Logical challenges with abstract algebra II | Abstract Algebra Math Foundations 215 | NJ Wildberger
There is a very big jump in going from finite algebraic objects to "infinite algebraic objects". For example, there is a huge difference, if one is interested in very precise definitions, between the concept of a finite group and the concept of an "infinite group". We illustrate this imp
From playlist Math Foundations
Abstract Algebra - 11.1 Fundamental Theorem of Finite Abelian Groups
We complete our study of Abstract Algebra in the topic of groups by studying the Fundamental Theorem of Finite Abelian Groups. This tells us that every finite abelian group is a direct product of cyclic groups of prime-power order. Video Chapters: Intro 0:00 Before the Fundamental Theorem
From playlist Abstract Algebra - Entire Course
In this video, Tori explains the meaning of a set. She looks into finite versus infinite sets, and explains elements.
From playlist Basics: College Algebra
RNT1.4. Ideals and Quotient Rings
Ring Theory: We define ideals in rings as an analogue of normal subgroups in group theory. We give a correspondence between (two-sided) ideals and kernels of homomorphisms using quotient rings. We also state the First Isomorphism Theorem for Rings and give examples.
From playlist Abstract Algebra
Abstract Algebra | What is a ring?
We give the definition of a ring and present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
RNT1.2.2. Order of a Finite Field
Abstract Algebra: Let F be a finite field. Prove that F has p^m elements, where p is prime and m gt 0. We note two approaches: one uses the Fundamental Theorem of Finite Abelian Groups, while the other uses linear algebra.
From playlist Abstract Algebra
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
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
Ring Examples (Abstract Algebra)
Rings are one of the key structures in Abstract Algebra. In this video we give lots of examples of rings: infinite rings, finite rings, commutative rings, noncommutative rings and more! Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦
From playlist Abstract Algebra
Peter SCHOLZE (oct 2011) - 5/6 Perfectoid Spaces and the Weight-Monodromy Conjecture
We will introduce the notion of perfectoid spaces. The theory can be seen as a kind of rigid geometry of infinite type, and the most important feature is that the theories over (deeply ramified extensions of) Q_p and over F_p((t)) are equivalent, generalizing to the relative situation a th
From playlist Peter SCHOLZE (oct 2011) - Perfectoid Spaces and the Weight-Monodromy Conjecture
Representation Theory(Repn Th) 5 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
Commutative algebra 8 (Noetherian modules)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we define Noetherian modules over a ring, and use the to prove Noether's theorem that the agerba of invariants
From playlist Commutative algebra
Commutative algebra 32 Zariski's lemma
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We state and prove Zariski's lemma: Any field that is a finitely generated algebra over a field is a finitely generated modu
From playlist Commutative algebra
On the notion of genus for division algebras and algebraic groups - Andrei Rapinchu
Joint IAS/Princeton University Number Theory Seminar Topic: On the notion of genus for division algebras and algebraic groups Speaker: Andrei Rapinchu Affiliation: University of Virginia Date: November 2, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Schemes 16: Morphisms of finite type
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We introduce three properties of morphisms: quasicompact, finite type, and locally of finite type, and give a few examples.
From playlist Algebraic geometry II: Schemes
Ariyan Javanpeykar: Arithmetic and algebraic hyperbolicity
Abstract: The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have onl
From playlist Algebraic and Complex Geometry
Pavel Etingof - "D-modules on Poisson varieties and Poisson traces"
Pavel Etingof delivers a research talk on "D-modules on Poisson varieties and Poisson traces" at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
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
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
Commutative algebra 7 (Finite generation of invariants)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we give the proof of Hilbert's theorem that the invariants of a finite group acting on a finite dimensional ve
From playlist Commutative algebra