Newton's Identity, Lesson 5: Symmetric Polynomials of Roots and Elementary Symmetric Polynomials
any symmetric polynomial can be expressed in terms of elementary symmetric polynomials. We introduce an algorithm in finding the polynomial with an example for cubic equations.
From playlist Newton's Identity for polynomials
Video4-3: Higher order Homogeneous equations with constant coeff. Elementary Differential Equations
Elementary Differential Equations Video4-3: Higher order Homogeneous equations with constant coefficients. Characteristic equations, roots, general solutions. Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMjZQyZtCq-0ol_jD
From playlist Elementary Differential Equations
Video6_5: General Theory on Homogeneous Linear Systems of ODEs. Elementary differential equations
Elementary differential equations Video6_5. General Theory on Homogeneous Linear Systems of ODEs: the principle of superposition, Wronskian of a set of vector-values functions, linear independence. Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMjZQyZtCq-0ol_jD
From playlist Elementary Differential Equations
This video defines elementary matrices and then provides several examples of determining if a given matrix is an elementary matrix. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Augmented Matrices
C07 Homogeneous linear differential equations with constant coefficients
An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.
From playlist Differential Equations
Video6_6: General solutions for Linear Systems of ODEs. Elementary differential equations
Elementary differential equations Video6_6. General solutions for Linear Systems of ODEs. Derivation. Example for the case of two distinct real eigenvalues. Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMjZQyZtCq-0ol_jD
From playlist Elementary Differential Equations
This lecture is part of an online course on rings and modules. We show that symmetric polynomials are polynomials in the elementary symmetric functions. Then we prove Newton's identities relating sums of powers to the elementary symmetric functions, and briefly discuss their relations wit
From playlist Rings and modules
Solving An INSANELY Hard Viral Math Problem
This seemingly simple viral problem is a lot harder than it looks--it is actually a problem from a university level mathematics textbook! In order to solve the problem, we take a journey through symmetry and group theory which leads to a simple formula for solving these kinds of equations.
From playlist Math Puzzles, Riddles And Brain Teasers
Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits I... - Srikanth Srinivasan
Computer Science/Discrete Mathematics Seminar I Topic: Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits I : An overview Speaker: Srikanth Srinivasan Affiliation: Aarhus University Date: September 27, 2021 Every multivariate polynomial P(x_1,...,x_n) can be written as a
From playlist Mathematics
The Three/Four bridge and solving quartic equations | Six 7 | Wild Egg
Solving polynomial equations, or equivalently finding factorizations into linear factors, is a major theme in algebra. Here we show how the general quartic equation can be so factored if we have a prior technology for solving quadratic and cubic equations. The key idea goes back to Lagra
From playlist Six: An elementary course in Pure Mathematics
Andrei Zelevinsky - "Cluster Algebras via Quivers with Potentials"
Research lecture at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Newton's Identity, Lesson 6.1: Computation of Cubic Discriminant (elementary symmetric polynomials)
any symmetric polynomial can be expressed in terms of elementary symmetric polynomials. We use two methods to calculate the expression of discriminant of cubic equations in terms of elementary symmetric polynomials.
From playlist Newton's Identity for polynomials
Vic Reiner, Lecture II - 11 February 2015
Vic Reiner (University of Minnesota) - Lecture II http://www.crm.sns.it/course/4036/ Many results in the combinatorics and invariant theory of reflection groups have q-analogues for the finite general linear groups GLn(Fq). These lectures will discuss several examples, and open questions
From playlist Algebraic topology, geometric and combinatorial group theory - 2015
Reduced row echelon form -- Elementary Linear Algebra
This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.
From playlist Elementary Linear Algebra
V8-8: Properties of Fourier series, linearity and convergence. Elementary Differential Equations
Properties of Fourier series, linearity and convergence. Examples. Elementary Differential Equations Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMj
From playlist Elementary Differential Equations
Nonlinear algebra, Lecture 10: "Invariant Theory", by Bernd Sturmfels
This is the tenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Video4-1: General theory of higher order linear equations. Elementary Differential Equations
Elementary Differential Equations Video4-1: General theory of higher order linear equations; Existence and uniqueness; general solutions; the wronskian determinant for n functions, linear dependency, ... Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMjZQyZtCq-0
From playlist Elementary Differential Equations
Commutative algebra 3 (What is a syzygy?)
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 give several examples of rings of invariants and syzygies. Correction: Near the end (last but one sheet) I missed out one
From playlist Commutative algebra