. Homotopic curves with fixed endpojnts; homotopic closed curves; deformation theorem. Winding number is an integer; Cauchy's Integral Formula
From playlist Course 8: Complex Analysis
The Frobenius Problem - Method for Finding the Frobenius Number of Two Numbers
Goes over how to find the Frobenius Number of two Numbers.
From playlist ℕumber Theory
Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - Philippe Nabonnand - 17/11/17
En partenariat avec le séminaire d’histoire des mathématiques de l’IHP Élie Cartan suit le cours de géométrie de Gaston Darboux Philippe Nabonnand, Archives Henri Poincaré, Université de Lorraine) À l’occasion du centenaire de la mort de Gaston Darboux, l’Institut Henri Poincaré souhaite
From playlist Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - 17/11/2017
Graph regularity and counting lemmas - Jacob Fox
Conference on Graphs and Analysis Jacob Fox June 5, 2012 More videos on http://video.ias.edu
From playlist Mathematics
Regularity methods in combinatorics, number theory, and computer science - Jacob Fox
Marston Morse Lectures Topic: Regularity methods in combinatorics, number theory, and computer science Speaker: Jacob Fox Affiliation: Stanford University Date: October 24, 2016 For more videos, visit http://video.ias.edu
From playlist Mathematics
9. Szemerédi's graph regularity lemma IV: induced removal lemma
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao explains a strengthening of the graph regulari
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
In this video, I prove the famous Riemann-Lebesgue lemma, which states that the Fourier transform of an integrable function must go to 0 as |z| goes to infinity. This is one of the results where the proof is more important than the theorem, because it's a very classical Lebesgue integral
From playlist Real Analysis