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
Dihedral Group (Abstract Algebra)
The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo
From playlist Abstract Algebra
Group theory 13: Dihedral groups
This lecture is part of an online mathematics course on group theory. It covers some basic properties of dihedral groups.
From playlist Group theory
In this veideo we continue our look in to the dihedral groups, specifically, the dihedral group with six elements. We note that two of the permutation in the group are special in that they commute with all the other elements in the group. In the next video I'll show you that these two el
From playlist Abstract algebra
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
Every Group is a Quotient of a Free Group
First isomorphism theorem: https://youtu.be/ssVIJO5uNeg An explanation of a proof that every finite group is a quotient of a free group. A similar proof also applies to infinite groups because we can consider a free group on an infinite number of elements! Group Theory playlist: https://
From playlist Group Theory
Center of a group in abstract algebra
After the previous video where we saw that two of the elements in the dihedral group in six elements commute with all the elements in the group, we finally get to define the center of a group. The center of a group is a subgroup and in this video we also go through the proof to show this.
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
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
The Embedding Problem of Infinitely Divisible Probability Measures on Groups by Riddhi Shah
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Galois theory: Wedderburn's theorem
This lecture is part of an online graduate course on Galois theory. We prove Wedderburn's theorem that all finite division algebras are fields. The proof uses cyclotomic polynomials.
From playlist Galois theory
Group theory 12: Cauchy's theorem
This lecture is part of an online mathematics course on group theory. It gives two proofs of Cauchy's theorem that if a prime p divides the order of a group then the group has an element of that order. It also uses Cauchy's theorem to classify the group of order 2p.
From playlist Group theory
Factor expressions by grouping
u12_l1_t1_we3 Factor expressions by grouping
From playlist Developmental Math 2
(Optional lecture) - Towards a classification of adelic Galois representations of elliptic curves
This is a lecture I gave at Zagreb's Number Theory Seminar, on Feb 25, 2021, on adelic Galois representations. While not a part of the graduate course on elliptic curves, it is a nice complement to some of the material we have seen on the Tate module.
From playlist Math Talks
Intro data manipulation with Pandas in Python: remove drop groupby plot | Data science Tutorial
Do you know the multiples ways to manipulate data and information using Pandas? How to select data? group by? In this tutorial of statistics and data science with Python we will discuss the data wrangling with python using Pandas. You'll learn how to: 1. Count values 2. Grouping by c
From playlist Python
Operation Nordwind 1945 - The 'Other' Battle of the Bulge
The stories of the last big German offensives on the Western Front in WWII - Operations Nordwind and Sonnenwende in Alsace, France, January 1945. Dr. Mark Felton is a well-known British historian, the author of 22 non-fiction books, including bestsellers 'Zero Night' and 'Castle of the Ea
From playlist Battle of Germany 1944-45
The idea of a quotient group follows easily from cosets and Lagrange's theorem. In this video, we start with a normal subgroup and develop the idea of a quotient group, by viewing each coset (together with the normal subgroup) as individual mathematical objects in a set. This set, under
From playlist Abstract algebra
Elliptic Curves of Ranks Zero and One by Christopher Skinner
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)