Graph connectivity | Theorems in graph theory | Theorems in discrete geometry | Polyhedral combinatorics
In polyhedral combinatorics, a branch of mathematics, Balinski's theorem is a statement about the graph-theoretic structure of three-dimensional convex polyhedra and higher-dimensional convex polytopes. It states that, if one forms an undirected graph from the vertices and edges of a convex d-dimensional convex polyhedron or polytope (its skeleton), then the resulting graph is at least d-vertex-connected: the removal of any d − 1 vertices leaves a connected subgraph. For instance, for a three-dimensional polyhedron, even if two of its vertices (together with their incident edges) are removed, for any pair of vertices there will still exist a path of vertices and edges connecting the pair. Balinski's theorem is named after mathematician Michel Balinski, who published its proof in 1961, although the three-dimensional case dates back to the earlier part of the 20th century and the discovery of Steinitz's theorem that the graphs of three-dimensional polyhedra are exactly the three-connected planar graphs. (Wikipedia).
Apportionment: Webster's Method
This video explains Webster's method of apportionment. Site: http://mathispower4u.com
From playlist Apportionment
Monotonicity of the Riemann zeta function and related functions - P Zvengrowski [2012]
General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences May 17, 2012 14:00, St. Petersburg, POMI, room 311 (27 Fontanka) Monotonicity of the Riemann zeta function and related functions P. Zvengrowski University o
From playlist Number Theory
Grigorios Fournodavlos - The mysterious nature of the Big Bang singularity - IPAM at UCLA
Recorded 29 October 2021. Grigorios Fournodavlos of Princeton University presents "The mysterious nature of the Big Bang singularity" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-mat
From playlist Workshop: Mathematical and Numerical Aspects of Gravitation
James Mingo: The infinitesimal Weingarten calculus
Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: The Weingarten calculus calculates matrix integrals over the unitary and orthogonal groups, in particular their large N behaviour. In this talk we shall look at the W
From playlist Noncommutative geometry meets topological recursion 2021
Oliver SCHNETZ - 2010-2020: a Decade of Quantum Computing
Supported by Dirk Kreimer, in 2010 I started analyzing and calculating high loop-order amplitudes in perturbative quantum field theory. The main tools were graphical functions, generalized single-valued hyperlogarithms (GSVHs), and the c_2-invariant. I will report on the progress that has
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Binet's formula | Lecture 5 | Fibonacci Numbers and the Golden Ratio
Derivation of Binet's formula, which is a closed form solution for the Fibonacci numbers. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confir
From playlist Fibonacci Numbers and the Golden Ratio
Zoom Talk & Problem Solving Session, Andrey Konyaev: Tuesday 15 February
SMRI -MATRIX Symposium: Nijenhuis Geometry and Integrable Systems Week 2 (MATRIX): Zoom Talk by Andrey Konyaev, followed by Problem Solving Session 15 February 2022 ---------------------------------------------------------------------------------------------------------------------- SMRI
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
Wim Veys : Zeta functions and monodromy
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 Number Theory
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
A Fibonacci bounded partial sum of the Harmonic series.
We determine the limit of a certain sequence defined in terms of Fibonacci and Harmonic numbers. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Identities involving Fibonacci numbers
Discrete Math - 4.1.1 Divisibility
The definition and properties of divisibility with proofs of several properties. Formulas for quotient and remainder, leading into modular arithmetic. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNU
From playlist Discrete Math I (Entire Course)
Number Theory | Divisibility Basics
We present some basics of divisibility from elementary number theory.
From playlist Divisibility and the Euclidean Algorithm
More identities involving the Riemann-Zeta function!
By applying some combinatorial tricks to an identity from https://youtu.be/2W2Ghi9idxM we are able to derive two identities involving the Riemann-Zeta function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
Calculus 1 (Stewart) Ep 22, Mean Value Theorem (Oct 28, 2021)
This is a recording of a live class for Math 1171, Calculus 1, an undergraduate course for math majors (and others) at Fairfield University, Fall 2021. The textbook is Stewart. PDF of the written notes, and a list of all episodes is at the class website. Class website: http://cstaecker.f
From playlist Math 1171 (Calculus 1) Fall 2021
Equidistribution of Unipotent Random Walks on Homogeneous spaces by Emmanuel Breuillard
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
What is Green's theorem? Chris Tisdell UNSW
This lecture discusses Green's theorem in the plane. Green's theorem not only gives a relationship between double integrals and line integrals, but it also gives a relationship between "curl" and "circulation". In addition, Gauss' divergence theorem in the plane is also discussed, whic
From playlist Vector Calculus @ UNSW Sydney. Dr Chris Tisdell
Real Analysis Ep 32: The Mean Value Theorem
Episode 32 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is more about the mean value theorem and related ideas. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker
From playlist Math 3371 (Real analysis) Fall 2020
Pythagorean theorem - What is it?
► My Geometry course: https://www.kristakingmath.com/geometry-course Pythagorean theorem is super important in math. You will probably learn about it for the first time in Algebra, but you will literally use it in Algebra, Geometry, Trigonometry, Precalculus, Calculus, and beyond! That’s
From playlist Geometry
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