Infinite Sum for e -- without Calculus (just a few limits)
The number e can be expressed as an infinite sum of factorial recipriocals. You usually see this for the first time in Calculus I when studying Taylor Series. In this video, we derive that sum using only a few limits, starting with the limit definition of the logarithm.
From playlist e
Modular forms: Fourier coefficients of Eisenstein series
This lecture is part of an online graduate course on modular forms. We calculate the Fourier coefficients of the Eisenstein series introduced in the previous lecture, and use them to construct the elliptic modular function. (Minor typo: in the definition of E10 I wrote 262 instead of 26
From playlist Modular forms
logarithm of a matrix. I calculate ln of a matrix by finding the eigenvalues and eigenvectors of that matrix and by using diagonalization. It's a very powerful tool that allows us to find exponentials, sin, cos, and powers of a matrix and relates to Fibonacci numbers as well. This is a mus
From playlist Eigenvalues
Fourier's Proof that e is Irrational
Joseph Fourier created an accessible proof that e is an irrational number. Here it is. Life of Riley by Kevin MacLeod Link: https://incompetech.filmmusic.io/song/3976-life-of-riley License: https://filmmusic.io/standard-license
From playlist e
Modular forms: Eisenstein series
This lecture is part of an online graduate course on modular forms. We give two ways of looking at modular forms: as functions of lattices in C, or as invariant forms. We use this to give two different ways of constructing Eisenstein series. For the other lectures in the course see http
From playlist Modular forms
Square root of a matrix: definition and calculation using eigenvalues. What does it mean for a matrix to have a square root? Check out my Eigenvalues playlist: https://www.youtube.com/watch?v=H-NxPABQlxI&list=PLJb1qAQIrmmC72x-amTHgG-H_5S19jOSf Subscribe to my channel: https://www.youtube
From playlist Eigenvalues
Find an Eigenvalue Given Matrix A and a Eigenvector
This video explains how to find an eigenvalue given a matrix and an eigenvector.
From playlist Eigenvalues and Eigenvectors
Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (5 of 35) What is an Eigenvector?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and show (in general) what is and how to find an eigenvector. Next video in this series can be seen at: https://youtu.be/SGJHiuRb4_s
From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS
IWASAWA: Lecture 4 - Christopher Skinner
Christopher Skinner Princeton University; Member, School of Mathemtics February 23, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
William Duke - The distribution of modular closed geodesics revisited.
December 15, 2014 - Analysis, Spectra, and Number theory: A conference in honor of Peter Sarnak on his 61st birthday. (Joint with O. Imamoglu and A. Toth) I will describe some recent work on an apparently overlooked $PSL(2,\Z)$ equidistribution problem, namely that for positive fundament
From playlist Analysis, Spectra, and Number Theory - A Conference in Honor of Peter Sarnak on His 61st Birthday
Lynne Walling: Understanding quadratic forms on lattices through generalised theta series
Abstract: Siegel introduced generalised theta series to study representation numbers of quadratic forms. Given an integral lattice L with quadratic form q, Siegel’s degree n theta series attached to L has a Fourier expansion supported on n-dimensional lattices, with Fourier coefficients th
From playlist Women at CIRM
The Eisenstein Ideal and its Application to W. Stein’s Conjecture....by Kenneth A. Ribet
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
Eisenstein series and the cubic moment for PGL(2) - Paul Nelson
Joint IAS/Princeton University Number Theory Seminar Eisenstein series and the cubic moment for PGL(2) Speaker: Paul Nelson Affiliation: ETH Zürich Date: January 30, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Ken Ribet, Ogg's conjecture for J0(N)
VaNTAGe seminar, May 10, 2022 Licensce: CC-BY-NC-SA Links to some of the papers mentioned in the talk: Mazur: http://www.numdam.org/article/PMIHES_1977__47__33_0.pdf Ogg: https://eudml.org/doc/142069 Stein Thesis: https://wstein.org/thesis/ Stein Book: https://wstein.org/books/modform/s
From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)
Eisenstein Series on Exceptional Groups, Graviton Scattering Amplitudes... - Stephen Miller
Stephen D. Miller Rutgers, The State University of New Jersey May 3, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Valentin Blomer - 4/4 Automorphic forms in higher rank
Valentin Blomer - Automorphic forms in higher rank
From playlist École d'été 2014 - Théorie analytique des nombres
Johnathan Hanke - Computer-Assisted Proofs in the Arithmetic of Quadratic Forms - IPAM at UCLA
Recorded 17 February 2023. Johnathan Hanke of Princeton University presents "Computer-Assisted Proofs in the Arithmetic of Quadratic Forms" at IPAM's Machine Assisted Proofs Workshop. Abstract: Since its early history, the ideas and results in arithmetic of quadratic forms have been inspir
From playlist 2023 Machine Assisted Proofs Workshop
Introduction to Modular Forms - Part 3 of 8
“Introduction to Modular Forms,” by Keith Conrad. Topics include Eisenstein series and q-expansions, applications to sums of squares and zeta-values, Hecke operators, eigenforms, and the L-function of a modular form. This is a video from CTNT, the Connecticut Summer School in Number Theor
From playlist CTNT 2016 - "Introduction to Modular Forms" by Keith Conrad
Abstract Algebra | Eisenstein's criterion
We present a proof of Eisenstein's criterion along with some examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathematics/ Research Gate profile: htt
From playlist Abstract Algebra