In this tutorial we define a subgroup and prove two theorem that help us identify a subgroup. These proofs are simple to understand. There are also two examples of subgroups.
From playlist Abstract algebra
Definition of a Subgroup and Proof that the Kernel is a Subgroup
We define what it means for H to be a subgroup of G and give clear criteria which you can follow in order to prove that a given subset is a subgroup. Then we prove that the kernel of f is a subgroup of G. I hope this helps someone learning abstract algebra. Useful Math Supplies https://am
From playlist Group Theory Problems
All About Subgroups | Abstract Algebra
We introduce subgroups, the definition of subgroup, examples and non-examples of subgroups, and we prove that subgroups are groups. We also do an example proving a subset is a subgroup. If G is a group and H is a nonempty subset of G, we say H is a subgroup of G if H is closed with respect
From playlist Abstract Algebra
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
Group theory 32: Subgroups of free groups
This lecture is part of an online mathematics course on group theory. We describe subgroups of free groups, show that they are free, calculate the number of generators, and give two examples.
From playlist Group theory
Fang Song - Introduction to quantum computing Part 2 of 3 - IPAM at UCLA
Recorded 26 July 2022. Fang Song of Portland State University presents "Introduction to quantum computing II" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: This lecture will focus on two major (families of) quantum algorithms: period finding (a.k.a. Hidd
From playlist 2022 Graduate Summer School on Post-quantum and Quantum Cryptography
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
Mathematical Ideas in Lattice Based Cryptography - Jill Pipher
2018 Program for Women and Mathematics Topic: Mathematical Ideas in Lattice Based Cryptography Speaker: Jill Pipher Affiliation: Brown University Date: May 21, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Researchers Use Group Theory to Speed Up Algorithms — Introduction to Groups
This is the most information-dense introduction to group theory you'll see on this website. If you're a computer scientist like me and have always wondered what group theory is useful for and why it even exists and furthermore don't want to bother spending hours learning the basics, this i
From playlist Summer of Math Exposition 2 videos
Marina Poulet, Université Claude Bernard Lyon 1
December 9, Marina Poulet, Université Claude Bernard Lyon 1 Zariski-dense subgroups of Galois groups for Mahler equations
From playlist Fall 2021 Online Kolchin Seminar in Differential Algebra
Noa Dagan - Can we improve fairness for subpopulations by utilizing medical data? Pt. 2/2
Recorded 14 July 2022. Noa Dagan of Harvard Medical School presents "Can we improve fairness for subpopulations by utilizing medical data?" at IPAM's Graduate Summer School on Algorithmic Fairness. Abstract: Medical data can be utilized to promote proactive, predictive, and personalized ca
From playlist 2022 Graduate Summer School on Algorithmic Fairness
Abstract Algebra | Cyclic Subgroups
We define the notion of a cyclic subgroup and give a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Vigleik Angeltveit: The Picard group of Equivariant Stable Homotopy Theory
Vigleik Angeltveit: The Picard group of Equivariant Stable Homotopy Theory and the Slice Spectral Sequence 30 September 2021 Abstract: Equivariant stable homotopy groups are usually graded on the real representation ring. But it is possible to grade them on the Picard group instead. I wi
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Twisted Patterson-Sullivan Measure and Applications to Growth Problems (Lecture-3) by Remi Coulon
PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE (ONLINE) ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Mahan M J (TIFR, Mumbai) DATE & TIME: 01 March 2021 to 12 March 2021 VENUE: Online Due to the ongoing COVID pandemic, the meeting will
From playlist Probabilistic Methods in Negative Curvature (Online)
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
Visual Group Theory, Lecture 3.1: Subgroups
Visual Group Theory, Lecture 3.1: Subgroups In this lecture, we begin by examining a property about Cayley graphs called "regularity" that we've hinted at but not yet spelled out explicitly. Next, we introduce the concept of a subgroup, provide some examples, and show how the subgroups of
From playlist Visual Group Theory
From playlist Thinking about Data
Before we carry on with our coset journey, we need to discover when the left- and right cosets are equal to each other. The obvious situation is when our group is Abelian. The other situation is when the subgroup is a normal subgroup. In this video I show you what a normal subgroup is a
From playlist Abstract algebra
Sang-hyun Kim: Optimal regularity of mapping class group actions on the circle
Abstract: We prove that for each finite index subgroup H of the mapping class group of a closed hyperbolic surface, and for each real number r greater than 1 there does not exist a faithful C^r-action (in Hölder's sense) of H on a circle. For this, we partially determine the optimal regu
From playlist SMRI Algebra and Geometry Online