Squares in number theory | Theorems in number theory
Jacobi's four-square theorem gives a formula for the number of ways that a given positive integer n can be represented as the sum of four squares. (Wikipedia).
Gentle example showing how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.
From playlist Multivariable calculus
Example discussing the Chain Rule for the Jacobian matrix. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
Jacobian chain rule and inverse function theorem
A lecture that discusses: the general chain rule for the Jacobian derivative; and the inverse function theorem. The concepts are illustrated via examples and are seen in university mathematics.
From playlist Several Variable Calculus / Vector Calculus
This video explains how to calculator a Jacobian for a change of variables.
From playlist Applications of Double Integrals: Mass, Center of Mass, Jacobian
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
Wronskian for {e^{3x}, e^{-x}, 2}
ODEs: Show that the set of functions {e^{3x}, e^{-x}, 2} is a linearly independent set. These functions are in the solution space of y''' -2y'' - 3y' = 0. We show linear independence by computing the Wronskian of the set. We also show linear independence by solving a system of linea
From playlist Differential Equations
Intro to Jacobian + differentiability
A lecture that introduces the Jacobian matrix and its determinant. Such ideas may be thought of as a general derivative of a vector-valued function of many variables and find uses in integration theory.
From playlist Several Variable Calculus / Vector Calculus
Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist Computer - Cryptography and Network Security
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)
CMPSC/Math 451. March 23, 2015. Error analysis of iterative methods. Least squares. Wen Shen
Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I
From playlist Numerical Computation spring 2015. Wen Shen. Penn State University.
8ECM Invited Lecture: Emmanuel Kowalski
From playlist 8ECM Invited Lectures
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
Colloquium MathAlp 2019 - Richard Montgomery
Oscillating about coplanarity in the 4 body problem For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known res
From playlist Colloquiums MathAlp
Boris Pioline : A string theorist view point on the genus-two Kawazumi-Zhang invariant
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Number Theory
Central Limit Theorems for linear statistics for biorthogonal ensembles - Maurice Duits
Maurice Duits SU April 2, 2014 For more videos, visit http://video.ias.edu
From playlist Mathematics
Introduction to Modular Forms - Part 5 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 Theo
From playlist CTNT 2016 - "Introduction to Modular Forms" by Keith Conrad
Rob Kusner: Willmore stability and conformal rigidity of minimal surfaces in S^n
A minimal surface M in the round sphere S^n is critical for area, as well as for the Willmore bending energy W=∫∫(1+H^2)da. Willmore stability of M is equivalent to a gap between −2 and 0 in its area-Jacobi operator spectrum. We show the W-stability of M persists in all higher dimensional
From playlist Geometry
Ex: Solve a Bernoulli Differential Equation Using Separation of Variables
This video explains how to solve a Bernoulli differential equation. http://mathispower4u.com
From playlist Bernoulli Differential Equations