Simplicial sets | Families of sets | Algebraic topology

In combinatorics, an abstract simplicial complex (ASC), often called an abstract complex or just a complex, is a family of sets that is closed under taking subsets, i.e., every subset of a set in the family is also in the family. It is a purely combinatorial description of the geometric notion of a simplicial complex. For example, in a 2-dimensional simplicial complex, the sets in the family are the triangles (sets of size 3), their edges (sets of size 2), and their vertices (sets of size 1). In the context of matroids and greedoids, abstract simplicial complexes are also called independence systems. An abstract simplex can be studied algebraically by forming its Stanley–Reisner ring; this sets up a powerful relation between combinatorics and commutative algebra. (Wikipedia).

What is the difference between imanginary numbers and complex numbers

http://'www.freemathvideos.com In this math tutorial I will show you how write a complex number in standard form after simple operations have been performed. You will learn how to find the value of real and imaginary numbers in a complex number and then write it in standard form. To simp

From playlist Simplify Rational Expressions

http://www.freemathvideos.com In this video playlist you will learn everything you need to know with complex and imaginary numbers

From playlist Simplify Rational Expressions

Simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

Simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions (Binomials) #Rational

Lecture 2A: What is a "Mesh?" (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

Simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

Francesca Tombari (6/8/20): Homotopical decompositions of simplicial and Vietoris Rips complexes

Title: Homotopical decompositions of simplicial and Vietoris Rips complexes Abstract: Motivated by the use in TDA of simplicial complexes arising from metric spaces, we study decompositions of simplicial complexes induced by coverings of their vertices. We define obstruction complexes to

From playlist ATMCS/AATRN 2020

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

Summary Simplifying rational expressions

From playlist Simplify Rational Expressions

Simplify a rational expression

From playlist Simplify Rational Expressions

Simplify a rational expression

From playlist Simplify Rational Expressions

Emily Riehl: On the ∞-topos semantics of homotopy type theory: All ∞-toposes have... - Lecture 3

HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 24, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M

From playlist Topology

Noether's works in Topology by Indranil Biswas

DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (

From playlist The Legacy of Emmy Noether

How to simplify a rational expressions

From playlist Simplify Rational Expressions

DSI | Hypergraphs and Topology for Data Science | By Emilie Purvine

Data scientists and applied mathematicians must grapple with complex data when analyzing complex systems. Analytical methods almost always represent phenomena as a much simpler level than the complex structure or dynamics inherent in systems, through either simpler measured or sampled data

From playlist DSI Virtual Seminar Series

Jesus De Loera: Tverberg-type theorems with altered nerves

Abstract: The classical Tverberg's theorem says that a set with sufficiently many points in R^d can always be partitioned into m parts so that the (m - 1)-simplex is the (nerve) intersection pattern of the convex hulls of the parts. Our main results demonstrate that Tverberg's theorem is b

From playlist Combinatorics

Emily Stark: Action rigidity for free products of hyperbolic manifold groups

CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 22, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM

From playlist Virtual Conference

Axioms for the Lefschetz number as a lattice valuation

"Axioms for the Lefschetz number as a lattice valuation" a research talk I gave at the conference on Nielsen Theory and Related Topics in Daejeon Korea, June 28, 2013. Chris Staecker's internet webarea: http://faculty.fairfield.edu/cstaecker/ Nielsen conference webarea: http://open.nims.r

From playlist Research & conference talks

High dimensional expanders – Alexander Lubotzky – ICM2018

Plenary Lecture 13 High dimensional expanders Alexander Lubotzky Abstract: Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways. In the last decad

From playlist Plenary Lectures

Simplify a rational expression by factoring

From playlist Simplify Rational Expressions