Math 101 091517 Introduction to Analysis 07 Consequences of Completeness
Least upper bound axiom implies a "greatest lower bound 'axiom'": that any set bounded below has a greatest lower bound. Archimedean Property of R.
From playlist Course 6: Introduction to Analysis (Fall 2017)
Upper and Lower Bound In this video, I define what it means for a set to be bounded above and bounded below. This will be useful in our definition of inf and sup. Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCZggpJZvUXnUzaw7fHCtoh
From playlist Real Numbers
Computing Limits from a Graph with Infinities
In this video I do an example of computing limits from a graph with infinities.
From playlist Limits
The limit is the limit is the limit is the limit
Here I evaluate a neat infinite limit with l'Hopital's rule... does it work though? Subscribe to my channel: https://youtube.com/drpeyam Check out my TikTok channel: https://www.tiktok.com/@drpeyam Follow me on Instagram: https://www.instagram.com/peyamstagram/ Follow me on Twitter: https
From playlist Calculus
Convergent sequences are bounded
Convergent Sequences are Bounded In this video, I show that if a sequence is convergent, then it must be bounded, that is some part of it doesn't go to infinity. This is an important result that is used over and over again in analysis. Enjoy! Other examples of limits can be seen in the
From playlist Sequences
A. Song - What is the (essential) minimal volume? 3
I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of resu
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Mokshay Madiman : Minicourse on information-theoretic geometry of metric measure
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Geometry
Proof: Convergent Sequence is Bounded | Real Analysis
Any convergent sequence must be bounded. We'll prove this basic result about convergent sequences in today's lesson. We use the definition of the limit of a sequence, a useful equivalence involving absolute value inequalities, and then considering a maximum and minimum will help us find an
From playlist Real Analysis
Jonathan Luk - A tale of two tails - IPAM at UCLA
Recorded 25 October 2021. Jonathan Luk of Stanford University presents "A tale of two tails" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: Motivated by the strong cosmic censorship conjecture, we study precise late-time tails for solutions to wave equa
From playlist Workshop: Mathematical and Numerical Aspects of Gravitation
A simple proof of a reverse Minkowski inequality - Noah Stephens-Davidowitz
Computer Science/Discrete Mathematics Seminar II Topic: A simple proof of a reverse Minkowski inequality Speaker: Noah Stephens-Davidowitz Affiliation: Visitor, School of Mathematics Date: April 17, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
A Fibonacci bounded partial sum of the Harmonic series.
We determine the limit of a certain sequence defined in terms of Fibonacci and Harmonic numbers. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Identities involving Fibonacci numbers
Stability of the spacetime positive mass theorem in spherical symmetry - Marcus Khuri
More videos on http://video.ias.edu
From playlist Mathematics
Limit Points In this video, I define the notion of a limit point (also known as a subsequential limit) and give some examples of limit points. Limit points are closed: https://youtu.be/b1jYloJXDYY Check out my Sequences Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCuFxFs
From playlist Sequences
Sergiu Klainerman - 3/4 On the Mathematical Theory of Black Holes
https://indico.math.cnrs.fr/event/3463/ The gravitational waves detected by LIGO were produced in the final faze of the inward spiraling of two black holes before they collided to produce a more massive black hole. The experiment is entirely consistent with the so called Final State Conjec
From playlist Sergiu Klainerman - On the Mathematical Theory of Black Holes
On the mathematical theory of black holes II - Sergiu Klainerman
Hermann Weyl Lectures Topic: On the mathematical theory of black holes II Speaker: Sergiu Klainerman Affiliation: Princeton University Date: October 16, 2017 For more videos, please visit http://video.ias.edu
From playlist Hermann Weyl Lectures
[ANT06] Real and imaginary embeddings
When we try to draw a real quadratic extension of Z in the complex plane, it collapses onto the real line - we don't get a lattice any more. We're going to prise it apart by drawing it on the real line in two different ways at once. We'll be able to recover a genuine notion of geometry, an
From playlist [ANT] An unorthodox introduction to algebraic number theory
Michael Damron (Georgia Tech) -- Critical first-passage percolation in two dimensions
In 2d first-passage percolation (FPP), we place nonnegative i.i.d. weights (t_e) on the edges of Z^2 and study the induced weighted graph pseudometric T = T(x,y). If we denote by p = P(t_e = 0), then there is a transition in the large-scale behavior of the model as p varies from 0 to 1. Wh
From playlist Columbia Probability Seminar
Aspects of Eternal Inflation, part 3 - Leonard Susskind
Aspects of Eternal Inflation, part 3 Leonard Susskind Stanford University July 20, 2011
From playlist PiTP 2011
Infinite Limits (Limit Example 10)
Epsilon Definition of a Limit In this video, I illustrate the epsilon-N definition of a limit by doing an example with an infinite limit. More precisely, I prove from scratch that the limit of sqrt(n-2)+3 is infinity Other examples of limits can be seen in the playlist below. Check ou
From playlist Sequences