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)
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
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
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
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
Computing homology groups | Algebraic Topology | NJ Wildberger
The definition of the homology groups H_n(X) of a space X, say a simplicial complex, is quite abstract: we consider the complex of abelian groups generated by vertices, edges, 2-dim faces etc, then define boundary maps between them, then take the quotient of kernels mod boundaries at each
From playlist Algebraic Topology
Where 09: Greg Skibiski, "Decoding the Urban DNA and Harnes
Greg Skibiski (Sense Networks) "Decoding the Urban DNA and Harnessing the Power of Social Intelligence"
From playlist Where 2.0 2009
Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger
This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk abou
From playlist MathHistory: A course in the History of Mathematics
Keiji Oguiso: Projective rational manifolds with non-finitely generated discrete automorphism...
We show, among other things, one way to construct a smooth complex projective rational variety of any dimension n ≥ 3, with discrete non-finitely generated automorphism group and with infinitely many mutually non-isomorphic real forms. This is a joint work in progress with Professors Tien-
From playlist Algebraic and Complex Geometry
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
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
Toshiaki Hishida : Lq-Lr estimates of a generalized Oseen evolution operator...
Abstract: Consider the motion of a viscous incompressible fluid in a 3D exterior domain D when a rigid body ℝ3∖D moves with prescribed time-dependent translational and angular velocities. For the linearized non-autonomous system, Lq-Lr smoothing action near t=s as well as generation of the
From playlist Mathematical Physics
Colloquium MathAlp 2017 - Maciej Zworski
Fractal uncertainty for transfer operators I will present a new explanation of the connection between the fractal uncertainty principle (FUP) of Bourgain-Dyatlov, a statement in harmonic analysis, and the existence of zero free strips for Selberg zeta functions, which is a statement in g
From playlist Colloquiums MathAlp
Now that we have defined and understand quotient groups, we need to look at product groups. In this video I define the product of two groups as well as the group operation, proving that it is indeed a group.
From playlist Abstract algebra