Definition of a Field In this video, I define the concept of a field, which is basically any set where you can add, subtract, add, and divide things. Then I show some neat properties that have to be true in fields. Enjoy! What is an Ordered Field: https://youtu.be/6mc5E6x7FMQ Check out
From playlist Real Numbers
Field Theory: Definition/ Axioms
This video is about the basics axioms of fields.
From playlist Basics: Field Theory
Field Definition (expanded) - Abstract Algebra
The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They
From playlist Abstract Algebra
The Structure of Fields: What is a field and a connection between groups and fields
This video is primarily meant to help develop some ideas around the structure of fields and a connection between groups and fields (which will allow me to create more abstract algebra videos in the future! 😀😅🤓) 00:00 Intro 01:04 What is a Field? Here we give the definition of a field in
From playlist The New CHALKboard
Abstract Algebra: The definition of a Field
Learn the definition of a Field, one of the central objects in abstract algebra. We give several familiar examples and a more unusual example. ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Make a one-time PayPal donation: https://www
From playlist Abstract Algebra
This video is about polynomials with coefficients in a field.
From playlist Basics: Field Theory
Field Theory -- Qbar, the field of algebraic numbers -- Lecture 8
In this video we show that QQbar, the algebraic closure of the rational numbers is countable.
From playlist Field Theory
What is Science? by Pierre Hohenberg (New York University)
28 December 2016, 16:00 to 17:00 VENUE ICTS campus, Bengaluru In this talk we propose a new definition of science based on the distinction between the activity of scientists and the product of that activity: the former is denoted (lower-case) science and the latter (upper-case) Science. Th
From playlist DISTINGUISHED LECTURES
Fields - Field Theory - Lecture 00
This is the first in a series of videos for my abstract algebra class during the 2020 shutdown. This lecture is intended to rapidly catch students up who are going to follow online and aren't from UVM. We are using Dummit and Foote.
From playlist Field Theory
Vincent Vargas - 3/4 Liouville conformal field theory and the DOZZ formula
Materials: http://marsweb.ihes.fr/Cours_Vargas.pdf Liouville conformal field theory (LCFT hereafter), introduced by Polyakov in his 1981 seminal work "Quantum geometry of bosonic strings", can be seen as a random version of the theory of Riemann surfaces. LCFT appears in Polyakov's work a
From playlist Vincent Vargas - Liouville conformal field theory and the DOZZ formula
Adolfo Guillot: Complete holomorphic vector fields and their singular points - lecture 1
CIRM VIRTUAL EVENT Recorded during the research school "Geometry and Dynamics of Foliations " the May 11, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on C
From playlist Virtual Conference
Riemannian Geometry - Definition: Oxford Mathematics 4th Year Student Lecture
Riemannian Geometry is the study of curved spaces. It is a powerful tool for taking local information to deduce global results, with applications across diverse areas including topology, group theory, analysis, general relativity and string theory. In these two introductory lectures
From playlist Oxford Mathematics Student Lectures - Riemannian Geometry
Alexandra SHLAPENTOKH - Defining Valuation Rings and Other Definability Problems in Number Theory
We discuss questions concerning first-order and existential definability over number fields and function fields in the language of rings and its extensions. In particular, we consider the problem of defining valuations rings over finite and infinite algebraic extensions
From playlist Mathematics is a long conversation: a celebration of Barry Mazur
The many facets of complexity of Beltrami fields in Euclidean space - Daniel Peralta-Salas
Workshop on the h-principle and beyond Topic: The many facets of complexity of Beltrami fields in Euclidean space Speaker: Daniel Peralta-Salas Affiliation: Instituto de Ciencias Matemáticas Date: November 02, 2021 Beltrami fields, that is vector fields on $\mathbb R^3$ whose curl is p
From playlist Mathematics
Vincent Vargas - 1/4 Liouville conformal field theory and the DOZZ formula
Materials: http://marsweb.ihes.fr/Cours_Vargas.pdf Liouville conformal field theory (LCFT hereafter), introduced by Polyakov in his 1981 seminal work "Quantum geometry of bosonic strings", can be seen as a random version of the theory of Riemann surfaces. LCFT appears in Polyakov's work a
From playlist Vincent Vargas - Liouville conformal field theory and the DOZZ formula
Tamagawa Numbers of Linear Algebraic Groups over (...) - Rosengarten - Workshop 2 - CEB T2 2019
Zev Rosengarten (Hebrew University of Jerusalem) / 26.06.2019 Tamagawa Numbers of Linear Algebraic Groups over Function Fields In 1981, Sansuc obtained a formula for Tamagawa numbers of reductive groups over number fields, modulo some then unknown results on the arithmetic of simply con
From playlist 2019 - T2 - Reinventing rational points
What is General Relativity? Lesson 58: Scalar Curvature Part 7: Pullback and Pushforward
What is General Relativity? Lesson 58: Scalar Curvature Part 7: Pullback and Pushforward This lecture covers the pullback of convector fields. Also, we cast pushforwards and pullbacks in terms of coordinate charts. Please consider supporting this channel via Patreon: https://www.patreon
From playlist What is General Relativity?
Tobias Braun - Orthogonal Determinants
Basic concepts and notions of orthogonal representations are in- troduced. If X : G → GL(V ) is a K-representation of a nite group G it may happen that its image X(G) xes a non-degenerate quadratic form q on V . In this case X and its character χ : G → K, g 7 → trace(X(g)) are called ortho
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Joe Neeman: Gaussian isoperimetry and related topics III
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
What Is a Field? - Instant Egghead #42
Contributing editor George Musser explains how physicists think about the universe using the fundamental concept of "the field". -- WATCH more Instant Egghead: http://goo.gl/CkXwKj SUBSCRIBE to our channel: http://goo.gl/fmoXZ VISIT ScientificAmerican.com for the latest science news:http
From playlist Quantum Field Theory