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
This lecture is part of an online course on rings and modules. We continue the previous lecture on complete rings by discussing Hensel's lemma for finding roots of polynomials over p-adic rings or over power series rings. We sketch two proofs, by slowly improving a root one digit at a tim
From playlist Rings and modules
In this video, I prove the famous Riemann-Lebesgue lemma, which states that the Fourier transform of an integrable function must go to 0 as |z| goes to infinity. This is one of the results where the proof is more important than the theorem, because it's a very classical Lebesgue integral
From playlist Real Analysis
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
Anthony Licata: Hilbert Schemes Lecture 7
SMRI Seminar Series: 'Hilbert Schemes' Lecture 7 Kleinian singularities 2 Anthony Licata (Australian National University) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students inter
From playlist SMRI Course: Hilbert Schemes
This lecture is part of an online course on rings and modules. We prove Hilbert's theorem that poynomial rings over fields are Noetherian, and use this to prove Hilbert's theorem about finite generation of algebras of invariants, at least for finite groups over the complex numbers. For
From playlist Rings and modules
Algebraic geometry 49: Hilbert polynomials
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a review of the Hilbert polynomial of a graded module over a graded ring, and classifies integer-valued polynomials.
From playlist Algebraic geometry I: Varieties
Commutative algebra 57: Krull versus Hilbert
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We continue the previous video by showing that the Krull dimension of a Noetherian local ring is at most the dimension defined
From playlist Commutative algebra
Galois theory: Hilbert's theorem 90
This lecture is part of an online graduate course on Galois theory. We discuss two forms of Hilbert's theorem 90: the original version for cyclic extensions, and Noether's more general version for arbitrary finite Galois extensions. The proofs use a lemma of Artin about the linear indepen
From playlist Galois theory
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 10) by Dror Varolin
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/2toQ.
From playlist 3D printing
Singular Learning Theory - Seminar 4 - From analytic to algebraic I
This seminar series is an introduction to Watanabe's Singular Learning Theory, a theory about algebraic geometry and statistical learning theory. In this seminar Spencer Wong gives the first of a series of talks about how the analytic function at the heart of singular learning theory (the
From playlist Metauni
Anthony Henderson: Hilbert Schemes Lecture 1
SMRI Seminar Series: 'Hilbert Schemes' Lecture 1 Introduction Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested in representa
From playlist SMRI Course: Hilbert Schemes
Wolfram Physics Project: Working Session Nov. 9, 2021 [Implementing Metamathematical Processes]
This is a Wolfram Physics Project working session on metamathematics in the Wolfram Model. 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 announcement post: http://wolfr.am/
From playlist Wolfram Physics Project Livestream Archive
Background material on the Cauchy-Riemann equations (Lecture 1) by Debraj Chakrabarti
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
MAST30026 Lecture 21: Coordinates in Hilbert space (Part 2)
I completed the proof that the complex exponential functions e^{in\theta} form an orthonormal family spanning a dense subspace of the L^2 space of the circle, and then developed enough of the abstract theory of orthonormal bases to prove that every vector in that L^2 space can be written a
From playlist MAST30026 Metric and Hilbert spaces
Classifies operators on the exterior algebra in terms of creation and annihilation operators, and develops the basics of entanglement in Hilbert spaces. This video is a recording made in a virtual world (https://www.roblox.com/games/6461013759/metauni-Locus-LC001) of a talking board, and
From playlist Metauni
Anthony Henderson: Hilbert Schemes Lecture 2
SMRI Seminar Series: 'Hilbert Schemes' Lecture 2 H is smooth Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested in representat
From playlist SMRI Course: Hilbert Schemes
MAST30026 Lecture 22: Urysohn's lemma
I gave the proof of Urysohn's lemma and briefly elaborated some of its important consequences. Given a pair of closed disjoint subsets of a normal topological space, the lemma asserts the existence of a real-valued continuous function on the space which takes the value 0 on the first close
From playlist MAST30026 Metric and Hilbert spaces