Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
Central Limit Theorem: Verification using Poisson Distribution with Lambda = 1
This script is to verify the Central Limit Theorem in probability theory or statistics. The Central Limit Theorem states that, regardless of the distribution of the population, the sampling distribution of the sample means, assuming all samples are identical in size, will approach a norma
From playlist Probability Theory/Statistics
Projection Theorem | Special Case of the Wigner–Eckart Theorem
The projection theorem is a special case of the Wigner–Eckart theorem, which generally involves spherical tensor operators. If we consider one example of a spherical tensor operator, a rank-1 spherical tensor, we can derive a powerful theorem, which states that expectation values of vector
From playlist Quantum Mechanics, Quantum Field Theory
In this video, I present another example of Stokes theorem, this time using it to calculate the line integral of a vector field. It is a very useful theorem that arises a lot in physics, for example in Maxwell's equations. Other Stokes Example: https://youtu.be/-fYbBSiqvUw Yet another Sto
From playlist Vector Calculus
Central Limit Theorem: Verification using Geometric Distribution with p = 0.8
This script is to verify the Central Limit Theorem in probability theory or statistics. The Central Limit Theorem states that, regardless of the distribution of the population, the sampling distribution of the sample means, assuming all samples are identical in size, will approach a norma
From playlist Probability Theory/Statistics
What is Stokes theorem? - Formula and examples
► My Vectors course: https://www.kristakingmath.com/vectors-course Where Green's theorem is a two-dimensional theorem that relates a line integral to the region it surrounds, Stokes theorem is a three-dimensional version relating a line integral to the surface it surrounds. For that reaso
From playlist Vectors
(PP 6.3) Gaussian coordinates does not imply (multivariate) Gaussian
An example illustrating the fact that a vector of Gaussian random variables is not necessarily (multivariate) Gaussian.
From playlist Probability Theory
Divergence Theorem. In this video, I give an example of the divergence theorem, also known as the Gauss-Green theorem, which helps us simplify surface integrals tremendously. It's, in my opinion, the most important theorem in multivariable calculus. It is also extremely useful in physics,
From playlist Vector Calculus
Harold Stark - The origins of conjectures on derivatives of L-functions at s=0 [1990’s]
slides for this talk: http://www.msri.org/realvideo/ln/msri/2001/rankin-L/stark/1/banner/01.html The origins of conjectures on derivatives of L-functions at s=0 Harold Stark http://www.msri.org/realvideo/ln/msri/2001/rankin-L/stark/1/index.html
From playlist Number Theory
A crash course in Algebraic Number Theory
A quick proof of the Prime Ideal Theorem (algebraic analog of the Prime Number Theorem) is presented. In algebraic number theory, the prime ideal theorem is the number field generalization of the prime number theorem. It provides an asymptotic formula for counting the number of prime idea
From playlist Number Theory
Proof - The Chain Rule of Differentiation
This video proves the chain rule of differentiation. http://mathispower4u.com
From playlist Calculus Proofs
optimization and Tropical Combinatorics (Lecture 3) by Michael Joswig
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study of
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Galois theory: Infinite Galois extensions
This lecture is part of an online graduate course on Galois theory. We show how to extend Galois theory to infinite Galois extensions. The main difference is that the Galois group has a topology, and intermediate field extensions now correspond to closed subgroups of the Galois group. We
From playlist Galois theory
Andrew Wiles: Fermat's Last theorem: abelian and non-abelian approaches
The successful approach to solving Fermat's problem reflects a move in number theory from abelian to non-abelian arithmetic. This lecture was held by Abel Laurate Sir Andrew Wiles at The University of Oslo, May 25, 2016 and was part of the Abel Prize Lectures in connection with the Abel P
From playlist Sir Andrew J. Wiles
Kevin Buzzard (lecture 1/20) Automorphic Forms And The Langlands Program [2017]
Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w
From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]
John Coates: (1/4) Classical algebraic Iwasawa theory [AWS 2018]
slides for this lecture: http://swc-alpha.math.arizona.edu/video/2018/2018CoatesLecture1Slides.pdf lecture notes: http://swc.math.arizona.edu/aws/2018/2018CoatesNotes.pdf CLASSICAL ALGEBRAIC IWASAWA THEORY. JOHN COATES If one wants to learn Iwasawa theory, the starting point has to be t
From playlist Number Theory
Hao Shen (Wisconsin) -- Stochastic quantization, large N, and mean field limit
We study "large N problems” in quantum field theory using SPDE methods via stochastic quantization. In the SPDE setting this is formulated as mean field problems. We will consider the vector Phi^4 model (i.e. linear sigma model), whose stochastic quantization is a system of N coupled dynam
From playlist Columbia Probability Seminar
An explanation of Stokes' theorem or Green's theorem in 3-space.
From playlist Advanced Calculus / Multivariable Calculus
16. Weber on Protestantism and Capitalism
Foundations of Modern Social Thought (SOCY 151) Max Weber wrote his best-known work after he recovered from a period of serious mental illness near the turn of the twentieth century. After he recovered, his work transitioned from enthusiastically capitalist and liberal in the tradition o
From playlist Foundations of Modern Social Theory with Iván Szelényi