Bang's theorem on tetrahedra

Theory of numbers: Gauss's lemma

This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di

From playlist Theory of numbers

Linear Equations in Primes and Nilpotent Groups - Tamar Ziegler

Tamar Ziegler Technion--Israel Institute of Technology January 30, 2011 A classical theorem of Dirichlet establishes the existence of infinitely many primes in arithmetic progressions, so long as there are no local obstructions. In 2006 Green and Tao set up a program for proving a vast gen

From playlist Mathematics

Theory of numbers: Fermat's theorem

This lecture is part of an online undergraduate course on the theory of numbers. We prove Fermat's theorem a^p = a mod p. We then define the order of a number mod p and use Fermat's theorem to show the order of a divides p-1. We apply this to testing some Fermat and Mersenne numbers to se

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)

Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

From playlist Calculus - The Fundamental Theorem of Calculus

Fourier series + Fourier's theorem

Free ebook http://tinyurl.com/EngMathYT A basic lecture on how to calculate Fourier series and a discussion of Fourier's theorem, which gives conditions under which a Fourier series will converge to a given function.

From playlist Engineering Mathematics

Eschermatics - Roger Penrose

Oxford Mathematics Public Lectures : Roger Penrose - Eschermatics Roger Penrose's relationship with the artist M.C. Escher was not just one of mutual admiration. Roger's thinking was consistently influenced by Escher, from the famous Penrose tiling to his groundbreaking work in cosmology.

From playlist The Roger Penrose Playlist

Hyperbolic Knot Theory (Lecture - 2) by Abhijit Champanerkar

PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl

From playlist Knots Through Web (Online)

Number Theory | A very special case of Fermat's Last Theorem

We prove a very simple case of Fermat's Last Theorem. Interestingly, this case is fairly easy to prove which highlights the allure of the theorem as a whole -- especially given the fact that much of modern number theory was developed as part of the program that ended in the full proof. ht

From playlist Number Theory

Hyperbolic Knot Theory (Lecture - 1) by Abhijit Champanerkar

PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl

From playlist Knots Through Web (Online)

Tetrahedral hyperbolic 3-manifolds and links by Andrei Vesnin

PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl

From playlist Knots Through Web (Online)

Barbara Nimershiem: Geometric Triangulations of a Family of Hyperbolic 3-Braids

Barbara Nimershiem, Franklin & Marshall College Title: Geometric Triangulations of a Family of Hyperbolic 3-Braids We construct topological triangulations for complements of $(-2, 3, n)$-pretzel knots and links with $n \geq 7$. Following a procedure outlined by Futer and Gueritaud, we use

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

Cascading Principles - Conrad Shawcross, Martin Bridson and James Sparks with Fatos Ustek

Whether a mathematician or an artist, when you begin you often don't know where you'll end up. In this fascinating discussion, artist Conrad Shawcross and mathematicians Martin Bridson and James Sparks explore connections between mathematics and art. An exhibition of Conrad's mathematical

From playlist Oxford Mathematics Public Lectures

François Guéritaud - 2/2 Geometric Structures on 3 Manifolds

From playlist Summer School 2019: Aspects of Geometric Group Theory

Number Theory - Fundamental Theorem of Arithmetic

Fundamental Theorem of Arithmetic and Proof. Building Block of further mathematics. Very important theorem in number theory and mathematics.

From playlist Proofs

10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof

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 In this first half of this lecture, Prof. Zhao shows how

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

Veering Dehn surgery - Saul Schleimer

Geometric Structures on 3-manifolds Topic: Veering Dehn surgery Speaker: Saul Schleimer Date: Tuesday, April 12 (Joint with Henry Segerman.) It is a theorem of Moise that every three-manifold admits a triangulation, and thus infinitely many. Thus, it can be difficult to learn anything

From playlist Mathematics

Number Theory | Fermat's Little Theorem

We state and prove Fermat's Little Theorem. www.michael-penn.net

From playlist Number Theory

The Signature and Natural Slope of Hyperbolic Knots - Marc Lackenby

DeepMind Workshop Topic: The Signature and Natural Slope of Hyperbolic Knots Speaker: Marc Lackenby Affiliation: University of Oxford Date: March 30, 2022 Andras Juhasz has explained in his talk how machine learning was used to discover a previously unknown relationship between invariant

From playlist DeepMind Workshop

Proof of Pythagoras' theorem - GCSE Maths

Support me on Patreon: https://www.patreon.com/mathsaurus A simple and elegant proof of Pythagoras' Theorem. Visit http://www.mathsaurus.com/ for more free GCSE and A-level maths videos and resources Visit the Mathsaurus Amazon shop at https://www.amazon.co.uk/shop/mathsaurus to see so

From playlist GCSE IGCSE Trigonometry