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
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Berge's lemma, an animated proof
Berge's lemma is a mathematical theorem in graph theory which states that a matching in a graph is of maximum cardinality if and only if it has no augmenting paths. But what do those terms even mean? And how do we prove Berge's lemma to be true? == CORRECTION: at 7:50, the red text should
From playlist Summer of Math Exposition Youtube Videos
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Problems, Paradoxes, and Sophisms
The Infinite Game of Chess (with Outray Chess)
An infinite game of chess with the Thue-Morse sequence. To avoid an infinite game of chess there was a rule that declared that a game would end if any sequence of moves were repeated three times in a row. However Dutch mathematician Max Euwe showed that the Thue-Morse sequence can define
From playlist My Maths Videos
Arne Martin Aurlien: Implement an Esoteric Programming Language for Fun | JSConf EU 2014
Inside most of us there’s a befunge programmer who wants to come out. When doing day-to-day “serious” programming it is usually a good idea to keep them as firmly locked up as possible. Let’s ignore that instinct for a little while. In this talk I’ll try to convince you why you should try
From playlist JSConf EU 2014
Koch Curve from Thue-Morse Turtle Graphics
This video shows the first 65536 steps of the turtle graphics construction of the Koch curve using the Thue-Morse sequence. To learn more about some of the amazing properties of Thue-Morse sequence, see this longer video: https://youtu.be/yqEIhdnfJxE.. #numbertheory #turtlegraphics ______
From playlist Fractals
The Thue-Morse Sequence (with visualizations)
In this video, we introduce the Prouhet-Thue-Morse sequence, which is a binary sequence. We discuss three methods to construct the sequence and then investigate some of the sequence's properties (including why it is the "fair sharing" sequence, the overlap-free property, its connection to
From playlist Fractals
Arul Shankar, Ordering elliptic curves by conductor
VaNTAGe seminar, on Oct 27, 2020 License: CC-BY-NC-SA. Closed captions provided by Rachana Madhukara.
From playlist Rational points on elliptic curves
Stephanie Chan, Integral points in families of elliptic curves
VaNTAGe Seminar, June 28, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk: Hindry-Silverman: https://eudml.org/doc/143604 Alpoge: https://arxiv.org/abs/1412.1047 Bhargava-Shankar: https://arxiv.org/abs/1312.7859 Brumer-McGuiness: https://www.ams.org/journal
From playlist Arithmetic Statistics II
Gary Walsh: On binary quartic Thue equations and related topics
CIRM VIRTUAL CONFERENCE Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the November 25, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
Hugh Montgomery: Moments of a Thue-Morse generating function
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 Number Theory
Regularity lemma and its applications Part I - Fan Wei
Computer Science/Discrete Mathematics Seminar II Topic: Regularity lemma and its applications Part I Speaker: Fan Wei Affiliation: Member, School of Mathematics Dater: December 3, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Problems, Paradoxes, and Sophisms
Symmetry in Physics | Noether's theorem
▶ Topics ◀ Global / Local Symmetries, Continuous / Discrete Symmetries ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on
From playlist Symmetry
Linear Algebra Vignette 3h: Easy Eigenvalues - The Grand Finale
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist A Vector Calculus Challenge
Michael Drmota: Automatic sequences along squares and primes
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 Number Theory
Proof & Explanation: Gauss's Lemma in Number Theory
Euler's criterion: https://youtu.be/2IBPOI43jek One common proof of quadratic reciprocity uses Gauss's lemma. To understand Gauss's lemma, here we prove how it works using Euler's criterion and the Legendre symbol. Quadratic Residues playlist: https://www.youtube.com/playlist?list=PLug5Z
From playlist Quadratic Residues
#MegaFavNumbers: 258,474,216. See https://www.youtube.com/watch?v=R2eQVqdUQLI&list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo. Further reading: The OEIS for the sequence: https://oeis.org/A001219 Another relevant sequence: https://oeis.org/A097571 S. P. Mohanty, Which triangular numbers are prod
From playlist MegaFavNumbers