Gaussian Integral 8 Original Way
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I present the classical way using polar coordinates, the one that Laplace original
From playlist Gaussian Integral
Gaussian Integral 7 Wallis Way
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using a technique that is very similar to the
From playlist Gaussian Integral
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using a Fubini-type argument, namely by calcu
From playlist Gaussian Integral
Number Theorem | Gauss' Theorem
We prove Gauss's Theorem. That is, we prove that the sum of values of the Euler phi function over divisors of n is equal to n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Number Theory
Gaussian Integral 6 Gamma Function
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I calculate the Gaussian integral by using properties of the gamma function, which
From playlist Gaussian Integral
Gaussian Integral 9 Stirling Way
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I use Stirling's formula to 'prove' the Gaussian integral, namely I show that in t
From playlist Gaussian Integral
Here I evaluate the Gaussian Integral in under a minute. This is a must-see for calculus lovers! Gaussian Integral: https://youtu.be/kpmRS4s6ZR4 Gaussian Integral Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCgLyHWMXGZnioRHLqOk2bW Subscribe to my channel: https://youtube.co
From playlist Gaussian Integral
(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
Quantum Integral. Gauss would be proud! I calculate the integral of x^2n e^-x^2 from -infinity to infinity, using Feynman's technique, as well as the Gaussian integral and differentiation. This integral appears over and over again in quantum mechanics and is useful for calculus and physics
From playlist Integrals
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
Introduction to number theory lecture 34. Gauss sums
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 Gauss sums and use them to give another proof of the law of quadratic reciprocity
From playlist Introduction to number theory (Berkeley Math 115)
Lecture 16: Discrete Curvature I (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
8ECM Invited Lecture: Emmanuel Kowalski
From playlist 8ECM Invited Lectures
Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 3
Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of
From playlist Hypergeometric Functions, Character Sums and Applications
Jeff Erickson - Lecture 1 - Two-dimensional computational topology - 18/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Jeff Erickson (University of Illinois at Urbana-Champaign, USA) Two-dimensional computational topology - Lecture 1 Abstract: This series of lectures will describe recent
From playlist Jeff Erickson - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
Lecture 17: Discrete Curvature II (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
But what is a neural network REALLY? #SoME2
My submission for 2022 #SoME2. In this video I try to explain what a neural network is in the simplest way possible. That means no linear algebra, no calculus, and definitely no statistics. The aim is to be accessible to absolutely anyone. 00:00 Intro 00:47 Gauss & Parametric Regression 0
From playlist Summer of Math Exposition 2 videos
Weil conjectures 4 Fermat hypersurfaces
This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T
From playlist Algebraic geometry: extra topics
The Riemann Hypothesis, Explained
The Riemann hypothesis is the most notorious unsolved problem in all of mathematics. Ever since it was first proposed by Bernhard Riemann in 1859, the conjecture has maintained the status of the "Holy Grail" of mathematics. In fact, the person who solves it will win a $1 million prize from
From playlist Explainers
(PP 6.10) Sum of independent Gaussians
A sum of independent (multivariate) Gaussians is (multivariate) Gaussian, with mean equal to the sum of the means, and covariance equal to the sum of the covariances.
From playlist Probability Theory