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
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
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
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
Michael Wibmer: Etale difference algebraic groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
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
CTNT 2018 - "Factoring with Elliptic Curves" by Jeremy Teitelbaum
This is lecture on "Factoring with Elliptic Curves", by Jeremy Teitelbaum, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2018 - Guest Lectures
Factoring with Elliptic Curves - Jeremy Teitelbaum [2018]
May 30: Jeremy Teitelbaum (UConn) Title: Factoring with elliptic curves. Abstract: Lenstra’s elliptic curve algorithm ([1]) for factoring is a standard piece of the toolkit for computational number theory. I will give a brief introduction to this algorithm. [1] H. Lenstra, Factoring integ
From playlist Number Theory
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
15 - Algorithmic aspects of the Galois theory in recent times
Orateur(s) : M. Singer Public : Tous Date : vendredi 28 octobre Lieu : Institut Henri Poincaré
From playlist Colloque Evariste Galois
FitzGerald Dynasty Family Tree | Irish Genealogy
Book series based on the Norman invasion of Ireland: https://www.ruadhbutler.com/ Download the chart (free): https://cdn.shopify.com/s/files/1/1835/6621/files/fitzgerald.png CREDITS: Chart: Matt Baker Script/Narration: Matt Baker Editing: Jack Rackam Intro animation: Syawish Rehman Int
From playlist Royal Family Trees
A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
Heuristics for lambda Invariants - Sonal Jain
Sonal Jain New York University February 17, 2011 The λλ-invariant is an invariant of an imaginary quadratic field that measures the growth of class numbers in cyclotomic towers over the field. It also measures the number of zeroes of an associated pp-adic L-function. In this talk, I will d
From playlist Mathematics
Pär Kurlberg: Class number statistics for imaginary quadratic fields Pär Kurlberg
Abstract: The number F(h) of imaginary quadratic fields with class number h is of classical interest: Gauss' class number problem asks for a determination of those fields counted by F(h). The unconditional computation of F(h) for h x is less or equal to y 100 was completed by M. Watkins, a
From playlist Number Theory
Nina Otter (4/23/19): The magnitude of a metric space
Title: The magnitude of a metric space Abstract: The magnitude is an isometric invariant of metric spaces that was introduced by Tom Leinster in 2010, and is currently the object of intense research. Magnitude encodes many invariants of a metric space such as volume, dimension, capacity,
From playlist AATRN 2019
Abstract Algebra | The dihedral group
We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
The Structure of the Group of Rational Points of an Abelian Variety (CTNT Online, June 12-14, 2020)
This video was created for the CTNT 2020 Conference (June 12-14, 2020): https://ctnt-summer.math.uconn.edu/ctnt-conference-2020-online/ (Preprint) The Structure of the Group of Rational Points of an Abelian Variety over a Finite Field: https://arxiv.org/abs/2006.00637 My contact informat
From playlist CTNT 2020 - Conference Videos
Abstract Algebra: We introduce the notion of a group and describe basic properties. Examples given include familiar abelian groups and the symmetric groups. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.o
From playlist Abstract Algebra