Alina Ostafe: Dynamical irreducibility of polynomials modulo primes
Abstract: In this talk we look at polynomials having the property that all compositional iterates are irreducible, which we call dynamical irreducible. After surveying some previous results (mostly over finite fields), we will concentrate on the question of the dynamical irreducibility of
From playlist Number Theory Down Under 9
What's so wrong with the Axiom of Choice ?
One of the Zermelo- Fraenkel axioms, called axiom of choice, is remarkably controversial. It links to linear algebra and several paradoxes- find out what is so strange about it ! (00:22) - Math objects as sets (00:54) - What axioms we use ? (01:30) - Understanding axiom of choice (03:2
From playlist Something you did not know...
The Simplest Math No One Can Agree on- A Paradox of Choice
To build our mathematics we need a starting point, rules to dictate what we can do and assumed basic truths to serve as a foundation as we seek understanding of higher level problems. But what happens when we can't agree on what we should start with?
From playlist Summer of Math Exposition Youtube Videos
The Axiom of Choice | Epic Math Time
The axiom of choice states that the cartesian product of nonempty sets is nonempty. This doesn't sound controversial, and it might not even sound interesting, but adopting the axiom of choice has far reaching consequences in mathematics, and applying it in proofs has a very distinctive qua
From playlist Latest Uploads
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
Introduction to the Cardinality of Sets and a Countability Proof
Introduction to Cardinality, Finite Sets, Infinite Sets, Countable Sets, and a Countability Proof - Definition of Cardinality. Two sets A, B have the same cardinality if there is a bijection between them. - Definition of finite and infinite sets. - Definition of a cardinal number. - Discu
From playlist Set Theory
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
Will Troiani - Proofs as permutations (Geometry of Interaction 0)
In the third of Will's talks on linear logic and proof nets, he introduces cut-elimination for multiplicative proof nets and shows how to associate permutations to a proof-net and its normal form, with the two permutations related by an interesting identity that is the starting point for G
From playlist Computation, Geometry, Logic seminar
Live CEOing Ep 28: Proofs in the Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Proofs in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Axiomatics and the least upper bound property (I) | Real numbers and limits Math Foundations 120
The role of axiomatics in mathematics is a highly contentious one. Originally the term always referred to Euclid, and his use of the term to mean `a self-evident truth that requires no proof '. However in modern times the meaning of the term has shifted dramatically, to the idea that an Ax
From playlist Math Foundations
Gabriel Goldberg: The Jackson analysis and the strongest hypotheses
HYBRID EVENT Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 13, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Logic and Foundations
Crisis in the Foundation of Mathematics | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi What if the foundation that all of mathematics is built upon isn't as firm as we thought it was? Note: The natural numbers sometimes include zero and sometimes don't -
From playlist An Infinite Playlist
Axioms of Constructive Set Theory Explained
In this video we're going to discuss the various axiom schemes of constructive set theories and how they relate to type theory. I cover BCST, ECST, IKP, KPI, KP, CST, CZF, IZF, Mac Lane, Z and variants equi-consistent to ETCS from category theory, and then of course ZF and ZFC. The text I
From playlist Logic
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We use the fiber product define last lecture to define group schemes, and give a few non-classical examples of them.
From playlist Algebraic geometry II: Schemes
Set Theory - Russell's Paradox: Oxford Mathematics 3rd Year Student Lecture
This is the second of four lectures from Robin Knight's 3rd Year Set Theory course. Robin writes: "Infinity baffled mathematicians, and everyone else, for thousands of years. But around 1870, Georg Cantor worked out how to study infinity in a way that made sense, and created set theory. M
From playlist Oxford Mathematics Student Lectures - Set Theory
Wolfram Physics Project: a Conversation on Current Work (Jan. 26, 2021)
This is a Wolfram Physics Project conversation on our continuing efforts to make progress on the fundamental theory of physics. Begins at 3:00 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Ch
From playlist Wolfram Physics Project Livestream Archive
Nonlinear algebra, Lecture 1: "Polynomials, Ideals, and Groebner Bases", by Bernd Sturmfels
This is the first lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences. Topics covered: polynomilas, ideals and Groebner bases.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
N and Order | Axiomatic Set Theory, Section 3.2
We prove the natural ordering on the natural numbers is a total order. Transitivity (0:00) Asymmetry (6:02) All elements are comparable (8:45)
From playlist Axiomatic Set Theory