Permutation Groups and Symmetric Groups | Abstract Algebra
We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory We will see the
From playlist Abstract Algebra
In this video we construct a symmetric group from the set that contains the six permutations of a 3 element group under composition of mappings as our binary operation. The specifics topics in this video include: permutations, sets, groups, injective, surjective, bijective mappings, onto
From playlist Abstract algebra
301.5A Permutation Groups: Intro and Goals
Goals for studying the properties of permutation groups. Plus, anagrams!
From playlist Modern Algebra - Chapter 16 (permutations)
Abstract Algebra: (Linear Algebra Required) The symmetric group S_n is realized as a matrix group using permutation matrices. That is, S_n is shown to the isomorphic to a subgroup of O(n), the group of nxn real orthogonal matrices. Applying Cayley's Theorem, we show that every finite gr
From playlist Abstract Algebra
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra - Chapter 16 (permutations)
301.5C Definition and "Stack Notation" for Permutations
What are permutations? They're *bijective functions* from a finite set to itself. They form a group under function composition, and we use "stack notation" to denote them in this video.
From playlist Modern Algebra - Chapter 16 (permutations)
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Group theory 28: Groups of order 120, 168
This lecture is part of an online math course on group theory. It discusses some examples of groups of order 120 or 168: the binary icosahedral group, the symmetric group, and the symmetries of the Fano plane.
From playlist Group theory
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
Alexander HULPKE - Computational group theory, cohomology of groups and topological methods 2
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
On the symmetries of and equivalence test for design polynomials by Nikhil Gupta
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Nexus Trimester - Qi Chen (The Chinese University of Hong Kong)
Partition-Symmetrical Entropy Functions Qi Chen (The Chinese University of Hong Kong) February 15, 2016 Abstract: Let N={1,…,n}. Let p={N1,…,Nt} be a t-partition of N. An entropy function h is called p-symmetrical if for all A, B⊂N, h(A)=h(B) whenever |A∩Ni|=|B∩Ni|, i=1,…,t. We prove that
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
RT1: Representation Theory Basics
Representation Theory: We present basic concepts about the representation theory of finite groups. Representations are defined, as are notions of invariant subspace, irreducibility and full reducibility. For a general finite group G, we suggest an analogue to the finite abelian case, whe
From playlist *** The Good Stuff ***
Representation Theory(Repn Th) 4 by Gerhard Hiss
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Representation Theory(Repn Th) 3 by Gerhard Hiss
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Global symmetry from local information: The Graph Isomorphism Problem – László Babai – ICM2018
Combinatorics | Mathematical Aspects of Computer Science Invited Lecture 13.4 | 14.5 Global symmetry from local information: The Graph Isomorphism Problem László Babai Abstract: Graph Isomorphism (GI) is one of a small number of natural algorithmic problems with unsettled complexity stat
From playlist Combinatorics
C. Matheus - Square tiled surfaces (Part 1)
) basic definitions and examples b) strata and genus c) reduced and primitive origamis, SL(2,R) action, Veech groups d) automorphisms and affine homeomorphisms e) homology of origamis f) Kontsevich-Zorich cocycle g) Lyapunov exponents of the Wollmilchsau
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications