What is length contraction? Length contraction gives the second piece (along with time dilation) of the puzzle that allows us to reconcile the fact that the speed of light is constant in all reference frames.
From playlist Relativity
The formal definition of a vector space.
From playlist Linear Algebra Done Right
Special Relativity: 2 - Spacetime Diagrams
An introduction to spacetime diagrams which are a valuable tool used to understand special relativity. The second in a series on special and general relativity. Let us know what you think of these videos by filling out our short survey at http://tinyurl.com/astronomy-pulsar. Thank you!
From playlist Special Relativity
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From playlist Science Unplugged: Special Relativity
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
A01 An introduction to a series on space medicine
A new series on space medicine.
From playlist Space Medicine
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From playlist Science Unplugged: General Relativity
What is (a) Space? From Zero to Geo 1.5
What is space? In this video, we learn about the many different things that we might call "space". We come up with both a geometric and an algebraic definition, and the discussion also leads us to the important concept of subspaces. Sorry for how long this video took to make! I mention
From playlist From Zero to Geo
Rings 12 Duality and injective modules
This lecture is part of an online course on rings and modules. We descibe some notions of duality for modules generalizing the dual of a vector space. We first discuss duality for free and projective modules, which is very siilar to the vector space case. Then we discuss duality for finit
From playlist Rings and modules
What is a Module? (Abstract Algebra)
A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an
From playlist Abstract Algebra
Lec 6 | MIT 6.033 Computer System Engineering, Spring 2005
Virtualization and Virtual Memory View the complete course at: http://ocw.mit.edu/6-033S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.033 Computer System Engineering, Spring 2005
Ilya Dumanski - Schubert varieties in the Beilinson-Drinfeld Grassmannian
Ilya Dumanski (MIT) The Borel-Weil theorem states that the space of sections of a certain line bundle on the flag variety is isomorphic to the irreducible representation of the corresponding reductive group. The classical result of Demazure describes the restriction of sections to the Sch
From playlist Azat Miftakhov Days Against the War
Marco Schlichting: Introduction to Higher Grothendieck Witt groups (Lecture 1)
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Hermitian K-theory and trace methods"
From playlist HIM Lectures: Junior Trimester Program "Topology"
Kazhdan-Lusztig category - Jin-Cheng Guu
Quantum Groups Seminar Topic: Kazhdan-Lusztig category Speaker: Jin-Cheng Guu Affiliation: Stony Brook University Date: May 06, 2021 For more video please visit http://video.ias.edu
From playlist Quantum Groups Seminar
Ben Elias: Categorifying Hecke algebras at prime roots of unity
Thirty years ago, Soergel changed the paradigm with his algebraic construction of the Hecke category. This is a categorification of the Hecke algebra at a generic parameter, where the parameter is categorified by a grading shift. One key open problem in categorification is to categorify He
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Commutative algebra 39 (Stably free modules)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We discuss the relation between stably free and free modules. We first give an example of a stably free module that is not fre
From playlist Commutative algebra
0:00 Motivation for studying modules 4:45 Definition of a vector space over a field 9:31 Definition of a module over a ring 12:12 Motivating example: structure of abelian groups 16:05 Motivating example: Jordan normal form 19:44 What unifies both examples (spoiler): Structure theorem for f
From playlist Abstract Algebra 2
Symmetries show up everywhere in physics. But what is a symmetry? While the symmetries of shapes can be interesting, a lot of times, we are more interested in symmetries of space or symmetries of spacetime. To describe these, we need to build "invariants" which give a mathematical represen
From playlist Relativity