Mathematical identities | Galois theory | Symmetric functions | Invariant theory | Linear algebra | Algebraic combinatorics | Group theory
In mathematics, Newton's identities, also known as the Girard–Newton formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials. Evaluated at the roots of a monic polynomial P in one variable, they allow expressing the sums of the k-th powers of all roots of P (counted with their multiplicity) in terms of the coefficients of P, without actually finding those roots. These identities were found by Isaac Newton around 1666, apparently in ignorance of earlier work (1629) by Albert Girard. They have applications in many areas of mathematics, including Galois theory, invariant theory, group theory, combinatorics, as well as further applications outside mathematics, including general relativity. (Wikipedia).
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From playlist Science Unplugged: Physics
Isaac Newton - English Physicist & Formulated the Laws of Gravity |Mini Bio | BIO
Watch a short biography of Isaac Newton, a key figure in the scientific revolution who is most famous for formulating laws of gravity. #Biography Subscribe for more Biography: http://aetv.us/2AsWMPH Delve deeper into Biography on our site: http://www.biography.com Follow Biography for mo
From playlist Genius & Innovation | A+E Networks
Teach Astronomy - Newton and Society
http://www.teachastronomy.com/ Newton's work was central not only to the history of physics and astronomy but to the history of ideas of Europe in the last 400 years. Newton's innovations in mechanics led to ways of harnessing energy and power in machines, and this within a few generation
From playlist 03. Concepts and History of Astronomy and Physics
Newton's Law of Universal Gravitation
You thought we were all done with Newton, didn't you? You figured that three laws are enough for any scientist. Well think again! Newton was quite the champ, and his work with gravity was revolutionary. I mean, the guy invented calculus so that he could do his work on gravity. So when he I
From playlist Classical Physics
http://www.teachastronomy.com/ Perhaps the greatest scientist who ever lived, Isaac Newton was born just after the death of Galileo. Lonely and moody as a child, his early education was unremarkable, but when he went to university at Cambridge his true intelligence came forth. During a t
From playlist 03. Concepts and History of Astronomy and Physics
Mechanics and curves | Math History | NJ Wildberger
The laws of motion as set out by Newton built upon work of Oresme, Galileo and others on dynamics, and the relations between distance, velocity and acceleration in trajectories. With Newton's laws and the calculus, a whole new arena of practical and theoretical investigations opened up to
From playlist MathHistory: A course in the History of Mathematics
WTF Is Gravity? Scientists Don’t Really Know Either (Part 1 of 3)
Gravity is a simple concept, but the “why” and the “how” are magnificently complicated. How much of gravity do we actually understand? Part 2 of 3 - https://youtu.be/lrP8ab5_-d8 Part 3 of 3 - https://youtu.be/pUsiorDJ_cM Read More: Newton’s Laws of Motion https://www.grc.nasa.gov/www/k-
From playlist Seeker Plus
Teach Astronomy - Newton and Cosmology
http://www.teachastronomy.com/ Newton viewed both time and space as smooth, absolute, and Euclidian. Newton's gravity law is an inverse square law, so the gravity of every object diminishes with the square of the distance. However it never reaches zero because one over the square of a la
From playlist 04. Chemistry and Physics
The Binomial Chu Vandermonde Identity: a new unification? | Algebraic Calculus Two | Wild Egg Maths
We suggest a novel unification of the Binomial and Chu Vandermonde identities, leading to an unusual introduction of the exponential polyseries, along with Newton's reciprocal polyseries. The main idea is to introduce a generalization of Knuth's rising and falling powers notation, which w
From playlist Algebraic Calculus Two
Tricks for Solving Coulomb's Law Problems
4 great tips for solving Coulomb's equation for Physics students. Help for AP Physics and College students. (Companion video to Charles Coulomb biography) My Patreon Page (thanks!): https://www.patreon.com/user?u=15291200 The music is from the awesome Kim Nalley of course www.KimNalley.
From playlist Misc Fun Videos
Newton's Method for finding roots of functions including finding a square root example and discussion of the order (newton's method is also known as Newton-Raphson method). Small correction around 2:26 the sign is incorrect it should be x_(n+1) = (1/2)(x_n + a/x_n). A video covering this m
From playlist Root Finding
Peter Benner: Matrix Equations and Model Reduction, Lecture 5
Peter Benner from the Max Planck Institute presents: Matrix Equations and Model Reduction; Lecture 5
From playlist Gene Golub SIAM Summer School Videos
Newton's Identity, Lesson 2: An Example (Quadratic Equations)
An example to solve two unknowns using the Newton's recurrence for roots of quadratics.
From playlist Newton's Identity for polynomials
Lecture 17 | Convex Optimization I (Stanford)
Professor Stephen Boyd, of the Stanford University Electrical Engineering department, continues his lecture on equality constrained minimization for the course, Convex Optimization I (EE 364A). Convex Optimization I concentrates on recognizing and solving convex optimization problems th
From playlist Lecture Collection | Convex Optimization
Jorge Nocedal: "Tutorial on Optimization Methods for Machine Learning, Pt. 1"
Graduate Summer School 2012: Deep Learning, Feature Learning "Tutorial on Optimization Methods for Machine Learning, Pt. 1" Jorge Nocedal, Northwestern University Institute for Pure and Applied Mathematics, UCLA July 19, 2012 For more information: https://www.ipam.ucla.edu/programs/summ
From playlist GSS2012: Deep Learning, Feature Learning
Coulomb's Law - Net Electric Force & Point Charges
This physics video tutorial explains the concept behind coulomb's law and how to use it calculate the electric force between two and three point charges. This video contains plenty of examples and practice problems for students taking high school or college level physics. Access The Full
From playlist New Physics Video Playlist
Newton's Identity, Lesson 4.1: An AMC 12 Problem, or how is x^3+y^3 related to x+y and x^2+y^2
2005 AMC 12B Problem 23
From playlist Newton's Identity for polynomials
Newton's Polyseries and the Harriot-Pascal Array | Algebraic Calculus Two 2 | Wild Egg Maths
We introduce the famous binomial series of Newton, extending the Binomial theorem to rational values of the exponent. With the Algebraic Calculus approach, we cannot interpret this formula in the usual way, as we have to stick with concrete arithmetic involving rational numbers. However we
From playlist Algebraic Calculus Two
Lecture 2A: Higher-order Procedures
MIT 6.001 Structure and Interpretation of Computer Programs, Spring 2005 Instructor: Harold Abelson, Gerald Jay Sussman, Julie Sussman View the complete course: https://ocw.mit.edu/6-001S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE18841CABEA24090 Higher-order Procedures
From playlist MIT 6.001 Structure and Interpretation, 1986
Newton’s method, and the fractal it creates that Newton knew nothing about
Who knew root-finding could be so complicated? Next part: https://youtu.be/LqbZpur38nw Special thanks to the following supporters: https://3b1b.co/lessons/newtons-fractal#thanks An equally valuable form of support is to simply share the videos. ------------------ Interactive for this vid
From playlist Explainers