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
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
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
This lecture is part of an online course on rings and modules. We continue the previous lecture on complete rings by discussing Hensel's lemma for finding roots of polynomials over p-adic rings or over power series rings. We sketch two proofs, by slowly improving a root one digit at a tim
From playlist Rings and modules
Burnside's Lemma (Part 1) - combining group theory and combinatorics
A result often used in math competitions, 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 transformed into one another by rotation different, like in this cas
From playlist Traditional topics, explained in a new way
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
Igor Kortchemski: Condensation in random trees - Lecture 1
We study a particular family of random trees which exhibit a condensation phenomenon (identified by Jonsson & Stefánsson in 2011), meaning that a unique vertex with macroscopic degree emerges. This falls into the more general framework of studying the geometric behavior of large random dis
From playlist Probability and Statistics
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
Rajat Subhra Hazra: Branching Random Walk with innite progeny mean
In this talk we discuss the extremes of branching random walks under the assumption that the underlying Galton-Watson tree has in nite progeny mean. It is assumed that the displacements are either regularly varying or they have lighter tails. In the regularly varying case, it is shown that
From playlist Probability and Statistics
Meltem Ünel: Height coupled trees
HYBRID EVENT Recorded during the meeting "Random Geometry" the January 20, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics
From playlist Probability and Statistics
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
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
How We Think with Bodies and Things
(May 7, 2010) David Kirsh, Professor of Cognitive Science at University of California-San Diego, discusses the concept of enactive thought and provides data from extensive ethnographic studies and a few simple experiments to prove that it exists. Stanford University: http://www.stanford.e
From playlist Lecture Collection | Human-Computer Interaction Seminar (2009-2010)
Taut foliations and cyclic branched covers - Cameron Gordon
Cameron Gordon, Univ Texas Workshop on Flows, Foliations and Contact Structures 2015-2016 Monday, December 7, 2015 - 08:00 to Friday, December 11, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 aca
From playlist Workshop on Flows, Foliations and Contact Structures
Axioms for the Lefschetz number as a lattice valuation
"Axioms for the Lefschetz number as a lattice valuation" a research talk I gave at the conference on Nielsen Theory and Related Topics in Daejeon Korea, June 28, 2013. Chris Staecker's internet webarea: http://faculty.fairfield.edu/cstaecker/ Nielsen conference webarea: http://open.nims.r
From playlist Research & conference talks
Math 135 Complex Analysis Lecture 21 041415: Calculus of Residues, ct'd.
Calculus of residues, continued. Realizing the improper (Fourier transform type) integral as the real or imaginary part of (part of) a contour integral; more subtle Fourier transform-type integrals via Jordan's lemma; improper integrals with simple poles on the real axis.
From playlist Course 8: Complex Analysis
Quadratic Reciprocity using Gauss's Lemma
Gauss's Lemma: https://youtu.be/JhbSYWA0COU Quadratic reciprocity is one of the most important results in elementary number theory when it comes to computing Legendre symbols. To prove it, we use a proof based on Gauss's lemma and Euler's criterion! Quadratic Residues playlist: https://w
From playlist Quadratic Residues
Geometry of the symmetric space SL(n,R)/SO(n,R)(Lecture – 01) by Pranab Sardar
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
