Set Theory (Part 3): Ordered Pairs and Cartesian Products
Please feel free to leave comments/questions on the video and practice problems below! In this video, I cover the Kuratowski definition of ordered pairs in terms of sets. This will allow us to speak of relations and functions in terms of sets as the basic mathematical objects and will ser
From playlist Set Theory by Mathoma
Silvia Steila: An overview over least fixed points in weak set theories
Given a monotone function on a complete lattice the least fixed point is defined as the minimum among the fixed points. Tarski Knaster Theorem states that every monotone function on a complete lattice has a least fixed point. There are two standard proofs of Tarski Knaster Theorem. The f
From playlist Workshop: "Proofs and Computation"
The Homework Problem That Started as a Phd Thesis: 14 set theorem
In a handful of introductory topology textbooks, Kuratowski's 14 set theorem is given as an exercise despite it being one of the results proven as a part of his phd thesis in 1922. This homework problem that started out as a phd thesis is not an easy exercise if you don't know how to think
From playlist The New CHALKboard
Extremal set theory - Andrey Kupavskii
Computer Science/Discrete Mathematics Seminar I Topic: Extremal set theory Speaker: Andrey Kupavskii Affiliation: Member, School of Mathematics Date: October 29, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Every Subset of a Linearly Independent Set is also Linearly Independent Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A proof that every subset of a linearly independent set is also linearly independent.
From playlist Proofs
MATH1081 Discrete Maths: Chapter 5 Question 27 a
This problem is about planar graphs. The theorem mentioned is Fáry's Theorem (1948); see http://bit.ly/1gmUrXT . Presented by Thomas Britz of the School of Mathematics and Statistics, Faculty of Science, UNSW.
From playlist MATH1081 Discrete Mathematics
Graph Theory: 61. Characterization of Planar Graphs
We have seen in a previous video that K5 and K3,3 are non-planar. In this video we define an elementary subdivision of a graph, as well as a subdivision of a graph. We then discuss the fact that if a graph G contains a subgraph which is a subdivision of a non-planar graph, then G is non-
From playlist Graph Theory part-10
Math 131 092116 Properties of Compact Sets
Properties of compact sets. Compact implies closed; closed subsets of compact sets are compact; collections of compact sets that satisfy the finite intersection property have a nonempty intersection; infinite subsets of compact sets must have a limit point; the infinite intersection of ne
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
The Empty Set is a Subset of Every Set Proof
Please subscribe:) https://goo.gl/JQ8Nys The Empty Set is a Subset of Every Set Proof B-Roll - Islandesque by Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/) Source: http://incompetech.com/music/royalty-free/index.html
From playlist Set Theory
Graph Theory: 62. Graph Minors and Wagner's Theorem
In this video, we begin with a visualisation of an edge contraction and discuss the fact that an edge contraction may be thought of as resulting in a multigraph or simple graph, depending on the application. We then state the definition a contraction of edge e in a graph G resulting in a
From playlist Graph Theory part-10
MATH1081 Discrete Maths: Chapter 5 Question 33 - Kuratowski's Theorem (part 1)
MATH1081 "Discrete Mathematics" Topic 5 Question 33a
From playlist MATH1081 Discrete Mathematics
MATH1081 Discrete Maths: Chapter 5 Question 33 - Kuratowski's Theorem (part 2)
MATH1081 "Discrete Mathematics" Topic 5 Question 33c
From playlist MATH1081 Discrete Mathematics
Rade Zivaljevic (6/27/17) Bedlewo: Topological methods in discrete geometry; new developments
Some new applications of the configurations space/test map scheme can be found in Chapter 21 of the latest (third) edition of the Handbook of Discrete and Computational Geometry [2]. In this lecture we focus on some of the new developments which, due to the limitations of space, may have b
From playlist Applied Topology in Będlewo 2017
A Classification of Planar Graphs - A Proof of Kuratowski's Theorem
A visually explained proof of Kuratowski's theorem, an interesting, important and useful result classifying "planar" graphs. Proof adapted from: http://math.uchicago.edu/~may/REU2017/REUPapers/Xu,Yifan.pdf and: https://www.math.cmu.edu/~mradclif/teaching/228F16/Kuratowski.pdf Also check
From playlist Summer of Math Exposition Youtube Videos
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
Marek Biskup: Extreme points of two dimensional discrete Gaussian free field part 3
This lecture was held during winter school (01.19.2015 - 01.23.2015)
From playlist HIM Lectures 2015
Featuring Professor Maria Chudnovsky from Princeton University - see part two about her work on Perfect Graphs - https://youtu.be/C4Zr4cOVm9g More links & stuff in full description below ↓↓↓ Correction at 13:58 - remove the word "not". Professor Chudnovsky's webpage: https://web.math.pri
From playlist Women in Mathematics - Numberphile
Set Theory (Part 2b): The Bogus Universal Set
Please feel free to leave comments/questions on the video below! In this video, I argue against the existence of the set of all sets and show that this claim is provable in ZFC. This theorem is very much tied to the Russell Paradox, besides being one of the problematic ideas in mathematic
From playlist Set Theory by Mathoma
Prove the Set of all Bounded Functions is a Subspace of a Vector Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Prove the Set of all Bounded Functions is a Subspace of a Vector Space
From playlist Proofs
Ulrich Bauer (3/4/22): Gromov hyperbolicity, geodesic defect, and apparent pairs in Rips filtrations
Motivated by computational aspects of persistent homology for Vietoris-Rips filtrations, we generalize a result of Eliyahu Rips on the contractibility of Vietoris-Rips complexes of geodesic spaces for a suitable parameter depending on the hyperbolicity of the space. We consider the notion
From playlist Vietoris-Rips Seminar