Lebesgue's universal covering problem

Universal covering spaces | Algebraic Topology | NJ Wildberger

We begin by giving some examples of the main theorem from the last lecture: that the associated homomorphism of fundamental groups associated to a covering space p:X to B injects pi(X) as a subgroup of pi(B). We look at helical coverings of a circle, and also a two-fold covering of the wed

From playlist Algebraic Topology

Lebesgue Integral Overview

In this video, I present an overview (without proofs) of the Lebesgue integral, which is a more general way of integrating a function. If you'd like to see proods of the statements, I recommend you look at fematika's channel, where he gives a more detailed look of the Lebesgue integral. In

From playlist Real Analysis

Coverings of the Circle

A covering of a topological space X is a topological space Y together with a continuous surjective map from X to Y that is locally bi-continuos. The infinite spiral is for example a covering of the circle. Notice how every path on the circle can be lifted to the spiral. If a coveri

From playlist Algebraic Topology

Lie Groups and Lie Algebras: Lesson 38 - Preparation for the concept of a Universal Covering Group

Lie Groups and Lie Algebras: Lesson 38 - Preparation for the Universal Covering Group concept In this lesson we examine another amazing connection between the algebraic properties of the Lie groups with topological properties. We will lay the foundation to understand how discrete invaria

From playlist Lie Groups and Lie Algebras

Measure Theory 2.1 : Lebesgue Outer Measure

In this video, I introduce the Lebesgue outer measure, and prove that it is, in fact, an outer measure. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Measure Theory

Riemann vs Lebesgue Integral

In this video, I show how to calculate the integral of x^3 from 0 to 1 but using the Lebesgue integral instead of the Riemann integral. My hope is to show you that they indeed produce the same answer, and that in fact Riemann integrable functions are also Lebesgue integrable. Enjoy!

From playlist Real Analysis

Vertex Covering Number of Complete Graphs | Graph Theory Exercises

We discuss and prove the vertex covering number of a complete graph Kn is n-1. That is, the minimum number of vertices needed to cover a complete graph is one less than its number of vertices. This is because, put simply, if we are missing at least 2 vertices in our attempted vertex cover,

From playlist Graph Theory Exercises

Vertex Covers and Vertex Covering Numbers | Graph Theory

We introduce vertex covers, minimum vertex covers, and vertex covering numbers! We'll see some examples and non-examples of vertex covers, as well as minimum vertex covers and some that aren't minimum. The number of vertices in a minimum vertex cover is called the vertex covering number of

From playlist Graph Theory

Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group

Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group We are finally in position to understand the nature of the Universal Covering Group and its connection to all the Lie groups which share a single Lie algebra. This is a critical lecture! In this lecture we simply state

From playlist Lie Groups and Lie Algebras

Lyapunov exponents for small random perturbations… - Alex Blumenthal

Symplectic Dynamics/Geometry Seminar Topic: Lyapunov exponents for small random perturbations of predominantly hyperbolic two dimensional volume-preserving diffeomorphisms, including the Standard Map Speaker: Alex Blumenthal Affiliation: University of Maryland Date: November 19, 2018 For

From playlist Mathematics

Marek Biskup: Extreme points of two dimensional discrete Gaussian free field (part 4)

Recent years have witnessed a lot of progress in the understanding of the two-dimensional Discrete Gaussian Free Field (DGFF). In my lectures I will discuss the asymptotic law of the extreme point process for the DGFF on lattice approximations of bounded open sets in the complex plane with

From playlist HIM Lectures 2015

Real Analysis - Eva Sincich - Lecture 01

From playlist Machine learning

My Math Book Collection (Math Books)

Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Thank you! Get the Books! (affiliate links) Schaum's Guide http://amzn.

From playlist Math Book Reviews

Uniform rectifiability via perimeter minimization III - Tatiana Toro

Women and Mathematics: Terng Lecture Course Topic: Uniform rectifiability via perimeter minimization III Speaker: Tatiana Toro Affiliation: University of Washington Date: May 23, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

Observable events" and "typical trajectories" in...dynamical systems - Lai-Sang Young

Analysis Seminar Topic: Observable events" and "typical trajectories" in finite and infinite dimensional dynamical systems Speaker: Lai-Sang Young Affiliation: New York University; Distinguished Visiting Professor, School of Mathematics and Natural Sciences Date: February 24, 2020 For mo

From playlist Mathematics

Lec 7 | MIT 6.450 Principles of Digital Communications I, Fall 2006

Lecture 7: High rate quantizers and waveform encoding View the complete course at: http://ocw.mit.edu/6-450F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.450 Principles of Digital Communications, I Fall 2006

Karma Dajani - An introduction to Ergodic Theory of Numbers (Part 2)

In this course we give an introduction to the ergodic theory behind common number expansions, like expansions to integer and non-integer bases, Luroth series and continued fraction expansion. Starting with basic ideas in ergodic theory such as ergodicity, the ergodic theorem and natural ex

From playlist École d’été 2013 - Théorie des nombres et dynamique

Dynamical systems, fractals and diophantine approximations – Carlos Gustavo Moreira – ICM2018

Plenary Lecture 6 Dynamical systems, fractal geometry and diophantine approximations Carlos Gustavo Moreira Abstract: We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related

From playlist Plenary Lectures

Symmetry and symmetry breaking: Rigidity and flows in elliptic PDEs – Maria Esteban – ICM2018

Partial Differential Equations | Mathematics in Science and Technology Invited Lecture 10.5 | 17.5 Symmetry and symmetry breaking: Rigidity and flows in elliptic PDEs Maria Esteban Abstract: The issue of symmetry and symmetry breaking is fundamental in all areas of science. Symmetry is o

From playlist Partial Differential Equations

Lagrange multipliers: 2 constraints

Free ebook http://tinyurl.com/EngMathYT A lecture showing how to apply the method of Lagrange multipliers where two contraints are involved.

From playlist Lagrange multipliers