Probability Distribution Functions
We explore the idea of continuous probability density functions in a classical context, with a ball bouncing around in a box, as a preparation for the study of wavefunctions in quantum mechanics.
From playlist Quantum Mechanics Uploads
Calculus - Find the limit of a function using epsilon and delta
This video shows how to use epsilon and delta to prove that the limit of a function is a certain value. This particular video uses a linear function to highlight the process and make it easier to understand. Later videos take care of more complicated functions and using epsilon and delta
From playlist Calculus
Limit Theories and Higher Order Fourier Analysis - Balazs Szegedy
Balazs Szegedy University of Toronto; Member, School of Mathematics October 4, 2011 We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large comp
From playlist Mathematics
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
Math 031 030317 Properties of Limits of Sequences
Example of proving a limit exists. Useful properties of limits of sequences: "limits and arithmetic", examples; "squeeze theorem", examples. Limits of sequences related to continuous functions (using L'Hopital's Rule), example.
From playlist Course 3: Calculus II (Spring 2017)
Limit Theories and Higher Order Fourier Analysis - Balazs Szegedy
Balazs Szegedy University of Toronto; Member, School of Mathematics October 11, 2011 We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large com
From playlist Mathematics
Christian Lehn (3/26/19): Limit theorems in topological data analysis
Title: Limit theorems in topological data analysis Abstract: In a joint work with S. Kališnik Verošek and V. Limic we generalize the notion of barcodes in topological data analysis in order to prove limit theorems for point clouds sampled from an unknown distribution as the number of poin
From playlist AATRN 2019
Random variables, means, variance and standard deviations | Probability and Statistics
We introduce the idea of a random variable X: a function on a probability space. Associated to such a function is something called a probability distribution, which assigns probabilities, say p_1,p_2,...,p_n to the various possible values of X, say x_1,x_2,...,x_n. The probabilities p_i h
From playlist Probability and Statistics: an introduction
Rapid and Accurate Reachability Analysis for Nonlinear Systems by Exploiting Model Redundancy
From playlist Spring 2019 Kolchin Seminar
Probability Distribution Functions and Cumulative Distribution Functions
In this video we discuss the concept of probability distributions. These commonly take one of two forms, either the probability distribution function, f(x), or the cumulative distribution function, F(x). We examine both discrete and continuous versions of both functions and illustrate th
From playlist Probability
Sarah Peluse: Bounds for subsets of 𝔽_p^n×𝔽_p^n without L’s
I will discuss the difficult problem of proving reasonable bounds in the multidimensional generalization of Szemer\’edi’s theorem, and describe a proof for such bounds for sets lacking nontrivial configurations of the form (x,y),(x,y+z),(x,y+2z),(x+z,y)
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
A stationary set method for estimating oscillatory integrals - Ruixiang Zhang
Analysis Seminar Topic: A stationary set method for estimating oscillatory integrals Speaker: Ruixiang Zhang Affiliation: University of Wisconsin-Madison; Member, School of Mathematics Date: March 22, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
2020.06.25 A. Teixeira - Random walks on dynamical random environments with non-uniform mixing (1/2)
In these two consecutive talks we will discuss recent results on the limiting behavior of random walks on dynamical random environments. The strength of these results depends a great deal on space-time mixing properties imposed to the environment but also on other features like the dimensi
From playlist One World Probability Seminar
Ruixiang Zhang (IAS): A stationary set method for estimating oscillatory integrals
In this talk, I will introduce a "stationary set" method that gives an upper bound with simple geometric meaning. The proof of this bound mainly relies on the theory of o-minimal structures. As an application of our bound, we obtain the sharp convergence exponent in the two dimensional Tar
From playlist Seminar Series "Harmonic Analysis from the Edge"
Ofer Zeitouni: Large Deviations at Work
This lecture was held at The University of Oslo, May 24, 2007 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2007 1. “A Short History of Large Deviations” by Srinivasa Varadhan, Abel Laureate 2007, Courant I
From playlist Abel Lectures
Diffuse Decompositions of Polynomials - Daniel Kane
Daniel Kane Stanford University April 22, 2013 We study some problems relating to polynomials evaluated either at random Gaussian or random Bernoulli inputs. We present some new work on a structure theorem for degree-d polynomials with Gaussian inputs. In particular, if p is a given degree
From playlist Mathematics
The moment-SOS hierarchy – Jean Lasserre – ICM2018
Control Theory and Optimization Invited Lecture 16.2 The moment-SOS hierarchy Jean Lasserre Abstract: The Moment-SOS hierarchy initially introduced in optimization in 2000, is based on the theory of the K-moment problem and its dual counterpart, polynomials that are positive on K. It tur
From playlist Control Theory and Optimization
Data Science - Part X - Time Series Forecasting
For downloadable versions of these lectures, please go to the following link: http://www.slideshare.net/DerekKane/presentations https://github.com/DerekKane/YouTube-Tutorials This lecture provides an overview of Time Series forecasting techniques and the process of creating effective for
From playlist Data Science
This calculus 2 video tutorial provides a basic introduction into probability density functions. It explains how to find the probability that a continuous random variable such as x in somewhere between two values by evaluating the definite integral from a to b. The probability is equival
From playlist New Calculus Video Playlist
Super-approximation II - Alireza Salehi Golsefidy
Speaker: Alireza Salehi Golsefidy (UCSD) Title: Super-approximation II I will explain the Bourgain-Gamburd method of proving spectral gap. The spirit of this method is behind all the recent results on this subject. Very roughly it says in order to prove spectral gap it is enough to sh
From playlist Mathematics