In mathematics, an abstract cell complex is an abstract set with Alexandrov topology in which a non-negative integer number called dimension is assigned to each point. The complex is called “abstract” since its points, which are called “cells”, are not subsets of a Hausdorff space as is the case in Euclidean and CW complexes. Abstract cell complexes play an important role in image analysis and computer graphics. (Wikipedia).

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

Groups in abstract algebra examples

In this tutorial I discuss two more examples of groups. The first contains four elements and they are the four fourth roots of 1. The second contains only three elements and they are the three cube roots of 1. Under the binary operation of multiplication, these sets are in fact groups.

From playlist Abstract algebra

Field Definition (expanded) - Abstract Algebra

The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They

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

Algebraic Structures: Groups, Rings, and Fields

This video covers the definitions for some basic algebraic structures, including groups and rings. I give examples of each and discuss how to verify the properties for each type of structure.

From playlist Abstract Algebra

Lecture 2. Homomorphisms and ideals

From playlist Abstract Algebra 2

Equivalence Relations Definition and Examples

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.

From playlist Abstract Algebra

Units in a Ring (Abstract Algebra)

The units in a ring are those elements which have an inverse under multiplication. They form a group, and this “group of units” is very important in algebraic number theory. Using units you can also define the idea of an “associate” which lets you generalize the fundamental theorem of ar

From playlist Abstract Algebra

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

October 3, 2007 lecture by Bill Thies for the Stanford University Computer Systems Colloquium (EE 380). Bill Thies provides an overview of microfluidic technologies from a computer science perspective, highlight areas in the which computer science researchers can contribute to this field;

From playlist Lecture Collection | Computer Systems Laboratory Colloquium (2007-2008)

Milner Award Lecture 2015: Reactive, real-time and hybrid computer systems

Listen to a world expert on computer science speak about advances in reactive, real-time, and hybrid computer systems. Milner Award Lecture 2015 delivered by Professor Thomas Henzinger, Institute of Science and Technology, at the Royal Society, London, on 18 November 2015. https://royal

From playlist Latest talks and lectures

The Inference of Nature: Cause and Effect in Molecular Biology, Moderated Conversation Neil Lawrence

The Inference of Nature: Cause and Effect in Molecular Biology Sarah Teichmann, Head of Cellular Genetics Programme, Wellcome Sanger Institute - Moderated Conversation with Neil Lawrence, DeepMind Professor of Machine Learning, University of Cambridge.

From playlist Franke Program in Science and the Humanities

Tropical Geometry - Lecture 6 - Structure Theorem | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

Calculating linguistic entropy

The complexity of linguistic patterns can be quantified and compared using two concepts from information theory. Using data from Greek, we find that paradigms' entropy — a measure of abstract inflectional complexity — can be quite high, but their conditional entropy — which reflects gramma

From playlist Summer of Math Exposition Youtube Videos

A New Cubulation Theorem for Hyperbolic Groups- Daniel Groves

Daniel Groves University of Illinois, Chicago October 27, 2015 https://www.math.ias.edu/seminars/abstract?event=83384 We prove that if a hyperbolic group G acts cocompactly on a CAT(0) cube complexes and the cell stabilizers are quasiconvex and virtually special, then G is virtually spec

From playlist Geometric Structures on 3-manifolds

(May 16, 2012) David Dill discusses how a continuing improvement of computing technology is making it possible to digitally model some biological systems. Stanford University: http://www.stanford.edu/ Stanford School of Engineering: http://soe.stanford.edu/ Stanford Computer Systems Co

From playlist Engineering

10 Relations (still with the not-so-exciting-stuff)

This video introduces relations between pairs of elements.

From playlist Abstract algebra

Lecture 14: Discrete Surfaces (Discrete Differential Geometry)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg

From playlist Discrete Differential Geometry - CMU 15-458/858