Splitting Homomorphism of R-Modules
A splitting, or section, is a homomorphism from the quotient module to the original module that gives a representative for each coset. If we have a splitting, we can prove that the module is isomorphic to a direct sum! This video is an explanation of how the splitting leads to an isomorphi
From playlist Ring & Module Theory
Learn to divide a binomial by a monomial
👉 Learn how to divide polynomials by a monomial using the long division algorithm. A monomial is an algebraic expression with one term while a polynomial is an algebraic expression with more than one term. To divide a polynomial by a monomial using the long division algorithm, we divide ea
From playlist Divide Polynomials using Long Division with monomial divisor
Decomposition by Inner Product with General Bases
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 4 Linear Algebra: Inner Products
Learn to divide a polynomial by a monomial
👉 Learn how to divide polynomials by a monomial using the long division algorithm. A monomial is an algebraic expression with one term while a polynomial is an algebraic expression with more than one term. To divide a polynomial by a monomial using the long division algorithm, we divide ea
From playlist Divide Polynomials using Long Division with monomial divisor
Dividing a trinomial by a monomial
👉 Learn how to divide polynomials by a monomial using the long division algorithm. A monomial is an algebraic expression with one term while a polynomial is an algebraic expression with more than one term. To divide a polynomial by a monomial using the long division algorithm, we divide ea
From playlist Divide Polynomials using Long Division with monomial divisor
Synthetically dividing with a fraction
👉 Learn how to divide polynomials by binomial divisors using the long division algorithm. A binomial is an algebraic expression having two terms. Before dividing a polynomial, it is usually important to arrange the divisor in the descending order of powers of the variable(s). To divide a p
From playlist Divide Polynomials using Long Division with linear binomial divisor
Breaking down long division step by step of polynomials
👉 Learn how to divide polynomials by binomial divisors using the long division algorithm. A binomial is an algebraic expression having two terms. Before dividing a polynomial, it is usually important to arrange the divisor in the descending order of powers of the variable(s). To divide a p
From playlist Divide Polynomials using Long Division with linear binomial divisor
Extremal Combinatorics with Po-Shen Loh 03/25 Wed
Carnegie Mellon University is protecting the community from the COVID-19 pandemic by running courses online for the Spring 2020 semester. This is the video stream for Po-Shen Loh’s PhD-level course 21-738 Extremal Combinatorics. Professor Loh will not be able to respond to questions or com
From playlist CMU PhD-Level Course 21-738 Extremal Combinatorics
Learn how to divide a polynomial by a monomial
👉 Learn how to divide polynomials by a monomial using the long division algorithm. A monomial is an algebraic expression with one term while a polynomial is an algebraic expression with more than one term. To divide a polynomial by a monomial using the long division algorithm, we divide ea
From playlist Divide Polynomials using Long Division with monomial divisor
Splitting Rent with Triangles | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi You can find out how to fairly divide rent between three different people even when you don’t know the third person’s preferences! Find out how with Sperner’s Lemma. T
From playlist An Infinite Playlist
7 juillet 2015
From playlist 2015 Summer School on Moduli Problems in Symplectic Geometry
Proof: Structure Theorem for Finitely Generated Torsion Modules Over a PID
This video has chapters to make the proof easier to follow. Splitting explanation: https://youtu.be/ZINtBNje_08 In this video we give a proof of the classification theorem using two smaller proofs by induction. We show both the elementary divisor form and the invariant factor form of a m
From playlist Ring & Module Theory
Field Theory - Automorphisms Groups of Fields/Galois Groups - Lecture 17
Given an extension of fields L over F we show that there is a surjective homomorphism Aut(Fbar/F) \to Aut(L/F).
From playlist Field Theory
NYT: Sperner's lemma defeats the rental harmony problem
TRICKY PROBLEM: A couple of friends want to rent an apartment. The rooms are quite different and the friends have different preferences and different ideas about what's worth what. Is there a way to split the rent and assign rooms to the friends so that everybody ends up being happy? In t
From playlist Recent videos
Initial Theta Data - part 02 - Transvections
In order to state the "technical part" of initial theta data we need to talk about bases of the l-torsion under the Tate uniformization. This can be found in Silverman's - Advanced Topics - Chapter V, section 6.
From playlist Initial Theta Data
In this video, we see how Pell's equation can be used to solve higher-order equations over the integers. We see another example of the importance of understanding which numbers are squares modulo each prime. The question was originally posed by Lucas: Nouvelles Annales de Mathématiques, s
From playlist [ANT] An unorthodox introduction to algebraic number theory
Transversality and super-rigidity in Gromov-Witten Theory (Lecture - 04) by Chris Wendl
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Dividing a polynomial by a monomial
👉 Learn how to divide polynomials by a monomial using the long division algorithm. A monomial is an algebraic expression with one term while a polynomial is an algebraic expression with more than one term. To divide a polynomial by a monomial using the long division algorithm, we divide ea
From playlist Divide Polynomials using Long Division with monomial divisor
Dividing a polynomial by a monomial
👉 Learn how to divide polynomials by a monomial using the long division algorithm. A monomial is an algebraic expression with one term while a polynomial is an algebraic expression with more than one term. To divide a polynomial by a monomial using the long division algorithm, we divide ea
From playlist Divide Polynomials using Long Division with monomial divisor