Ordered field

What is a field ?

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

Math 101 090817 Introduction to Analysis 04 Ordered fields

Ordered sets. Examples. Ordered fields. Properties of ordered fields.

From playlist Course 6: Introduction to Analysis (Fall 2017)

What is a real number?

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

Orders on Sets: Part 1 - Partial Orders

This was recorded as supplemental material for Math 115AH at UCLA in the spring quarter of 2020. In this video, I discuss the concept and definition of a partial order.

From playlist Orders on Sets

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

14 Ordering of sets

The elements of a set can be ordered by a relation. Some relation cause proper ordering and some, partial ordering. Have a look at some examples.

From playlist Abstract algebra

Math 101 Introduction to Analysis 091415: Fields, Ordered Fields

Fields. Field axioms. Examples and non-examples of fields. Properties of fields. Ordered sets. Ordered fields. Properties of ordered fields.

From playlist Course 6: Introduction to Analysis

Set Theory (Part 11): Ordering of the Natural Numbers

Please feel free to leave comments/questions on the video and practice problems below! In this video, we utilize the definition of natural number to speak of ordering on the set of all natural numbers. In addition, the well-ordering principle and trichotomy law are proved.

From playlist Set Theory by Mathoma

Order of Elements in a Group | Abstract Algebra

We introduce the order of group elements in this Abstract Algebra lessons. We'll see the definition of the order of an element in a group, several examples of finding the order of an element in a group, and we will introduce two basic but important results concerning distinct powers of ele

From playlist Abstract Algebra

Galois theory: Finite fields

This lecture is part of an online graduate course on Galois theory. We use the theory of splitting fields to classify finite fields: there is one of each prime power order (up to isomorphism). We give a few examples of small order, and point out that there seems to be no good choice for

From playlist Galois theory

Introduction to number theory lecture 30. Fields in number theory

This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We extend some of the results we proved about the integers mod p to more general fields.

From playlist Introduction to number theory (Berkeley Math 115)

Self-force and radiation reaction in general relativity by Adam Pound ( Lecture 6 )

PROGRAM SUMMER SCHOOL ON GRAVITATIONAL WAVE ASTRONOMY ORGANIZERS : Parameswaran Ajith, K. G. Arun and Bala R. Iyer DATE : 15 July 2019 to 26 July 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore This school is part of the annual ICTS summer schools on gravitational-wave (GW) astronomy.

From playlist Summer School on Gravitational Wave Astronomy -2019

algebraic geometry 30 The Ax Grothendieck theorem

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the Ax-Grothendieck theorem, which states that an injective regular map between varieties is surjective. The proof uses a strange technique: first prove the resu

From playlist Algebraic geometry I: Varieties

Galois theory: Examples of Galois extensions

This lecture is part of an online graduate course on Galois theory. We give several examples of Galois extensions, and work out the correspondence between subfields and subgroups explicitly.

From playlist Galois theory

Non-monogenic Division Fields of Elliptic Curves, Hanson Smith

Abstract: This talk will serve as an exposition of a recent preprint investigating the division fields of elliptic curves. In this work we show that for various positive integers n there exist of infinite families of elliptic curves over Q with n-division fields, Q(E[n]), that are not mono

From playlist My Students

Álvaro Lozano-Robledo: Recent progress in the classification of torsion subgroups of...

Abstract: This talk will be a survey of recent results and methods used in the classification of torsion subgroups of elliptic curves over finite and infinite extensions of the rationals, and over function fields. Recording during the meeting "Diophantine Geometry" the May 22, 2018 at th

From playlist Math Talks

1. Introduction to Effective Field Theory (EFT)

MIT 8.851 Effective Field Theory, Spring 2013 View the complete course: http://ocw.mit.edu/8-851S13 Instructor: Iain Stewart In this lecture, the professor discussed EFT of Hydrogen, top-down and bottom-up, and renormalizable EFT. License: Creative Commons BY-NC-SA More information at ht

From playlist MIT 8.851 Effective Field Theory, Spring 2013

Lecture 33. Finite fields

From playlist Abstract Algebra 2

Field Theory - Algebraically Closed Fields - Lecture 9

In this video we define what an algebraically closed field and assert without proof that they exist. We also explain why if you can find a single root for any polynomial, then you can find them all.

From playlist Field Theory