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
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Math 031 041917 Taylor's Theorem and the Lagrange Remainder Theorem (no sound)
Motivation: how do you know of the Taylor series converges back to the original function? Statement of Taylor's Theorem (+ Lagrange Remainder Formula). Example application: showing that the Taylor series for the sine recovers the sine (at x = 1; then for general x). Same application for
From playlist Course 3: Calculus II (Spring 2017)
Math 131 Fall 2018 102418 Taylor's Theorem; Introduction to Sequences
Sketch of proof of L'Hopital's Rule. Taylor's theorem: definition of Taylor polynomial. Proof of Taylor's theorem. Introduction to sequences. Definition of convergence of a sequence (in a metric space). Example. Implications of convergence to a point: every neighborhood of the point
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Math 031 Spring 2018 050218 Convergence of Taylor Series
Recall Lagrange Remainder Theorem. Example of using the theorem to prove convergence of a Taylor series of a function to that function: the exponential function. Example: the sine function. Error estimation. Extra topic: using power series to define complex-valued functions. Euler's f
From playlist Course 3: Calculus II (Spring 2018)
Intro to Cauchy Sequences and Cauchy Criterion | Real Analysis
What are Cauchy sequences? We introduce the Cauchy criterion for sequences and discuss its importance. A sequence is Cauchy if and only if it converges. So Cauchy sequences are another way of characterizing convergence without involving the limit. A sequence being Cauchy roughly means that
From playlist Real Analysis
Jeff Calder: "An intro to concentration of measure with applications to graph-based l... (Part 2/2)"
Watch part 1/2 here: https://youtu.be/Q5fB5Ldzo-g High Dimensional Hamilton-Jacobi PDEs Tutorials 2020 "An introduction to concentration of measure with applications to graph-based learning (Part 2/2)" Jeff Calder, University of Minnesota - Twin Cities Abstract: We will give a gentle in
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
General strong polarization - Madhu Sudan
Computer Science/Discrete Mathematics Seminar I Topic: Locally symmetric spaces: pp-adic aspects Speaker: General strong polarization Affiliation: Harvard University Date: December 4, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Newton's Method Interval of Convergence
How to find the Interval of Convergence for Newton-type methods such as Newton's Method, Secant Method, and Finite Difference Method including discussion on Damped Newton's Method and widening the convergence interval. Example code in R hosted on Github: https://github.com/osveliz/numerica
From playlist Root Finding
Math 139 Fourier Analysis Lecture 10.1 L^2 convergence of Fourier Series
(Unfortunately I taped only part of this lecture.) Fourier series converges to the function in the L^2 sense.
From playlist Course 8: Fourier Analysis
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
15. Graph limits II: regularity and counting
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao explains how graph limits can be used to gener
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
David Kelly: Fast slow systems with chaotic noise
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 Probability and Statistics
Xiaolu Tan: On the martingale optimal transport duality in the Skorokhod space
We study a martingale optimal transport problem in the Skorokhod space of cadlag paths, under finitely or infinitely many marginals constraint. To establish a general duality result, we utilize a Wasserstein type topology on the space of measures on the real value space, and the S-topology
From playlist HIM Lectures 2015
The Divergence Theorem, a visual explanation
This video talks about the divergence theorem, one of the fundamental theorems of multivariable calculus. The divergence theorem relates a flux integral to a triple integral. Green's Theorem: https://youtu.be/8SwKD5_VL5o Line Integrals: https://youtu.be/dnGDmZynvYY Follow Me! https://i
From playlist Multivariable Calculus
Wilhem Stannat - Fluctuation limits for mean-field interacting nonlinear Hawkes processes
---------------------------------- Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75005 PARIS http://www.ihp.fr/ Rejoingez les réseaux sociaux de l'IHP pour être au courant de nos actualités : - Facebook : https://www.facebook.com/InstitutHenriPoincare/ - Twitter : https://twitter
From playlist Workshop "Workshop on Mathematical Modeling and Statistical Analysis in Neuroscience" - January 31st - February 4th, 2022
16. Graph limits III: compactness and applications
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Continuing the discussion of graph limits, Prof. Zhao pro
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
This is the final lecture on "A Markovian perspective on some singular SPDEs" taught by Professor Nicolas Perkowski. For more materials and slides visit: https://sites.google.com/view/oneworld-pderandom/home
From playlist Summer School on PDE & Randomness
FinMath L2-1: The general Ito integral
Welcome to the second lesson of Financial Mathematics! This is a course I teach in the master in applied mathematics of Delft University of Technology. I simply record my live classes to be shared online. I make use of my own lecture notes. The first chapter, which we are using in the v
From playlist Financial Mathematics
Math 131 Fall 2018 111418 Sequences and Series of Functions
Statement of Abel's theorem on the Cauchy product. Comments about rearrangements of infinite series. Introduction to sequences and series of functions. Definition of pointwise convergence. Example (x^n on [0,1]); nonexample ("blimp functions"). Unsatisfying interaction of pointwise co
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)