Concept

Simplex

Related lectures (31)

Simplices

Covers the concept of simplices in delta complexes and explains the standard n-simplex and the ordering of vertices.

Simplicial Homology: Structure and Complexes

Covers the structure of topological spaces with A-complexes and chain complexes.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

A Lemma: Introduction to Homology Groups

Introduces the concept of homology groups and focuses on a lemma about free abelian groups.

Homotopy: Degree

Covers the concept of degree in homotopy theory and the structure of complexes with two simplices.

Singular Homology: First Properties

Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.

Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Simplicial and Singular Homology Equivalence

Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.

Mixing Models: Quadratic & Cubic, Constraints, Transformations

Explores quadratic and cubic models, constraints, transformations, and representations in mixing models.

Singular homology

Introduces singular homology, defining singular simplices and explaining the chain complex construction.

Nerves and Geometric Realization

Covers the explicit computations of nerves of categories and geometric realisations of simplicial sets.

Response Surfaces I: LoF and Plans

Explores lack of fit concept and experimental designs for second-degree functions.

Simplex algorithm: From vertex to vertex

Explains the simplex algorithm process of finding the next vertex and selecting variables.

Linear Programming: Solving LPs

Covers the process of solving Linear Programs (LPs) using the simplex method.

Simplex Algorithm: Initial Tableau, Simple Case

Covers the simplex algorithm applied to the simple case of inequality constraints.

The Simplex Algorithm: Efficiency and Degeneracy

Covers the Simplex Algorithm, focusing on efficiency and degeneracy in linear optimization problems.

Linear Programming Basics

Covers the basics of linear programming and the simplex method, focusing on finding optimal solutions and handling degeneracy.

Natural Examples of Simplicial Sets

Introduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.

Homology Theorem

Covers the proof of Theorem A, discussing homology, quotients, and isomorphisms.

Mixing Space I

Explores mixing space, ternary diagrams, greenhouse optimization, and solution scenarios.