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
Ordered Fields In this video, I define the notion of an order (or inequality) and then define the concept of an ordered field, and use this to give a definition of R using axioms. Actual Construction of R (with cuts): https://youtu.be/ZWRnZhYv0G0 COOL Construction of R (with sequences)
From playlist Real Numbers
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
Fields are a fundamental concept in analysis (and many areas of math). Here we will look at the field axioms and define what it means to be a field. I hope you learn something and enjoy! *Real Analysis Course Disclaimer* - It's very possible I will be using slightly different definitions,
From playlist Real Analysis Course
Physicists discuss the central role that fields play in modern physics as well as how they use fields in their area of study. This video is part of Perimeter Institute's free educational resource Fields. Download the teacher's guide, modifiable worksheets, and supporting materials at: ht
From playlist Classroom Resources
Field Examples - Infinite Fields (Abstract Algebra)
Fields are a key structure in Abstract Algebra. Today we give lots of examples of infinite fields, including the rational numbers, real numbers, complex numbers and more. We also show you how to extend fields using polynomial equations and convergent sequences. Be sure to subscribe so y
From playlist Abstract Algebra
The realm of natural numbers | Data structures in Mathematics Math Foundations 155
Here we look at a somewhat unfamiliar aspect of arithmetic with natural numbers, motivated by operations with multisets, and ultimately forming a main ingredient for that theory. We look at natural numbers, together with 0, under three operations: addition, union and intersection. We will
From playlist Math Foundations
Field Theory: Definition/ Axioms
This video is about the basics axioms of fields.
From playlist Basics: Field Theory
Maria Ines de Frutos Fernandez - Formalizing Norm Extensions and Applications to Number Theory
Recorded 16 February 2023. Maria Ines de Frutos Fernandez of Imperial College London presents "Formalizing Norm Extensions and Applications to Number Theory" at IPAM's Machine Assisted Proofs Workshop. Abstract: Let K be a eld complete with respect to a nonarchimedean real-valued norm, and
From playlist 2023 Machine Assisted Proofs Workshop
Séminaire Bourbaki - 21/06/2014 - 3/4 - Thomas C. HALES
Developments in formal proofs A for mal proof is a proof that can be read and verified by computer, directly from the fundamental rules of logic and the foundational axioms of mathematics. The technology behind for mal proofs has been under development for decades and grew out of efforts i
From playlist Bourbaki - 21 juin 2014
J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part2)
In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field k. Then the arithmetic counterpart of the dimension h0(C,V)=dimkΓ(C,V) of the space of section
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Dominique Cerveau - Holomorphic foliations of codimension one, elementary theory (Part 3)
In this introductory course I will present the basic notions, both local and global, using classical examples. I will explain statements in connection with the resolution of singularities with for instance the singular Frobenius Theorem or the Liouvilian integration. I will also present so
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
What is General Relativity? Lesson 39: The curvature - formal introduction
What is General Relativity? Lesson 39: The curvature - formal introduction The Riemann Curvature Tensor is presented as a strictly formal object. Take note of an error captured by viewer "Endevor" in the comments. I may redo this video soon to fix it! Please consider supporting this chan
From playlist What is General Relativity?
Vincent Bagayoko, École Polytechnique
February 26, Vincent Bagayoko, École Polytechnique Three flavors of H-fields
From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra
Quantization By Branes And Geometric Langlands Lecture 2 by Edward Witten
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Gérald DUNNE - Resurgent Trans-series Analysis of Hopf Algebraic Renormalization
In the Kreimer-Connes Hopf algebraic approach to renormalization, for certain QFTs the Dyson-Schwinger equations can be reduced to nonlinear differential equations. I describe methods based on Ecalle's theory of resurgent trans-series to extract non-perturbative information from these Dyso
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Introduction to Resurgence, Trans-series and Non-perturbative Physics - I by Gerald Dunne
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Multivariable Calculus | What is a vector field.
We introduce the notion of a vector field and give some graphical examples. We also define a conservative vector field with examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus