Here I prove the Heine-Borel Theorem, one of the most fundamental theorems in analysis. It says that in R^n, all boxes must be compact. The proof itself is very neat, and uses a bisection-type argument. Enjoy! Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHG
From playlist Topology
Math 131 Fall 2018 100318 Heine Borel Theorem
Definition of limit point compactness. Compact implies limit point compact. A nested sequence of closed intervals has a nonempty intersection. k-cells are compact. Heine-Borel Theorem: in Euclidean space, compactness, limit point compactness, and being closed and bounded are equivalent
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Math 131 092616 Heine Borel, Connected Sets, Limits in Metric Spaces
Heine-Borel Theorem, connected sets, limits in metric spaces, uniqueness of limits
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Solve a Bernoulli Differential Equation (Part 2)
This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
Illustrates the solution of a Bernoulli first-order differential equation. Free books: http://bookboon.com/en/differential-equations-with-youtube-examples-ebook http://www.math.ust.hk/~machas/differential-equations.pdf
From playlist Differential Equations with YouTube Examples
Solve a Bernoulli Differential Equation Initial Value Problem
This video provides an example of how to solve an Bernoulli Differential Equations Initial Value Problem. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
(PP 1.8) Measure theory: CDFs and Borel Probability Measures
Correspondence between Borel probability measures on R and CDFs (cumulative distribution functions). A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4 You can skip the measure theory (Section 1) if you're not in
From playlist Probability Theory
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
Natasha Dobrinen: Borel sets of Rado graphs are Ramsey
The Galvin-Prikry theorem states that Borel partitions of the Baire space are Ramsey. Thus, given any Borel subset $\chi$ of the Baire space and an infinite set $N$, there is an infinite subset $M$ of $N$ such that $\left [M \right ]^{\omega }$ is either contained in $\chi$ or disjoint fr
From playlist Combinatorics
Stavros Garoufalidis - Arithmetic Resurgence of Quantum Invariants
I will explain some conjectures concerning arithmetic resurgence of quantum knot and 3-manifold invariants formulated in an earlier work of mine in 2008, as well as numerical tests of those conjectures and their relations to quantum modular forms, state integrals and their q-series. Joint
From playlist Resurgence in Mathematics and Physics
Semantic models for higher-order Bayesian inference - Sam Staton, University of Oxford
In this talk I will discuss probabilistic programming as a method of Bayesian modelling and inference, with a focus on fully featured probabilistic programming languages with higher order functions, soft constraints, and continuous distributions. These languages are pushing the limits of e
From playlist Logic and learning workshop
Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger
The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon
From playlist Math Foundations
Differential Equations | Abel's Theorem
We present Abel's Theorem with a proof. http://www.michael-penn.net
From playlist Differential Equations
Introduction to Resurgence, Trans-series and Non-perturbative Physics - I by Gerald Dunne
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Measurable equidecompositions – András Máthé – ICM2018
Analysis and Operator Algebras Invited Lecture 8.8 Measurable equidecompositions András Máthé Abstract: The famous Banach–Tarski paradox and Hilbert’s third problem are part of story of paradoxical equidecompositions and invariant finitely additive measures. We review some of the classic
From playlist Analysis & Operator Algebras
Real Analysis - Part 14 - Heine-Borel theorem [dark versio]
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From playlist Real Analysis [dark version]
Real Analysis - Part 14 - Heine-Borel theorem
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics Or via Patreon: https://www.patreon.com/bsom Or via other methods: https://thebrightsideofmathematics.
From playlist Real Analysis
Sergei Gukov - Resurgence and Modularity
Why do modular forms tend to have integer coefficients in their q-expansion? Are they counting something? And, can we "categorify" a modular form by representing it as a graded Euler characteristic of some homology theory? There are several ways to answer these questions, e.g. the one base
From playlist 7ème Séminaire Itzykson : « Résurgence et quantification »
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations