In the mathematical theory of metric spaces, ε-nets, ε-packings, ε-coverings, uniformly discrete sets, relatively dense sets, and Delone sets (named after Boris Delone) are several closely related definitions of well-spaced sets of points, and the packing radius and covering radius of these sets measure how well-spaced they are. These sets have applications in coding theory, approximation algorithms, and the theory of quasicrystals. (Wikipedia).
The perfect number of axioms | Axiomatic Set Theory, Section 1.1
In this video we introduce 6 of the axioms of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) The Axiom of Existence: (2:39) The Axiom of Extensionality: (4:20) The Axiom Schema of Comprehension: (6:15) The Axiom of Pair (12:16) The Axiom of Union (15:15) T
From playlist Axiomatic Set Theory
What is the complement of a set? Sets in mathematics are very cool, and one of my favorite thins in set theory is the complement and the universal set. In this video we will define complement in set theory, and in order to do so you will also need to know the meaning of universal set. I go
From playlist Set Theory
Set Theory (Part 18): The Rational Numbers are Countably Infinite
Please feel free to leave comments/questions on the video and practice problems below! In this video, we will show that the rational numbers are equinumerous to the the natural numbers and integers. First, we will go over the standard argument listing out the rational numbers in a table a
From playlist Set Theory by Mathoma
How do I make a round dice set?
Today I will make some unusual dice. They will not be square but round and we will make them completely out of metal, with a wooden stand. Enjoy! #dice#W&M#lathe
From playlist Random problems
Introducing Infinity | Set Theory, Section 3.1
In this video we define inductive sets, the natural numbers, the axiom of infinity, and the standard order relation on the natural numbers. My Twitter: https://twitter.com/KristapsBalodi3 Intro (0:00) Defining Natural Numbers as Sets (1:19) Definition of Inductive Sets (5:07) The Axiom o
From playlist Axiomatic Set Theory
Presentation of the T1 2019 "The mathematics of imaging"
From January 7th to April 5th, 2019, mathematicians from all over the world meet at the IHP to share their research about the mathematics of imaging. Julie Delon and Gabriel Peyré present in this video the main concrete applications of image processing : astrophysics, medicine, social netw
From playlist 2019 - T1 - The Mathematics of Imaging
Set Theory (Part 12): Constructing the Integers
Please feel free to leave comments/questions on the video and practice problems below! In this video, we will use the natural numbers to construct the integers as a quotient set, building upon the ideas of Cartesian product and equivalence relations. We will also set up arithmetic on the
From playlist Set Theory by Mathoma
Boris Solomyak: Lecture on Delone sets and Tilings
Abstract: In this lecture we focus on selected topics around the themes: Delone sets as models for quasicrystals, inflation symmetries and expansion constants, substitution Delone sets and tilings, and associated dynamical systems. Recording during the Jean-Morlet chair research school "T
From playlist Dynamical Systems and Ordinary Differential Equations
C. Judge - Systoles in translation surfaces
I will discuss joint work with Hugo Parlier concerning the shortest noncontractible loops—’systoles’—in a translation surface. In particular, we provide estimates (some sharp) on the number of systoles (up to homotopy) in the strata H(2g-2) and the stratum H(1,1). We also determine the ma
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
This video introduces the basic vocabulary used in set theory. http://mathispower4u.wordpress.com/
From playlist Sets
Benjamin Schweinhart (4/3/18): Persistent homology and the upper box dimension
We prove the first results relating persistent homology to a classically defined fractal dimension. Several previous studies have demonstrated an empirical relationship between persistent homology and fractal dimension; our results are the first rigorous analogue of those comparisons. Spe
From playlist AATRN 2018
Arul Shankar, Ordering elliptic curves by conductor
VaNTAGe seminar, on Oct 27, 2020 License: CC-BY-NC-SA. Closed captions provided by Rachana Madhukara.
From playlist Rational points on elliptic curves
See http://thedicelab.com/ for more details. These dice are available at http://www.mathartfun.com/shopsite_sc/store/html/DiceLabDice.html
From playlist Dice
Albert Hammond Jr - 100-99 feat. GoldLink [OFFICIAL VIDEO]
Albert Hammond Jr's new single "100-99 (feat. GoldLink)" is out now. Listen to the single and pre-order his upcoming album 'Melodies On Hiatus' here: https://ffm.to/melodiesonhiatus Follow Albert Hammond Jr: Instagram: https://www.instagram.com/alberthammondjr/ TikTok: https://www.tikto
From playlist 🆕🎧 New Alternative 40 Chart | Updated Weekly
C-minimal valued fields - F. Delon - Workshop 2 - CEB T1 2018
Fran¸coise Delon (CNRS – Université Paris Diderot) / 07.03.2018 C-minimal valued fields. A natural language to study valued fields is Ldiv := (+, −, ·, 0, 1, div) where div(x, y) is a binary predicate interpreted by v(x) ≤ v(y). An expansion (K,L) of (K,Ldiv) is C-minimal if for every el
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Morphine & Heroin - Periodic Table of Videos
Morphine and heroin are among the strongest painkillers known to science. More links in description below ↓↓↓ Support Periodic Videos on Patreon: https://www.patreon.com/periodicvideos A video on every element: http://bit.ly/118elements More at http://www.periodicvideos.com/ Follow us
From playlist Molecular Videos - Periodic Videos
BANDE-ANNONCE - Univers Convergents, le ciné-club scientifique
C'est reparti pour la 5ème édition du ciné-club Univers Convergents, de janvier à juin 2018, les derniers mardi du mois, au cinéma le GRAND ACTION. Le plus grand ciné-club scientifique ! Mathématiques, physique, astronomie, se discutent à travers de grands films : - Le mystère de la matièr
From playlist Ciné-Club Univers Convergents
Math Park - 20/04/2013 - Julie Delon, Des Mathématiques à la photographie numérique.
Les capteurs utilisés en photographie numérique ont des caractéristiques intrinsèques limitant la qualité de leurs mesures (bruit, dynamique limitée), et ce d'autant plus que leurs dimensions sont réduites (smartphones). Ces limitations se traduisent par une perte de qualité immédiate lors
From playlist Séminaire Mathematic Park
Claudia Fevola - KP Solitons from Tropical Limits
In this talk, we study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations. Riemann’s theta function becomes a finite exponential sum that is supported on a Delaunay polytope. We introduce the Hirota variety which parametrizes a
From playlist Research Spotlight
Set Theory (Part 15a): Decimals, Binary, and Dedekind Cuts
Please leave your comments, questions, and thoughts below! In this video, I talk about the relation between our everyday notions of real numbers as infinite decimal expansions and think about how we can interchange a cut with a decimal expansion. I also introduce binary representations fo
From playlist Set Theory by Mathoma