FIT2.3.3. Algebraic Extensions
Field Theory: We define an algebraic extension of a field F and show that successive algebraic extensions are also algebraic. This gives a useful criterion for checking algberaic elements. We finish with algebraic closures.
From playlist Abstract Algebra
Field Theory: Let F be a subfield of the field K. We consider K as a vector space over F and define the degree of K over F as the dimension. We give a degree formula for successive extensions, and consider extensions in terms of bases. EDIT: Typo - around 3:15, it should be cube root(2
From playlist Abstract Algebra
Infinite Limits With Equal Exponents (Calculus)
#Calculus #Math #Engineering #tiktok #NicholasGKK #shorts
From playlist Calculus
What is a continuous extension?
Continuous Extension In this video, I define the concept of a continuous extension of a function and show that a function has a continuous extension if and only if it is uniformly continuous. This explains yet again why uniform continuity is so awesome Uniform Continuity: https://youtu.b
From playlist Limits and Continuity
Epsilon delta limit (Example 3): Infinite limit at a point
This is the continuation of the epsilon-delta series! You can find Examples 1 and 2 on blackpenredpen's channel. Here I use an epsilon-delta argument to calculate an infinite limit, and at the same time I'm showing you how to calculate a right-hand-side limit. Enjoy!
From playlist Calculus
Basic/Primitive Extensions and Minimal Polynomials - Field Theory - Lecture 02
A "basic" or "primitive" extension of a field F is a new field F(alpha) where alpha in K an extension of F. We give some basic properties of extensions. Most importantly introduce the concept of minimal polynomials. @MatthewSalomone has some good videos on this already which might be mor
From playlist 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
Field Theory: We consider the case of simple extensions, where we adjoin a single element to a given field. The cases of transcendental and algebraic arise, depending on whether the kernel of the evaluation map is zero or not. In the algebraic case, we define the minimal polynomial, show
From playlist Abstract Algebra
Volker Kaibel: A simple geometric proof showing that almost all 01 polytopes have exponential ...
We show that for a random d-dimensional 0/1-polytope the smallest size of any semidefinite extended formulation is exponential in d by building upon nothing else than a simple well-known property of maximum volume inscribed ellipsoids of convex bodies. In particular, the proof does not rel
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
A tongue-in-cheek look at the use of limits in the life sciences.
From playlist Life Science Math: Limits in calculus
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
CTNT 2020 - Upper Ramification Groups for Arbitrary Valuation Rings - Vaidehee Thatte
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
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
Title: Strongly Étale Difference Algebras and Babbitt's Decomposition
From playlist Fall 2015
Kevin Buzzard (lecture 3/20) Automorphic Forms And The Langlands Program [2017]
Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w
From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]
(IC 4.9) Optimality of Huffman codes (part 4) - extension and contraction
We prove that Huffman codes are optimal. In part 4, we define the H-extension and H-contraction. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F
From playlist Information theory and Coding
What is an Injective Function? Definition and Explanation
An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
Elliptic Curves - Lecture 19b - Elliptic curves over local fields (the action of inertia)
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves