RA1.1. Real Analysis: Introduction
Real Analysis: We introduce some notions important to real analysis, in particular, the relationship between the rational and real numbers. Prerequisites may be found in the Math Major Basics playlist.
From playlist Real Analysis
Real Analysis Chapter 1: The Axiom of Completeness
Welcome to the next part of my series on Real Analysis! Today we're covering the Axiom of Completeness, which is what opens the door for us to explore the wonderful world of the real number line, as it distinguishes the set of real numbers from that of the rational numbers. It allows us
From playlist Real Analysis
Real Analysis - Part 1 - Numbers
Here, I present the first video in my Real Analysis series. It is all about numbers by showing the path to the real numbers, which we will need in this course. I explain the natural numbers, the integers and the rational numbers. I apologise for my pronunciation. The focus is on the math
From playlist Real Analysis (English)
Real Analysis | The Supremum and Completeness of ℝ
We look at the notions of upper and lower bounds as well as least upper bounds and greatest lower bounds of sets of real numbers. We also prove an important classification lemma of least upper bounds. Finally, the completeness axiom of the real numbers is presented. Please Subscribe: ht
From playlist Real Analysis
What are complex numbers? | Essence of complex analysis #2
A complete guide to the basics of complex numbers. Feel free to pause and catch a breath if you feel like it - it's meant to be a crash course! Complex numbers are useful in basically all sorts of applications, because even in the real world, making things complex sometimes, oxymoronicall
From playlist Essence of complex analysis
The deep structure of the rational numbers | Real numbers and limits Math Foundations 95
The rational numbers deserve a lot of attention, as they are the heart of mathematics. I am hopeful that modern mathematics will (slowly) swing around to the crucial realization that a lot of things which are currently framed in terms of "real numbers" are more properly understood in terms
From playlist Math Foundations
Real Analysis: Noting that we assume only naive set theory and basic properties of the natural numbers for this playlist, we give a brief account of some issues in the quest for mathematical rigor. These include the Axiom of Choice, the Law of the Excluded Middle, and Godel's Incompleten
From playlist Real Analysis
The mostly absent theory of real numbers|Real numbers + limits Math Foundations 115 | N J Wildberger
In this video we ask the question: how do standard treatments of calculus and analysis deal with the vexatious issue of defining real numbers and their supposed arithmetic?? We pull out a selection of popular Calculus and Analysis texts, and go through them with a view of finding out: wha
From playlist Math Foundations
Jonathan Hickman: The helical maximal function
The circular maximal function is a singular variant of the familiar Hardy--Littlewood maximal function. Rather than take maximal averages over concentric balls, we take maximal averages over concentric circles in the plane. The study of this operator is closely related to certain GMT packi
From playlist Seminar Series "Harmonic Analysis from the Edge"
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
Real Analysis | The countability of the rational numbers.
We present a proof of the countability of the rational numbers. Our approach is to represent the set of rational numbers as a countable union of disjoint finite sets. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.ne
From playlist Real Analysis
Hardy-Littlewood and Chowla Type Conjectures in the Presence of a Siegel Zero - Terence Tao
Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory Topic: Hardy-Littlewood and Chowla Type Conjectures in the Presence of a Siegel Zero Speaker: Terence Tao Affiliation: Member, School of Mathematics Date: February 27 2023 We discuss some consequences of the existen
From playlist Mathematics
[BOURBAKI 2017] 17/06/2017 - 2/4 - Lillian PIERCE
The Vinogradov Mean Value Theorem [after Bourgain, Demeter and Guth, and Wooley] ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://twitter.com/InHe
From playlist BOURBAKI - 2017
Opening Remarks and History of the math talks - Peter Sarnak, Hugh Montgomery and Jon Keating
50 Years of Number Theory and Random Matrix Theory Conference Topic: Opening Remarks and History of the math talks Speakers: Peter Sarnak, Hugh Montgomery and Jon Keating Date: June 21 2022
From playlist Mathematics
A New Approach to the Inverse Littlewood-Offord Problem - Hoi H. Nguyen
Hoi H. Nguyen Rutgers, The State University of New Jersey February 1, 2010 Let η1, . . . , ηn be iid Bernoulli random variables, taking values 1, −1 with probability 1/2. Given a multiset V of n integers v1, . . . , vn, we define the concentration probability as ρ(V ) := supx P(v1η1 + · ·
From playlist Mathematics
From playlist Contributed talks One World Symposium 2020
8ECM Invited Lecture: Rupert Frank
From playlist 8ECM Invited Lectures
Gérard Kerkyacharian: Wavelet: from statistic to geometry
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 30 years of wavelets
Neighborhood of a Point in Real Analysis | Real Analysis
What is an epsilon neighborhood of a point in real analysis? We introduce the definition of the neighborhood of a point and show how the definition of the limit of a sequence can be rewritten in terms of neighborhoods. The concept of a neighborhood is important, so it's handy to have this
From playlist Real Analysis
Kannan Soundararajan - Selberg's Contributions to the Theory of Riemann Zeta Function [2008]
http://www.ams.org/notices/200906/rtx090600692p-corrected.pdf January 11, 2008 3:00 PM Peter Goddard, Director Welcome Kannan Soundararajan Selberg's Contributions to the Theory of Riemann Zeta Function and Dirichlet L-Functions Atle Selberg Memorial Memorial Program in Honor of His
From playlist Number Theory