Abstract algebra

Closure with a twist

Closure with a twist is a property of subsets of an algebraic structure. A subset of an algebraic structure is said to exhibit closure with a twist if for every two elements there exists an automorphism of and an element such that where "" is notation for an operation on preserved by . Two examples of algebraic structures which exhibit closure with a twist are the cwatset and the generalized cwatset, or GC-set. (Wikipedia).

Video thumbnail

Wedge mechanism 24

Loose the screw for moving the stopper to new position and then tighten it. The stopper is kept immobile by wedge mechnism.

From playlist Mechanisms

Video thumbnail

Slider crank mechanism with satellite pulley

The diameter of the big pulley is double the one of the green pulley. The length of each crank = R The slider's stroke = 4R The belt should be toothed. It is possible to use chain drive instead of belt one. STEP files of this video: http://www.mediafire.com/file/frn0cmys8sedruy/SliderCrank

From playlist Mechanisms

Video thumbnail

B22 Introduction to Substitutions

An overview of the three type of substitutions as a new method of solving linear, exact, and "almost" separable differential equations.

From playlist Differential Equations

Video thumbnail

Slider clamp 1

Turn yellow screw for clamping or releasing green slider. Cone portion of the screw raises pink stud for clamping.

From playlist Mechanisms

Video thumbnail

C56 Continuation of previous problem

Adding a bit more depth to the previous problem.

From playlist Differential Equations

Video thumbnail

Winding number

In this video, I define the concept of a winding number of a curve around a point, which intuitively measures how many times a curve loops around a point. For example, for a circle (or any simple closed curve), the winding number should be 1, but for the curve in the thumbnail, the winding

From playlist Multivariable Calculus

Video thumbnail

Can you solve this unique challenge?

Spring/Latch Polymagnets: this pair of coded magnets attract but don’t touch in a state of stable equilibrium at a distance of 1/2 cm- but if one magnet is turned a half twist they latch together. Magnetic viewing film reveals the specific and complex arrangement of N and S poles that allo

From playlist physicsfun PUZZLES, ILLUSIONS & CHALLENGES

Video thumbnail

A02 Independence of the solution set

The independence of a linear system. How to make sure that a set of solutions are not constant multiples of each other.

From playlist A Second Course in Differential Equations

Video thumbnail

C52 Introduction to nonlinear DEs

A first look at nonlinear differential equations. In this first video examples are shown of equations that still have explicit solutions.

From playlist Differential Equations

Video thumbnail

B. Weiss - Horocycle dynamics (Part 1)

A major challenge in dynamics on moduli spaces is to understand the behavior of the horocycle flow. We will motivate this problem and discuss what is known and what is not known about it, focusing on the genus 2 case. Specific topics to be covered include: * SL_2(R) orbit closures and inva

From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

Video thumbnail

Barbara Nimershiem: Geometric Triangulations of a Family of Hyperbolic 3-Braids

Barbara Nimershiem, Franklin & Marshall College Title: Geometric Triangulations of a Family of Hyperbolic 3-Braids We construct topological triangulations for complements of $(-2, 3, n)$-pretzel knots and links with $n \geq 7$. Following a procedure outlined by Futer and Gueritaud, we use

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

Video thumbnail

Samuel Grushevsky: Limits of zeroes of holomorphic differential on stable nodal Riemann surfaces

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Dynamical Systems and Ordinary Differential Equations

Video thumbnail

Profinite Completions and Representation Rigidity - Ryan Spitler

Arithmetic Groups Topic: Profinite Completions and Representation Rigidity Speaker: Ryan Spitler Affiliation: Rice University Date: February 02, 2022 Taking up the terminology established in the first lecture, in 1970 Grothendieck showed that when two groups (G,H) form a Grothendieck pai

From playlist Mathematics

Video thumbnail

James Freitag 9/12/14 Part 2

Title: Effective Bounds For Finite Differential-Algebraic Varieties (Part I)

From playlist Fall 2014

Video thumbnail

Yves Andre: A Remark on the Tate Conjecture

Talk by Yves Andres in Global Noncommutative Geometry Seminar (Americas) on May 6, 2022, https://globalncgseminar.org/talks/tba-31/

From playlist Global Noncommutative Geometry Seminar (Americas)

Video thumbnail

Alex Wright - Minicourse - Lecture 5

Alex Wright Dynamics, geometry, and the moduli space of Riemann surfaces We will discuss the GL(2,R) action on the Hodge bundle over the moduli space of Riemann surfaces. This is a very friendly action, because it can be explained using the usual action of GL(2,R) on polygons in the plane

From playlist Maryland Analysis and Geometry Atelier

Video thumbnail

algebraic geometry 17 Affine and projective varieties

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between affine and projective varieties, with some examples such as a cubic curve and the twisted cubic.

From playlist Algebraic geometry I: Varieties

Video thumbnail

Spring toggle mechanism 9

Spring toggle mechanism enables to reach end positions of a lever quickly and holds it there firmly. The pink double crank represents action from outside.

From playlist Mechanisms

Video thumbnail

Astrophysical Dynamos by Kandaswamy Subramanian (Part 2)

GdR Dynamo 2015 PROGRAM LINK: www.icts.res.in/program/GDR2015 DATES : 01 Jun, 2015 - 12 Jun, 2015 VENUE : ICTS-TIFR, IISc campus, Bangalore DESCRIPTION : Dynamo or self-induced magnetic field generation in nature and laboratory is a very important area of research in physics, astrop

From playlist GdR Dynamo 2015

Related pages

Order (group theory) | Algebraic structure | If and only if | Operation (mathematics) | Closure (mathematics) | Automorphism | Group (mathematics) | Identity element | Permutation | Symmetric group | Direct product | Element (mathematics) | Mathematics | Set (mathematics) | Lagrange's theorem (group theory) | Cyclic group | Cycle notation | Subset | Subgroup | Projection (mathematics) | Cardinality | Modular arithmetic