Paul Shafer:Reverse mathematics of Caristi's fixed point theorem and Ekeland's variational principle
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Caristi's fixed point theorem is a fixed point theorem for functions that are controlled by continuous functions but are necessarily continuous themselves. Let a 'Caristi
From playlist Workshop: "Proofs and Computation"
In this video, I prove a very neat result about fixed points and give some cool applications. This is a must-see for calculus lovers, enjoy! Old Fixed Point Video: https://youtu.be/zEe5J3X6ISE Banach Fixed Point Theorem: https://youtu.be/9jL8iHw0ans Continuity Playlist: https://www.youtu
From playlist Calculus
Visual Group Theory, Lecture 5.4: Fixed points and Cauchy's theorem
Visual Group Theory, Lecture 5.4: Fixed points and Cauchy's theorem We begin with a small lemma stating that if a group of prime order acts on a set S, then the number of fixed points is congruent to the size of the set, modulo p. We need this result to prove Cauchy's theorem, which says
From playlist Visual Group Theory
Fixed and Periodic Points | Nathan Dalaklis
Fixed Points and Periodic points are two mathematical objects that come up all over the place in Dynamical systems, Differential equations, and surprisingly in Topology as well. In these videos, I introduce the concepts of fixed points and periodic points and gradually build to a proof of
From playlist The New CHALKboard
Fixed points and stability: one dimension
Shows how to determine the fixed points and their linear stability of a first-order nonlinear differential equation. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org
From playlist Differential Equations
Public Lecture 3 - Frank den Hollander “Comment mieux comprendre le comportement...
Frank den Hollander “Comment mieux comprendre le comportement des réseaux complexes?" Partout dans le monde les gens sont connectés à travers des réseaux. Pensez à Internet, Facebook et Twitter, mais aussi au trafic routier, transport de marchandises, téléphone mobile et à l'électricité.
From playlist T1-2015 : Disordered systems, random spatial processes and some applications
Math 131 111416 Sequences of Functions: Pointwise and Uniform Convergence
Definition of pointwise convergence. Examples, nonexamples. Pointwise convergence does not preserve continuity, differentiability, or integrability, or commute with differentiation or integration. Uniform convergence. Cauchy criterion for uniform convergence. Weierstrass M-test to imp
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Math 131 092816 Continuity; Continuity and Compactness
Review definition of limit. Definition of continuity at a point; remark about isolated points; connection with limits. Composition of continuous functions. Alternate characterization of continuous functions (topological definition). Continuity and compactness: continuous image of a com
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Viviani's Theorem | Visualization and Proof
A visual proof of Viviani's theorem. For any point inside an equilateral triangle, the sum of its perpendicular distances from the three sides is constant. And, this sum is equal to the length of the triangle's altitude. Follow: https://instagram.com/doubleroot.in Music by CeeaDidIt from
From playlist Summer of Math Exposition Youtube Videos
Ex: Determine the Distance Between Two Points Using the Pythagorean Theorem
This video explains how to determine the distance between two points on the coordinate plane using the Pythagorean Theorem. http://mathispower4u.com
From playlist Using the Pythagorean Theorem
Fixed points in digital topology
A talk given by Chris Staecker at King Mongkut's University of Technology Thonburi, Bangkok, Thailand, on October 11 2019. This is the second in a series of 3 talks given at KMUTT. Includes an introduction to graph-theoretical ("Rosenfeld style") digital topology, and some basic results a
From playlist Research & conference talks
Axioms for the fixed point index of an n-valued map
A research talk I gave at KU Leuven Kulak in Kortrijk, Belgium on June 4, 2019, at the conference on Nielsen Theory and Related Topics. The first 20 minutes is mostly about the Euler characteristic, and should be understandable to all mathematicians. The audience was other researchers in t
From playlist Research & conference talks
Piotr Przytycki: Torsion groups do not act on 2-dimensional CAT(0) complexes
We show, under mild hypotheses, that if each element of a finitely generated group acting on a 2-dimensional CAT(0) complex has a fixed point, then the action is trivial. In particular, all actions of finitely generated torsion groups on such complexes are trivial. As an ingredient, we pro
From playlist Geometry
Intro to Nielsen fixed point theory
A talk given by Chris Staecker at King Mongkut's University of Technology Thonburi, Bangkok, Thailand, on October 10 2019. Covers basic definitions and results of Nielsen fixed point theory, plus a few minutes about Nielsen-type theories for coincidence and periodic points. Should be und
From playlist Research & conference talks
Proving Brouwer's Fixed Point Theorem | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi There is a proof for Brouwer's Fixed Point Theorem that uses a bridge - or portal - between geometry and algebra. Tweet at us! @pbsinfinite Facebook: facebook.com/pbs
From playlist An Infinite Playlist
Group theory 4: Lagrange's theorem
This is lecture 4 of an online course on mathematical group theory. It introduces Lagrange's theorem that the order of a subgroup divides the order of a group, and uses it to show that all groups of prime order are cyclic, and to prove Fermat's theorem and Euler's theorem.
From playlist Group theory
The Hartman-Grobman Theorem, Structural Stability of Linearization, and Stable/Unstable Manifolds
This video explores a central result in dynamical systems: The Hartman-Grobman theorem. This theorem establishes when a fixed point of a nonlinear system will resemble its linearization. In particular, hyperbolic fixed points, where every eigenvalue has a non-zero real part, will be "str
From playlist Engineering Math: Differential Equations and Dynamical Systems
Giancarlo Travaglini: Pick’s theorem and Riemann sums: a Fourier analytic tale
VIRTUAL LECTURE We show a connection between Fourier series and a celebrated theorem of G. Pick on the number of integer points in an integer polygon. Then we discuss an Euler-Maclaurin formula over polygons. Recording during the meeting "Discrepancy Theory and Applications" Find thi
From playlist Virtual Conference