Polynomial functions | Algebraic geometry
In mathematics, the Newton polytope is an integral polytope associated with a multivariate polynomial. It can be used to analyze the polynomial's behavior when specific variables are considered relative to the others. Specifically, given a vector of variables and a finite family of pairwise distinct vectors from each encoding the exponents within a monomial, consider the multivariate polynomial where we use the shorthand notation for the monomial . Then the Newton polytope associated to is the convex hull of the vectors ; that is The Newton polytope satisfies the following homomorphism-type property: where the addition is in the sense of Minkowski. Newton polytopes are the central object of study in tropical geometry and characterize the Gröbner bases for an ideal. (Wikipedia).
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From playlist Science Unplugged: Physics
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
Aaron Sidford: Introduction to interior point methods for discrete optimization, lecture II
Over the past decade interior point methods (IPMs) have played a pivotal role in mul- tiple algorithmic advances. IPMs have been leveraged to obtain improved running times for solving a growing list of both continuous and combinatorial optimization problems including maximum flow, bipartit
From playlist Summer School on modern directions in discrete optimization
Tropical Geometry - Lecture 8 - Surfaces | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Maria Angelica Cueto - "Implicitization of surfaces via geometric tropicalization"
Implicitization of surfaces via geometric tropicalization - Research lecture at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Factors of sparse polynomials: structural results and some algorithms - Shubhangi Saraf
Computer Science/Discrete Mathematics Seminar II Topic: Factors of sparse polynomials: structural results and some algorithms Speaker: Shubhangi Saraf Affiliation: Member, School of Mathematics Date: March 26, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Aaron Sidford: Introduction to interior point methods for discrete optimization, lecture III
Over the past decade interior point methods (IPMs) have played a pivotal role in mul- tiple algorithmic advances. IPMs have been leveraged to obtain improved running times for solving a growing list of both continuous and combinatorial optimization problems including maximum flow, bipartit
From playlist Summer School on modern directions in discrete optimization
Tropical Geometry - Lecture 12 - Geometric Tropicalization | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Towards a theory of non-commutative optimization...… -Rafael Oliveira
Computer Science/Discrete Mathematics Seminar I Topic: Towards a theory of non-commutative optimization: geodesic 1st and 2nd order methods for moment maps and polytopes Speaker: Rafael Oliveira Affiliation:University of Toronto Date: October 22, 2019 For more video please visit http://v
From playlist Mathematics
Tropical Geometry - Lecture 5 - Fundamental Theorem | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
This video explains Newton's Method and provides an example. It also shows how to use the table feature of the graphing calculator to perform the calculations needed for Newton's Method. http://mathispower4u.wordpress.com/
From playlist Newton’s Method and L’Hopital’s Rule
Polynomial systems and mixed volumes - Ricky I Liu
Computer Science/Discrete Mathematics Seminar II Topic: Polynomial systems and mixed volumes Speaker: Ricky I Liu Affiliation: Member, School of Mathematics Date: March 16, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
From playlist Physics - Newton's law videos for analysis