An introduction to Legendre Polynomials and the Legendre-Fourier Series.
From playlist Mathematical Physics II Uploads
An example of expanding a function in a Legendre-Fourier Series.
From playlist Mathematical Physics II Uploads
In this video I derive three series representations for Legendre Polynomials. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F
From playlist Fourier
In this video I briefly introduce Legendre Polynomials via the Rodrigues formula. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F
From playlist Fourier
Legendre's Formula and prove that the product of n consecutive integers is divisible by n factorial
We prove a common fact in number theory: the product of n consecutive integers is divisible by n factorial Reference: 1. p-adic valuation https://en.wikipedia.org/wiki/P-adic_valuation 2. Legendre Formula for p-adic valuation for n factorial: https://en.wikipedia.org/wiki/Legendre%27s_f
From playlist Elementary Number Theory
Theory of numbers: Jacobi symbol
This lecture is part of an online undergraduate course on the theory of numbers. We define the Jacobi symbol as an extension of the Legendre symbol, and show how to use it to calculate the Legendre symbol fast. We also briefly mention the Kronecker symbol. For the other lectures in t
From playlist Theory of numbers
Proof of Multiplication Rule for Legendre Symbol
Proof that quadratic residues always have even index: https://youtu.be/zs0ZtQzVBSE Intro to indices: https://youtu.be/jLeNX2jYuUs One of the most important properties of the Legendre symbol is that we can split up the Legendre symbol of a product. Using the power of indices, we can easi
From playlist Quadratic Residues
Legendre Symbol Definition and Example
Intro to quadratic residues: https://youtu.be/M6gDsFhQugM The Legendre symbol is a useful notation for describing whether a number is a quadratic residue mod p. Here we explain what the Legendre symbol is and do a practice example with quadratic residues mod 5. Quadratic Residues playli
From playlist Quadratic Residues
Introduction to number theory lecture 32. Calculation of the Legendre symbol
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We use Gauss's lemma to find out when -2, 3, 5, are quadratic residues of a prime and give
From playlist Introduction to number theory (Berkeley Math 115)
[Lesson 25] QED Prerequisites Scattering 2
We follow the derivation of the associated Legendre polynomials using the reference "The Functions of Mathematical Physics" by Harry Hochstadt as our guide. The goal is to take ownership of these functions so we can confidently advance our understanding of the partial wave expansion of pla
From playlist QED- Prerequisite Topics
"How to Verify the Riemann Hypothesis for the First 1,000 Zeta Zeros" by Ghaith Hiary
An overview of algorithms and methods that mathematicians in the 19th century and the first half of the 20th century used to verify the Riemann hypothesis. The resulting numerical computations, which used hand calculations and mechanical calculators, include those by Gram, Lindelöf, Backlu
From playlist Number Theory Research Unit at CAMS - AUB
Why did they prove this amazing theorem in 200 different ways? Quadratic Reciprocity MASTERCLASS
The longest Mathologer video ever, just shy of an hour (eventually it's going to happen :) One video I've been meaning to make for a long, long time. A Mathologerization of the Law of Quadratic Reciprocity. This is another one of my MASTERCLASS videos. The slide show consists of 550 slides
From playlist Recent videos
Theory of numbers: Quadratic reciprocity
This lecture is part of an online undergraduate course on the theory of numbers. We state and law of quadratic reciprocity for Legendre symbols, and prove it using Gauss sums. As applications we show how to use it to calculate Legendre symbols and to test Fermat numbers to see if they are
From playlist Theory of numbers
Advice for Research Maths | Properties of Legendre and Gegenbauer polynomials | Wild Egg Maths
To try to understand how to apply two dimensional maxel magic to the family of Legendre polynomials, let's look at some properties of these polynumbers, including differential equations, connections with Chebyshev polynomials, and how they arise from the geometry of the sphere and an assoc
From playlist Maxel inverses and orthogonal polynomials (non-Members)
Gaussian Quadrature | Lecture 40 | Numerical Methods for Engineers
An explanation of Gaussian quadrature. An example of how to calculate the weights and nodes for two-point Legendre-Gauss quadrature. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engi
From playlist Numerical Methods for Engineers
Introduction to number theory lecture 35 Jacobi symbol
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We define the Jacobi symbol and prove its basic properties, and show how to calculate it fa
From playlist Introduction to number theory (Berkeley Math 115)
Augmentations, generating families and micro local sheaves by Michael G Sullivan
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
De Moivre's formula: a COOL proof
A quick way of proving De Moivre's formula! Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook Hi again everyone, Chris Tisdell here again. In this presentation I am going to continue my series of videos on complex numbers. In particular, in this presentation, I am g
From playlist Intro to Complex Numbers