Abstract Algebra | The third isomorphism theorem for groups.
We prove the third isomorphism theorem for groups. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
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
Lie groups: Poincare-Birkhoff-Witt theorem
This lecture is part of an online graduate course on Lie groups. We state the Poincare-Birkhoff Witt theorem, which shows that the universal enveloping algebra (UEA) of a Lie algebra is the same size as a polynomial algebra. We prove it for Lie algebras of Lie groups and sketch a proof of
From playlist Lie groups
In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
From playlist Algebra
This lecture is part of an online graduate course on Lie groups. We define the Lie algebra of a Lie group in two ways, and show that it satisfied the Jacobi identity. The we calculate the Lie algebras of a few Lie groups. For the other lectures in the course see https://www.youtube.co
From playlist Lie groups
Lie derivatives of differential forms
Introduces the lie derivative, and its action on differential forms. This is applied to symplectic geometry, with proof that the lie derivative of the symplectic form along a Hamiltonian vector field is zero. This is really an application of the wonderfully named "Cartan's magic formula"
From playlist Symplectic geometry and mechanics
This lecture is part of an online graduate course on Lie groups. This lecture is about Lie's theorem, which implies that a complex solvable Lie algebra is isomorphic to a subalgebra of the upper triangular matrices. . For the other lectures in the course see https://www.youtube.com/playl
From playlist Lie groups
Lie Groups and Lie Algebras: Lesson 26: Review!
Lie Groups and Lie Algebras: Lesson 26: Review! It never hurts to recap! https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
The Lie-algebra of Quaternion algebras and their Lie-subalgebras
In this video we discuss the Lie-algebras of general quaternion algebras over general fields, especially as the Lie-algebra is naturally given for 2x2 representations. The video follows a longer video I previously did on quaternions, but this time I focus on the Lie-algebra operation. I st
From playlist Algebra
Duality: magic in simple geometry #SoME2
Two inaccuracies: 2:33 explains the first property (2:16), not the second one (2:24) Narration at 5:52 should be "intersections of GREEN and orange lines" Time stamps: 0:00 — Intro 0:47 — Polar transform 4:46 — Desargues's Theorem 6:29 — Pappus's Theorem 7:18 — Sylvester-Gallai Theorem 8
From playlist Summer of Math Exposition 2 videos
Minerva Lectures 2013 - Terence Tao Talk 1: Sets with few ordinary lines
For more information please visit: http://math.princeton.edu/events/seminars/minerva-lectures/minerva-lecture-i-sets-few-ordinary-lines
From playlist Minerva Lecture Terence Tao
Elias Koutsoupias: Game Theory 2/2 🎲 CERN
This lecture series will present the main directions of Algorithmic Game Theory, a new field that has emerged in the last two decades at the interface of Game Theory and Computer Science, because of the unprecedented growth in size, complexity, and impact of the Internet and the Web. These
From playlist CERN Academic Lectures
algebraic geometry 16 Desargues's theorem
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers Desargues's theorem and duality of projective space.
From playlist Algebraic geometry I: Varieties
Bisectors, Medians, Altitudes, MidSegments, and Inequalities (Complete Geometry Course Lesson 6)
This is the sixth lesson of Mario's Math Tutoring's Complete Geometry Course here on YouTube. We discuss bisectors, medians, altitudes, mid segments and inequalities in triangles. Join this channel to help support this content: https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/joi
From playlist Geometry Course (Complete Course - Mario's Math Tutoring)
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)
A Miraculous Proof (Ptolemy's Theorem) - Numberphile
Featuring Zvezdelina Stankova... Want more? Part 2 (bringing in Pentagons and the Golden Ratio) is at: https://youtu.be/o3QBgkQi_HA More links & stuff in full description below ↓↓↓ Zvezda's Numberphile playlist: http://bit.ly/zvezda_videos Zvezda's webpage: https://math.berkeley.edu/~s
From playlist Women in Mathematics - Numberphile
Perspectives in Math and Art by Supurna Sinha
KAAPI WITH KURIOSITY PERSPECTIVES IN MATH AND ART SPEAKER: Supurna Sinha (Raman Research Institute, Bengaluru) WHEN: 4:00 pm to 5:30 pm Sunday, 24 April 2022 WHERE: Jawaharlal Nehru Planetarium, Bengaluru Abstract: The European renaissance saw the merging of mathematics and art in th
From playlist Kaapi With Kuriosity (A Monthly Public Lecture Series)
Lars Thorge Jensen: Cellularity of the p-Kazhdan-Lusztig Basis for Symmetric Groups
After recalling the most important results about Kazhdan-Lusztig cells for symmetric groups, I will introduce the p-Kazhdan-Lusztig basis and give a complete description of p-cells for symmetric groups. After that I will mention important consequences of the Perron-Frobenius theorem for p-
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
D. Loughran - Sieving rational points on algebraic varieties
Sieves are an important tool in analytic number theory. In a typical sieve problem, one is given a list of p-adic conditions for all primes p, and the challenge is to count the number of integers which satisfy all these p-adic conditions. In this talk we present some versions of sieves for
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Lie derivative pt. 2: Properties and general tensors
Part 1: https://youtu.be/vFsqbsRl_K0 Updated version with the sign error fixed (sort of). The previous version of this video contained an ugly sign error as pointed out by Magist. It should now be clear what the correct sign is. Unfortunately, I also had to cut out part of the video becau
From playlist Lie derivative