Topology | Simplicial sets | Families of sets
In topology, the nerve complex of a set family is an abstract complex that records the pattern of intersections between the sets in the family. It was introduced by Pavel Alexandrov and now has many variants and generalisations, among them the Čech nerve of a cover, which in turn is generalised by hypercoverings. It captures many of the interesting topological properties in an algorithmic or combinatorial way. (Wikipedia).
Complex numbers can be represented three ways on the complex plane: cartesian coordinates, radius and angle, and exponential form.
From playlist Electrical engineering
Complex Numbers for ODEs (1 of 4)
ODEs: We define and present basic properties of the complex numbers. This part includes addition, subtraction, scalar multiplication, complex conjugate and modulus.
From playlist Differential Equations
What are complex numbers? | Essence of complex analysis #2
A complete guide to the basics of complex numbers. Feel free to pause and catch a breath if you feel like it - it's meant to be a crash course! Complex numbers are useful in basically all sorts of applications, because even in the real world, making things complex sometimes, oxymoronicall
From playlist Essence of complex analysis
Some Basic Properties of Complex Numbers
This video describes some of the more basic properties of complex numbers.
From playlist Basics: Complex Analysis
Differential Equations: Complex Roots of the Characteristic Equation
Homogeneous, constant-coefficient differential equations have a characteristic or auxiliary equation. The solution(s) of this equation yield the particular solutions to the homogeneous differential equation which, when combined, produce a general solution. In this video, we explore the cas
From playlist Differential Equations
How to solve differentiable equations with logarithms
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
Complex Numbers as Points (1 of 4: Geometric Meaning of Addition)
More resources available at www.misterwootube.com
From playlist Complex Numbers
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
Primoz Skraba (2/28/18): An approximate nerve theorem
The Nerve Theorem is an implicit tool in most applications of topological data analysis relating the topological type of a suitably nice space with a combinatorial description of the space, namely, the nerve of a cover of that space. It is required that it is a good cover, that each elemen
From playlist AATRN 2018
Bradley Nelson (2/19/22): Parameterized Vietoris-Rips Filtrations via Covers
A challenge in computational topology is to deal with large filtered geometric complexes built from point cloud data such as Vietoris-Rips filtrations. This has led to the development of schemes for parallel computation and compression which restrict simplices to lie in open sets in a cove
From playlist Vietoris-Rips Seminar
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 4
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Žiga Virk (9/25/19): Geometric interpretation of persistence
Title: Geometric interpretation of persistence Abstract: Given a reasonably nice metric space X, its filtration by complexes and the corresponding persistent homology provide a multi-scale representation of X. At small scales the complexes usually reconstruct the homotopy type of the spac
From playlist AATRN 2019
Bianca B. Dornelas: Sparse Higher Order Čech Filtrations
Poster: https://sites.google.com/view/aatrn-poster-session/posters Arxiv Paper: Upcoming The kth fold filtration at parameter r, whose nerve is the kth order Čech filtration at r, is formed by the intersections of k balls with radius r. We construct an approximation for the kth fold filtr
From playlist Poster Session Videos
Higher Algebra 1: ∞-Categories
In this video, we introduce ∞-categories. This is the first of a series of videos towards a reasonably non-technical overview over stable ∞-categories and Higher Algebra, which are intended to be watchable independently from the main lecture. Further resources: M.Boardman and R.Vogt. Homo
From playlist Higher Algebra
Definition of complex exponential function using Taylor series. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org/learn/differential-equations-engineers Vector Calcu
From playlist Differential Equations
17. Cochlear nucleus: Tonotopy, unit types and cell types
MIT 9.04 Sensory Systems, Fall 2013 View the complete course: http://ocw.mit.edu/9-04F13 Instructor: Chris Brown This video covers the anatomy and physiology of the auditory central nervous system and the cochlear nucleus and introduces auditory implants. License: Creative Commons BY-NC-
From playlist MIT 9.04 Sensory Systems, Fall 2013
Homotopy Category As a Localization by Rekha Santhanam
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
From playlist Complex Analysis Made Simple
MFEM Workshop 2021| Modeling Peripheral Nerve Stimulations (PNS) in Magnetic Resonance Imaging (MRI)
The LLNL-led MFEM (Modular Finite Element Methods) project provides high-order mathematical calculations for large-scale scientific simulations. The project’s first community workshop was held virtually on October 20, 2021, with participants around the world. Learn more about MFEM at https
From playlist MFEM Community Workshop 2021
