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
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
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
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
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
This lecture is part of an online graduate course on Lie groups. We give an introductory survey of Lie groups theory by describing some examples of Lie groups in low dimensions. Some recommended books: Lie algebras and Lie groups by Serre (anything by Serre is well worth reading) Repre
From playlist Lie groups
Lie groups: Lie groups and Lie algebras
This lecture is part of an online graduate course on Lie groups. We discuss the relation between Lie groups and Lie algebras, and give several examples showing how they behave differently. Lie algebras turn out to correspond more closely to the simply connected Lie groups. We then explain
From playlist Lie groups
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Excel & Statistics 46: Chebyshev's Theorem
Download Excel Start File 1: https://people.highline.edu/mgirvin/AllClasses/210M/Content/ch03/Busn210ch03.xls Download Excel Finished File 1: https://people.highline.edu/mgirvin/AllClasses/210M/Content/ch03/Busn210ch03Finished.xls Download Excel Start File 2: https://people.highline.edu/mg
From playlist Excel 2007 Statistics: Charts, Functions, Formulas
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
Excel 2010 Statistics #31: z-Scores, Chebyshev's Theorem and Empirical Rule
Download Excel File #1: https://people.highline.edu/mgirvin/AllClasses/210Excel2010/Content/Ch03/Excel2010StatisticsCh03correct.xlsm Download Excel File #2: https://people.highline.edu/mgirvin/AllClasses/210Excel2010/Content/Ch03/Excel2010StatisticsCh03SecondFile.xlsm Download Excel File #
From playlist Excel 2010 Statistics Formulas Functions Charts PivotTables
Roger Heath-Brown: The Determinant Method, Lecture II
Lecture 1 will set the background for the course, describing the problem of counting rational points on algebraic varieties, the phenomena that can arise, and some of the results which have been proved. Lecture 2 will prove the basic theorem of the p-adic Determinant Method. Lecture 3 will
From playlist Harmonic Analysis and Analytic Number Theory
Proof: An Edge is a Bridge iff it Lies on No Cycles | Graph Theory
An edge of a graph is a bridge if and only if it lies on no cycles. We prove this characterization of graph bridges in today's graph theory lesson! My lesson on bridges: https://www.youtube.com/watch?v=zj_aFVuUATM Proof that a walk implies a path: https://www.youtube.com/watch?v=728bZWwT
From playlist Graph Theory
Recovering elliptic curves from their p-torsion - Benjamin Bakker
Benjamin Bakker New York University May 2, 2014 Given an elliptic curve EE over a field kk, its p-torsion EpEp gives a 2-dimensional representation of the Galois group GkGk over đť”˝pFp. The Frey-Mazur conjecture asserts that for k=â„šk=Q and p13p13, EE is in fact determined up to isogeny by th
From playlist Mathematics
The Polynomial Method and Applications From Finite Field Kakeya to Distinct Distances - Larry Guth
Larry Guth University of Toronto; Member, School of Mathematics April 22, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
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
Lie groups: Baker Campbell Hausdorff formula
This lecture is part of an online graduate course on Lie groups. We state the Baker Campbell Hausdorff formula for exp(A)exp(B). As applications we show that a Lie group is determined up to local isomorphism by its Lie algebra, and homomorphisms from a simply connected Lie group are deter
From playlist Lie groups
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)