In mathematics, Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions about the integers and integer-valued functions. One basic idea underlying it is that different prime numbers are, in some serious sense, like independent random variables. This however is not an idea that has a unique useful formal expression. The founders of the theory were Paul Erdős, Aurel Wintner and Mark Kac during the 1930s, one of the periods of investigation in analytic number theory. Foundational results include the and the Erdős–Kac theorem on additive functions. (Wikipedia).
Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
The Prime Number Theorem, an introduction ← Number Theory
An introduction to the meaning and history of the prime number theorem - a fundamental result from analytic number theory. Narrated by Cissy Jones Artwork by Kim Parkhurst, Katrina de Dios and Olga Reukova Written & Produced by Michael Harrison & Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways t
From playlist Number Theory
Prove that there is a prime number between n and n!
A simple number theory proof problem regarding prime number distribution: Prove that there is a prime number between n and n! Please Like, Share and Subscribe!
From playlist Elementary Number Theory
Intro to Number Theory and The Divisibility Relation
This video introduces the divisibility relation and provided several examples. mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)
Introduction to number theory lecture 43 Gaussian integers
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 give some applications of Gaussian integers to the binary quadratic form x^2+y^2. The t
From playlist Introduction to number theory (Berkeley Math 115)
Abundant, Deficient, and Perfect Numbers ← number theory ← axioms
Integers vary wildly in how "divisible" they are. One way to measure divisibility is to add all the divisors. This leads to 3 categories of whole numbers: abundant, deficient, and perfect numbers. We show there are an infinite number of abundant and deficient numbers, and then talk abou
From playlist Number Theory
Theory of numbers:Introduction
This lecture is part of an online undergraduate course on the theory of numbers. This is the introductory lecture, which gives an informal survey of some of the topics to be covered in the course, such as Diophantine equations, quadratic reciprocity, and binary quadratic forms.
From playlist Theory of numbers
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
Seminar In the Analysis and Methods of PDE (SIAM PDE): Andrea R. Nahmod
Title: Gibbs measures and propagation of randomness under the flow of nonlinear dispersive PDE Date: Thursday, May 5, 2022, 11:30 am EDT Speaker: Andrea R. Nahmod, University of Massachusetts Amherst The COVID-19 pandemic and consequent social distancing call for online venues of research
From playlist Seminar In the Analysis and Methods of PDE (SIAM PDE)
Semantic models for higher-order Bayesian inference - Sam Staton, University of Oxford
In this talk I will discuss probabilistic programming as a method of Bayesian modelling and inference, with a focus on fully featured probabilistic programming languages with higher order functions, soft constraints, and continuous distributions. These languages are pushing the limits of e
From playlist Logic and learning workshop
Number Theory 2.1 : Prime Number Theorem Introduction (PNT 1/5)
In this video, I introduce the idea of the prime number theorem and how one might go about proving it. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Number Theory
Probability theory and AI | The Royal Society
Join Professor Zoubin Ghahramani to explore the foundations of probabilistic AI and how it relates to deep learning. 🔔Subscribe to our channel for exciting science videos and live events, many hosted by Brian Cox, our Professor for Public Engagement: https://bit.ly/3fQIFXB #Probability #A
From playlist Latest talks and lectures
Probabilistic logic programming and its applications - Luc De Raedt, Leuven
Probabilistic programs combine the power of programming languages with that of probabilistic graphical models. There has been a lot of progress in this paradigm over the past twenty years. This talk will introduce probabilistic logic programming languages, which are based on Sato's distrib
From playlist Logic and learning workshop
Stanford EE104: Introduction to Machine Learning | 2020 | Lecture 16 - probabilistic classification
Professor Sanjay Lall Electrical Engineering To follow along with the course schedule and syllabus, visit: http://ee104.stanford.edu To view all online courses and programs offered by Stanford, visit: https://online.stanford.edu/
From playlist Stanford EE104: Introduction to Machine Learning Full Course
6th HLF – Lecture: Gregory Margulis
Gregory Margulis: "On the early history of expanders" The notion of an expander was introduced in early nineteen seventies by M.S.Pinsker in his work on the complexity of a concentrator. In recent decades the theory of expanders attracted a lot of attention and became a rather big industr
From playlist Related videos on other channels
Total Functions in the Polynomial Hierarchy - Robert Kleinberg
Computer Science/Discrete Mathematics Seminar I Topic: Total Functions in the Polynomial Hierarchy Speaker: Robert Kleinberg Affiliation: Cornell University Date: February 08, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Probabilistic Graphical Models (PGMs) In Python | Graphical Models Tutorial | Edureka
🔥 Post Graduate Diploma in Artificial Intelligence by E&ICT Academy NIT Warangal: https://www.edureka.co/executive-programs/machine-learning-and-ai This Edureka "Graphical Models" video answers the question "Why do we need Probabilistic Graphical Models?" and how are they compare to Neural
From playlist Machine Learning Algorithms in Python (With Demo) | Edureka
Theory of numbers: Multiplicative functions
This lecture is part of an online undergraduate course on the theory of numbers. Multiplicative functions are functions such that f(mn)=f(m)f(n) whenever m and n are coprime. We discuss some examples, such as the number of divisors, the sum of the divisors, and Euler's totient function.
From playlist Theory of numbers
Probabilistic conformal block and its semi-classical limit - Promit Ghosal
Probability Seminar Topic: Probabilistic conformal block and its semi-classical limit Speaker: Promit Ghosal Affiliation: Massachusetts Institute of Technology Date: September 09, 2022 Conformal blocks are fundamental objects in the conformal bootstrap program of 2D conformal field theor
From playlist Mathematics