Theorems in algebraic topology | Homological algebra

In algebraic topology, a discipline within mathematics, the acyclic models theorem can be used to show that two homology theories are isomorphic. The theorem was developed by topologists Samuel Eilenberg and Saunders MacLane. They discovered that, when topologists were writing proofs to establish equivalence of various homology theories, there were numerous similarities in the processes. Eilenberg and MacLane then discovered the theorem to generalize this process. It can be used to prove the Eilenberg–Zilber theorem; this leads to the idea of the model category. (Wikipedia).

Linear regression ANOVA ANCOVA Logistic Regression

In this video tutorial you will learn about the fundamentals of linear modeling: linear regression, analysis of variance, analysis of covariance, and logistic regression. I work through the results of these tests on the white board, so no code and no complicated equations. Linear regressi

From playlist Statistics

Linear, Quadratic, and Exponential Models

Linear, Quadratic, and Exponential Models

From playlist ck12.org Algebra 1 Examples

Intro to Linear Systems: 2 Equations, 2 Unknowns - Dr Chris Tisdell Live Stream

Free ebook http://tinyurl.com/EngMathYT Basic introduction to linear systems. We discuss the case with 2 equations and 2 unknowns. A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that ar

From playlist Intro to Linear Systems

Discrete-Time Dynamical Systems

This video shows how discrete-time dynamical systems may be induced from continuous-time systems. https://www.eigensteve.com/

From playlist Data-Driven Dynamical Systems

See complete series on data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P In this lesson, we have discussed binary tree in detail. We have talked about different types of binary tree like "complete binary tree", "perfect binary tree" and "balance

From playlist Data structures

Review of Linear Time Invariant Systems

http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files. Review: systems, linear systems, time invariant systems, impulse response and convolution, linear constant-coefficient difference equations

From playlist Introduction and Background

What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational

We've mentioned in passing some different ways to classify numbers, like rational, irrational, real, imaginary, integers, fractions, and more. If this is confusing, then take a look at this handy-dandy guide to the taxonomy of numbers! It turns out we can use a hierarchical scheme just lik

From playlist Algebra 1 & 2

Introduces notation and formulas for exponential growth models, with solutions to guided problems.

From playlist Discrete Math

Stable Homotopy Seminar, 4: Model categories (Ivo Vekemans)

This talk by Ivo Vekemans is a thorough introduction to model categories, presenting: weak factorization systems; the definition of model category and major examples (simplicial sets, topological spaces, and chain complexes); notions of homotopy in a model category, and the homotopy catego

From playlist Stable Homotopy Seminar

ITHT: Part 12- Model Structure on Topological Spaces

Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#TheClassicalModelStructureOfTopologicalSpaces Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtub...

From playlist Introduction to Homotopy Theory

Stable Homotopy Seminar, 8: The Stable Model Category of Spectra

We discuss the enrichment of spectra over spaces, and the compatibility of this enrichment with the model structure. Then we define the stable model structure by adding extra cofibrations to the levelwise model category of spectra, and restricting the weak equivalences to those maps which

From playlist Stable Homotopy Seminar

ITHT: Part 9- The Homotopy Category

Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#TheHomotopyCategory Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtube Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Nam

From playlist Introduction to Homotopy Theory

Stable Homotopy Seminar, 7: Constructing Model Categories

A stroll through the recognition theorem for cofibrantly generated model categories, using it to construct (1) the Quillen/Serre model structure on topological spaces and (2) the levelwise model structure on spectra. The latter captures the idea that spectra are sequences of spaces, but no

From playlist Stable Homotopy Seminar

What's a Directed Acyclic Graph (DAG)?

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From playlist Programming

Introduction to Homotopy Theory: Part 8- Homotopy in Model Categories

Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#homotopy_2 Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtube Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remembe

From playlist Introduction to Homotopy Theory

ITHT: Part 10- Derived Functors

Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#DerivedFunctors Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtub... Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name:

From playlist Introduction to Homotopy Theory

ITHT: Part 11- Quillen Adjunctions

Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#QuillenAdjunctions Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtub... Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Na

From playlist Introduction to Homotopy Theory

The Anatomy of a Dynamical System

Dynamical systems are how we model the changing world around us. This video explores the components that make up a dynamical system. Follow updates on Twitter @eigensteve website: eigensteve.com

From playlist Research Abstracts from Brunton Lab

Introduction to Homotopy Theory: Part 7- Small Object, Retract Arguments

Credits: nLab: https://ncatlab.org/nlab/show/Introdu... Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtube Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remember (Extended Mix)" • YouTube Track

From playlist Introduction to Homotopy Theory