Field Theory - (optional) Primitive Element Theorem - Lecture 15
For finite extensions L \supset F we show that there exists an element \gamma in L such that F(\gamma) = L. This is called the primitive element theorem.
From playlist Field Theory
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
MATH3411 Information, Codes and Ciphers We construct the finite field given in part a), as a vector space and as a table of powers of a primitive roots. We then find all primitive elements of this field. Presented by Thomas Britz, School of Mathematics and Statistics, Faculty of Science,
From playlist MATH3411 Information, Codes and Ciphers
Primitive Roots - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Degrees in Towers - Field Theory - Lecture 05
Let L contain K which contains F where all extensions are finite. In this video we prove [L:F] = [L:K][K:F]. This is a super useful formula.
From playlist Field Theory
Multisets and a new framework for arithmetic | Data Structures Math Foundations 187
Here we go back to the first videos in this series and recast that discussion in a more solid direction by utilizing our understanding of multisets. The crucial point is to define what a natural number is in a clear way. This issue is far more subtle than is generally acknowledged. For u
From playlist Math Foundations
Galois theory: Primitive elements
This lecture is part of an online graduate course on Galois theory. We show that any finite separable extension of fields has a primitive element (or generator) and given n example of a finite non-separable extension with no primitive elements.
From playlist Galois theory
Sets might contain an element that can be identified as an identity element under some binary operation. Performing the operation between the identity element and any arbitrary element in the set must result in the arbitrary element. An example is the identity element for the binary opera
From playlist Abstract algebra
Number Theory | Primitive Roots modulo n: Definition and Examples
We give the definition of a primitive root modulo n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Primitive Roots Modulo n
Perfectoid spaces (Lecture 2) by Kiran Kedlaya
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
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)
Lecture 34. Galois groups and fixed fields
From playlist Abstract Algebra 2
Structure of group rings and the group of units of integral group rings (Lecture 2) by Eric Jespers
PROGRAM : GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fun
From playlist Group Algebras, Representations And Computation
Ling Long - Hypergeometric Functions, Character Sums and Applications - Lecture 5
Title: Hypergeometric Functions, Character Sums and Applications Speaker: Prof. Ling Long, Louisiana State University Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of
From playlist Hypergeometric Functions, Character Sums and Applications
José Felipe Voloch: Generators of elliptic curves over finite fields
Abstract: We will discuss some problems and results connected with finding generators for the group of rational points of elliptic curves over finite fields and connect this with the analogue for elliptic curves over function fields of Artin's conjecture for primitive roots. Recording du
From playlist Number Theory
MATH3411 Information, Codes and Ciphers We find the primitive elements for the integers modulo some integer n, here n = 17. Presented by Thomas Britz, School of Mathematics and Statistics, Faculty of Science, UNSW Australia
From playlist MATH3411 Information, Codes and Ciphers
Reconsidering natural numbers and arithmetical expressions | Data structures Math Foundations 185
It is time to turn our gaze back to the true foundations of the subject: arithmetic with natural numbers. But now we know that the issue of "What exactly is a natural number?" is fraught with subtlety. We adopt a famous dictum of Errett Bishop, and start to make meaningful distinctions bet
From playlist Math Foundations
Imprimitive irreducible representations of finite quasisimple groups by Gerhard Hiss
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods