In mathematics, Burnside's theorem in group theory states that if G is a finite group of order where p and q are prime numbers, and a and b are non-negative integers, then G is solvable. Hence eachnon-Abelian finite simple group has order divisible by at least three distinct primes. (Wikipedia).
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
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
What is Stokes theorem? - Formula and examples
► My Vectors course: https://www.kristakingmath.com/vectors-course Where Green's theorem is a two-dimensional theorem that relates a line integral to the region it surrounds, Stokes theorem is a three-dimensional version relating a line integral to the surface it surrounds. For that reaso
From playlist Vectors
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
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
Representation theory: Burnside's theorem
In this talk we prove Burnside's theorem, that any group whose order is of the form p^aq^b for primes p and q is solvable. We first discuss characters of the center of the group ring of G, and use this to show that a certain number related to a character value is an algebraic integer. We
From playlist Representation theory
Katrin Tent: Burnside groups of relatively small odd exponent
The lecture was held within the framework of the Hausdorff Trimester Program: Logic and Algorithms in Group Theory. Abstract: (joint work with A. Atkarskaya and E. Rips) The free Burnside group B(n,m) of exponent m is the quotient of the free group on n generators by the normal subgroup
From playlist HIM Lectures: Trimester Program "Logic and Algorithms in Group Theory"
Physics Ch 67.1 Advanced E&M: Review Vectors (67 of 113) Stoke's Theorem
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn that Stoke’s Theorem (The Fundamental Theorem of Curl) means the “bending” or curl of the vector field everywhere on th
From playlist PHYSICS 67.1 ADVANCED E&M VECTORS & FIELDS
Rings and midules 3: Burnside ring and rings of differential operators
This lecture is part of an online course on rings and modules. We discuss a few assorted examples of rings. The Burnside ring of a group is a ring constructed form the permutation representations. The ring of differentail operators is a ring whose modules are related to differential equat
From playlist Rings and modules
Benjamin Böhme: The Dress splitting and equivariant commutative multiplications
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Fusion systems and equivariant algebraic topology"
From playlist HIM Lectures: Junior Trimester Program "Topology"
Spatial refinements and Khovanov homology – Robert Lipshitz & Sucharit Sarkar – ICM2018
Topology Invited Lecture 6.11 Spatial refinements and Khovanov homology Robert Lipshitz & Sucharit Sarkar Abstract: We review the construction and context of a stable homotopy refinement of Khovanov homology. © International Congress of Mathematicians – ICM www.icm2018.org Os direi
From playlist Topology
Discrete Math II - 10.8.S2 Graphs and Groups: Polya's Theorem
This content is also not covered in your textbook, but is another method for graph coloring. In this method, we focus on the number and length of cycles for the permutations that represent each symmetry. Video Chapters: Intro 0:00 Rotations of a Square with Permutations 0:12 Reflectio
From playlist Discrete Math II/Combinatorics (entire course)
Regular permutation groups and Cayley graphs
Cheryl Praeger (University of Western Australia). Plenary Lecture from the 1st PRIMA Congress, 2009. Plenary Lecture 11. Abstract: Regular permutation groups are the 'smallest' transitive groups of permutations, and have been studied for more than a century. They occur, in particular, as
From playlist PRIMA2009
Group actions on 1-manifolds: A list of very concrete open questions – Andrés Navas – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.8 Group actions on 1-manifolds: A list of very concrete open questions Andrés Navas Abstract: Over the last four decades, group actions on manifolds have deserved much attention by people coming from different fields
From playlist Dynamical Systems and ODE
Group theory 10: Burnside's lemma
This is lecture 10 of an online mathematics course on group theory. It introduces Burnside's lemma and uses it to find the number of ways to arrange 8 non-attacking rooks on a chessboard, up to symmetry.
From playlist Group theory
In this video, I present Stokes' Theorem, which is a three-dimensional generalization of Green's theorem. It relates the line integral of a vector field over a curve to the surface integral of the curl of that vector field over the corresponding surface. After presenting an example, I expl
From playlist Multivariable Calculus
GT23. Composition and Classification
Abstract Algebra: We use composition series as another technique for studying finite groups, which leads to the notion of solvable groups and puts the focus on simple groups. From there, we survey the classification of finite simple groups and the Monster group.
From playlist Abstract Algebra