Functional analysis | Generalized manifolds | Generalized functions | Differential topology
In mathematics, more particularly in functional analysis, differential topology, and geometric measure theory, a k-current in the sense of Georges de Rham is a functional on the space of compactly supported differential k-forms, on a smooth manifold M. Currents formally behave like Schwartz distributions on a space of differential forms, but in a geometric setting, they can represent integration over a submanifold, generalizing the Dirac delta function, or more generally even directional derivatives of delta functions (multipoles) spread out along subsets of M. (Wikipedia).
Using Algebra and Geometry in the Real World
You hear terms like “algebra” and “geometry” and these theories we memorized in high school start to dance a jig in our heads – a jig many of us weren’t overly interested in! But the past decade has seen an explosion of applications of algebra, geometry, and topology to the real world, lik
From playlist What is math used for?
Putting an opinion on YouTube - what could possibly go wrong! This is a bit more bloggy than I usually like to do. I'll be back next time with some proper mathematics. "What is the point of mathematics?"
From playlist My Maths Videos
When did modern physics begin?
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From playlist Science Unplugged: Physics
Maths for Programmers: Introduction (What Is Discrete Mathematics?)
Transcript: In this video, I will be explaining what Discrete Mathematics is, and why it's important for the field of Computer Science and Programming. Discrete Mathematics is a branch of mathematics that deals with discrete or finite sets of elements rather than continuous or infinite s
From playlist Maths for Programmers
Modern Physics || Modern Physics Full Lecture Course
Modern physics is an effort to understand the underlying processes of the interactions with matter, utilizing the tools of science and engineering. In general, the term is used to refer to any branch of #physics either developed in the early 20th century and onward, or branches greatly inf
From playlist Physics
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From playlist Science Unplugged: Mathematics
What is Abstract Algebra? (Modern Algebra)
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in t
From playlist Abstract Algebra
Welcome to the Mathematical Universe
Look around you. Underlying every aspect of the world is a language that we all know, though our use and expertise may vary. This language, mathematics, can be used to describe everything from the proliferation of waves through a medium to how many seeds will fit on a sunflower. The harder
From playlist Mathematics
Complex numbers & basic calculations. Chris Tisdell UNSW Sydney
This is a basic video on the operations and calculations with complex numbers like division and multiplication. By using an example I show how to simplfy expressions involving complex numbers. Such ideas are seen in high-school and first-year university mathematics. Complex numbers ar
From playlist A First Course in University Mathematics Revision Videos
A Mathematical Definition of an Algorithm | The Art Of Computer Programming Visualised #SoME1
A visual explanation of the mathematical definition of an algorithm inspired by the book series "The Art of Computer Programming" by Donald Knuth. Timestamps: 0:00 0. Motivation 1:05 1. High-level Overview 3:23 2. Implementation 6:11 3.1 States 7:46 3.2 State Transitions 9:36 4. A Side No
From playlist Summer of Math Exposition Youtube Videos
IDM 2021 Online Celebration - English Session
Live Streamed talks during the 2021 International Day of Mathematics Global Online celebration. 0:00 - Intro with Günter M. Ziegler, Freie Universität Berlin, Germany 2:48 - Welcoming message by UNESCO Director General Audrey Azoulay 6:36 - The IDM 2021 Theme / Christiane Rousseau, Canada
From playlist Collaborations
ASVAB Math – Challenge Yourself With This Math Problem
Excellent ASVAB scores will allow you to have many MOS’s to select from when you enlist in the US Military. However, you need to have strong math skills for the ASVAB. In this video I will go over a math problem involving direction and speed - you should be able to solve if you expect to d
From playlist Test Prep Math
Patrick Massot - Why Explain Mathematics to Computers?
A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk, I'll describe what formalization looks like, what kind of things it teaches us, and how it could even turn out to be us
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
The Mathematics of Consciousness (Integrated Information Theory)
Entry for the #3Blue1Brown Summer of Math Exposition 2022 (#SoME2) by Rodrigo Coin Curvo & Alexander Maier Read more about Integrated Information Theory and the #neuroscience of #consciousness: http://www.scholarpedia.org/article/Integrated_information_theory Also, check out Rodrigo's e
From playlist Summer of Math Exposition 2 videos
Points de Lagrange : un ticket (...) - Emmanuel Trélat - Mathématiques et mouvements - 13/03/18
Points de Lagrange : un ticket gratuit vers les étoiles ? Résumé : Les points de Lagrange sont des points d’équilibre dans la dynamique céleste, en lesquels les forces gravitationnelles s’annihilent. L’étude de la dynamique au voisinage de ces points (c’est-à-dire, l’étude des trajectoire
From playlist Mathématiques et mouvements - 13/03/2018
Corona „Herd-Immunity“ and all that (part 1 of 7)
My name is Stephan Luckhaus, I am currently the senator for mathematics in our (german) national academy Leopoldina. I do not agree with the recommendations of our academy for the covid pandemic. Based on the data on the epidemy in Germany, published by the Robert Koch Institute and on a c
From playlist Talks of Mathematics Münster's reseachers
3. Driven Harmonic Oscillators
View the complete OCW resource: http://ocw.mit.edu/resources/res-8-005-vibrations-and-waves-problem-solving-fall-2012/ Instructor: Wit Busza First, advice on how, in general, one approaches the solving of "physics problems." Then three very different oscillating systems, and how in each t
From playlist 8.03 - MIT Help Sessions by Professor Wit Busza
Physics 13.2.1b - Conventional Current
A discussion of "conventional current". From the Physics course by Derek Owens
From playlist Physics - Electric Circuits
Breakthrough Prize in Mathematics 2014
Breakthrough Prize in Mathematics 2014 recipients talking about mathematics
From playlist Actualités