(ML 7.7.A1) Dirichlet distribution
Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.
From playlist Machine Learning
Math 139 Fourier Analysis Lecture 38: Finishing proof of Dirichlet's theorem
Showing the non-vanishing of the L-function for real Dirichlet characters. Approximation of L(1,X) with hyperbolic sums to finish the theorem.
From playlist Course 8: Fourier Analysis
(ML 7.8) Dirichlet-Categorical model (part 2)
The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.
From playlist Machine Learning
Dirichlet Eta Function - Integral Representation
Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna
From playlist Integrals
(ML 7.7) Dirichlet-Categorical model (part 1)
The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.
From playlist Machine Learning
Large sieve inequalities for families of L-functions
50 Years of Number Theory and Random Matrix Theory Conference Topic: Large sieve inequalities for families of L-functions Speaker: Matt Young Affiliation: Texas A&M University Date: June 21, 2022 Large sieve inequalities are useful and flexible tools for understanding families of L-funct
From playlist Mathematics
What are Hyperbolas? | Ch 1, Hyperbolic Trigonometry
This is the first chapter in a series about hyperbolas from first principles, reimagining trigonometry using hyperbolas instead of circles. This first chapter defines hyperbolas and hyperbolic relationships and sets some foreshadowings for later chapters This is my completed submission t
From playlist Summer of Math Exposition 2 videos
Richard Pinch: Fermat's Last Theorem [1994]
Richard Pinch: Fermat's Last Theorem Based on the 1994 London Mathematical Society Popular Lectures, this special 'television lecture' entitled "Fermat's last theorem" is presented by Dr Richard Pinch. The London Mathematical Society is one of the oldest mathematical societies, founded i
From playlist Mathematics
[ANT07] Units and logarithm space (+ bonus theorems)
There are infinitely many units in Z[â2]. How can we write them down? How can we figure out their multiplicative structure? (Plus, now that we've come this far, a few theorems to make the link between this course and more traditional courses.)
From playlist [ANT] An unorthodox introduction to algebraic number theory
Terence Tao: Approximants for classical arithmetic functions
Terence Tao (University of California Los Angeles) 27 September 2021 ----------------------------------------------------------------------------------------------------------------------------------------------------- Number Theory Down Under 9 27 â 29 September 2021 Conference homepage:
From playlist Number Theory Down Under 9
COOL Dirichlet Integral. I calculate the integral of sin(x)/x from 0 to infinity using Feynman's technique and a cool and unexpected geometric series that involves differentiation and integration. Lots of multiples of pi involved. Related to the Fresnel integral. This method doesn't use an
From playlist Integrals
Calderon problem (Lecture 1) by Venkateswaran P Krishnan
DISCUSSION MEETING WORKSHOP ON INVERSE PROBLEMS AND RELATED TOPICS (ONLINE) ORGANIZERS: Rakesh (University of Delaware, USA) and Venkateswaran P Krishnan (TIFR-CAM, India) DATE: 25 October 2021 to 29 October 2021 VENUE: Online This week-long program will consist of several lectures by
From playlist Workshop on Inverse Problems and Related Topics (Online)
How to solve trigonometric equation with tangent
ð Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Taking the Square Root
How to find all the solutions to a trigonometric equation
ð Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Taking the Square Root
Farzana Nasrin (8/29/21): Random Persistence Diagram Generator
We will discuss in this talk a method of generating random persistence diagrams (RPDG). RPDG is underpinned (i) by a parametric model based on pairwise interacting point processes for inference of persistence diagrams (PDs) and (ii) by a reversible jump Markov chain Monte Carlo (RJ-MCMC) a
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
This talk by Unal Goktas presents an overview of solution methods for partial differential equations (PDEs) in the Wolfram Language. It covers not only the classical methods but also relatively modern approaches, as well as how to compute exact solutions for PDEs. The talk includes example
From playlist Wolfram Technology Conference 2020
Theory of numbers: Dirichlet series
This lecture is part of an online undergraduate course on the theory of numbers. We describe the correspondence between Dirichlet series and arithmetic functions, and work out the Dirichlet series of the arithmetic functions in the previous lecture. Correction: Dave Neary pointed out t
From playlist Theory of numbers
James Maynard: Half-isolated zeros and zero-density estimates
We introduce a new zero-detecting method which is sensitive to the vertical distribution of zeros of the zeta function. This allows us to show that there are few 'half-isolated' zeros, and allows us to improve the classical zero density result to N(Ï,T)âŠT24(1âÏ)/11+o(1) if we assume that t
From playlist Seminar Series "Harmonic Analysis from the Edge"
Halley's Method for Systems of Nonlinear Equations
Halley's Method for Solving Systems of Nonlinear Equations. Submission for The Summer of Math Exposition. Lesson includes motivation & explanation of notation, description of the method, numerical example, discussion of order, and comparison with the Method of Tangent Hyperbolas. Example c
From playlist Solving Systems of Nonlinear Equations
Solving a trigonometric equation on the interval of 0 and 2pi
ð Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Taking the Square Root