Theorems in geometry | Geometry of numbers
Blichfeldt's theorem is a mathematical theorem in the geometry of numbers, stating that whenever a bounded set in the Euclidean plane has area , it can be translated so that it includes at least points of the integer lattice. Equivalently, every bounded set of area contains a set of points whose coordinates all differ by integers. This theorem can be generalized to other lattices and to higher dimensions, and can be interpreted as a continuous version of the pigeonhole principle. It is named after Danish-American mathematician Hans Frederick Blichfeldt, who published it in 1914. Some sources call it Blichfeldt's principle or Blichfeldt's lemma. (Wikipedia).
In this video, I present another example of Stokes theorem, this time using it to calculate the line integral of a vector field. It is a very useful theorem that arises a lot in physics, for example in Maxwell's equations. Other Stokes Example: https://youtu.be/-fYbBSiqvUw Yet another Sto
From playlist Vector Calculus
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
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)
Thrive: The Evolution of a Game
In which I examine the past, present and future of an evolution game forged from the ashes of Spore and perhaps destined for the stars. Thrive website: https://revolutionarygamesstudio.com/ Download the Thrive launcher: https://github.com/Revolutionary-Games/Thrive-Launcher/releases/late
From playlist Video Essays
Functional Analysis Lecture 14 2014 03 11 BMO is the dual of H^1; Distributions
Showing that integration against a BMO function is a bounded linear functional on Hardy space (using the atomic decomposition): case of an L^infinity function; case of general BMO function. Proof of converse statement. Distributions. Set D of infinitely differentiable functions of compa
From playlist Course 9: Basic Functional and Harmonic Analysis
Calculus - The Fundamental Theorem, Part 2
The Fundamental Theorem of Calculus. A discussion of the antiderivative function and how it relates to the area under a graph.
From playlist Calculus - The Fundamental Theorem of Calculus
Ex 2: Rolle's Theorem with Product Rule
This video provides an example of how to apply Rolle's Theorem. http://mathispower4u.com
From playlist Rolle’s Theorem and the Mean Value Theorem
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)
Multivariable Calculus | Differentiable implies continuous.
We prove the classic result that if a function is differentiable, then it is continuous. To start, we prove this for a two variable function and then repeat for an n-variable function. http://www.michael-penn.net https://www.researchgate.net/profile/Michael_Penn5 http://www.randolphcolleg
From playlist Multivariable Calculus
This video states Fubini's Theorem and illustrated the theorem graphically. http://mathispower4u.wordpress.com/
From playlist Double Integrals
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®
B24 Introduction to the Bernoulli Equation
The Bernoulli equation follows from a linear equation in standard form.
From playlist Differential Equations
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