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)
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Applying reimann sum for the midpoint rule and 3 partitions
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
The Quasi-Polynomial Freiman-Ruzsa Theorem of Sanders - Shachar Lovett
Shachar Lovett Institute for Advanced Study March 20, 2012 The polynomial Freiman-Ruzsa conjecture is one of the important open problems in additive combinatorics. In computer science, it already has several diverse applications: explicit constructions of two-source extractors; improved bo
From playlist Mathematics
Dimitri Zvonkine - On two ELSV formulas
The ELSV formula (discovered by Ekedahl, Lando, Shapiro and Vainshtein) is an equality between two numbers. The first one is a Hurwitz number that can be defined as the number of factorizations of a given permutation into transpositions. The second is the integral of a characteristic class
From playlist 4th Itzykson Colloquium - Moduli Spaces and Quantum Curves
Find the max and min from a quadratic on a closed interval
👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
I derive the celebrated Kirchhoff Formula, which gives the solution of the wave equation in 3 dimension, enjoy! Euler-Poisson-Darboux Equation: https://youtu.be/lIdrncWaZPY Partial Differential Equations playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCXfuXUAt9dT1Gjy_GK89OH Su
From playlist Partial Differential Equations
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation
Introduction to additive combinatorics lecture 5.8 --- Freiman homomorphisms and isomorphisms.
The notion of a Freiman homomorphism and the closely related notion of a Freiman isomorphism are fundamental concepts in additive combinatorics. Here I explain what they are and prove a lemma that states that a subset A of F_p^N such that kA - kA is not too large is "k-isomorphic" to a sub
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
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
Wolfram Physics Project: Working Session Sept. 15, 2020 [Physicalization of Metamathematics]
This is a Wolfram Physics Project working session on metamathematics and its physicalization in the Wolfram Model. Begins at 10:15 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the
From playlist Wolfram Physics Project Livestream Archive
Johnathan Bush (7/8/2020): Borsuk–Ulam theorems for maps into higher-dimensional codomains
Title: Borsuk–Ulam theorems for maps into higher-dimensional codomains Abstract: I will describe Borsuk-Ulam theorems for maps of spheres into higher-dimensional codomains. Given a continuous map from a sphere to Euclidean space, we say the map is odd if it respects the standard antipodal
From playlist AATRN 2020
Worldwide Calculus: Extrema and the Mean Value Theorem
Lecture on 'Extrema and the Mean Value Theorem' from 'Worldwide Differential Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Stokes' Theorem and Green's Theorem
Stokes' theorem is an extremely powerful result in mathematical physics. It allows us to quantify how much a vector field is circulating or rotating, based on the integral of the curl. @eigensteve on Twitter eigensteve.com databookuw.com %%% CHAPTERS %%% 0:00 Stoke's Theorem Overview
From playlist Engineering Math: Vector Calculus and Partial Differential Equations
Green's Theorem. Chris Tisdell UNSW
This is the 2nd lecture on Green's theorem and its use. In this lecture we explore some interesting applications of Green's theorem and present several examples. Also some proofs are discussed.
From playlist Vector Calculus @ UNSW Sydney. Dr Chris Tisdell
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems