Dynamical systems

Rational dependence

In mathematics, a collection of real numbers is rationally independent if none of them can be written as a linear combination of the other numbers in the collection with rational coefficients. A collection of numbers which is not rationally independent is called rationally dependent. For instance we have the following example. Because if we let , then . (Wikipedia).

Video thumbnail

Simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

Video thumbnail

Simplifying rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions (Binomials) #Rational

Video thumbnail

Simplifying a rational expression with a trinomial

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

Video thumbnail

Factoring out the GCF to simplify the rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions (Binomials) #Rational

Video thumbnail

Simplifying a rational expression by factoring two trinomials

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

Video thumbnail

Simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

Video thumbnail

Factoring out the GCF from the denominator to help you simplify your rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions (Binomials) #Rational

Video thumbnail

Simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions (Binomials) #Rational

Video thumbnail

Simplify a rational expression

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

Video thumbnail

A Family of Rationally Extended Real and PT Symmetric Complex Potentials by Rajesh Kumar Yadav

PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a

From playlist Non-Hermitian Physics (ONLINE)

Video thumbnail

DART VII Thomas Scanlon

Title: Algebraic Independence of Functions Satisfying Nonlinear Polynomial Mahler Equations

From playlist Differential Algebra and Related Topics VII (2016)

Video thumbnail

Point-counting and diophantine applications - Jonathan Pila

Hermann Weyl Lectures Topic: Point-counting and diophantine applications Speaker: Jonathan Pila Affiliation: University of Oxford Date: October 23, 2018 For more video please visit http://video.ias.edu

From playlist Hermann Weyl Lectures

Video thumbnail

Mod-04 Lec-32 Rationalisability and Beliefs

Game Theory and Economics by Dr. Debarshi Das, Department of Humanities and Social Sciences, IIT Guwahati. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Game Theory and Economics | CosmoLearning.org Economics

Video thumbnail

The Study of Wave Interactions: Where Beautiful Mathematical Ideas Come... II - Gigliola Staffilani

Emmy Noether Lectures Topic: The Study of Wave Interactions: Where Beautiful Mathematical Ideas Come Together Speaker: Gigliola Staffilani Affiliation: Massachusetts Institute of Technology Date: January 25, 2023 Phenomena involving interactions of waves happen at different scales and i

From playlist Mathematics

Video thumbnail

Geometry of tropical varieties with a view toward applications (Lecture 2) by Omid Amini

PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS : Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE : 27 June 2022 to 08 July 2022 VENUE : Madhava Lecture Hall and Online Algebraic geometry is the study

From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)

Video thumbnail

Integration Sucks

Think you can integrate every function? Unfortunately you can't, but it's not your fault! In this case, it's the math that's wrong and needs to be updated (just like sometimes you update your operating system). This video presents the limit of Riemann (calculus-style) integration and the b

From playlist Integration

Video thumbnail

Ruyong Feng, Chinese Academy of Sciences

October 14, Ruyong Feng, Chinese Academy of Sciences Effective height inequality of points on a plane algebraic curve

From playlist Fall 2021 Online Kolchin Seminar in Differential Algebra

Video thumbnail

Thierry Combot, University of Burgundy

February 24, Thierry Combot, University of Burgundy Symbolic integration on planar differential foliations

From playlist Spring 2023 Online Kolchin Seminar in Differential Algebra

Video thumbnail

Simplify a rational expression with two trinomials

Learn how to simplify rational expressions. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. To simplify a rational expression, we factor completely the numerator and the denominator of the rational

From playlist Simplify Rational Expressions

Video thumbnail

Aaron Pixton - The stable pairs equivariant descendent vertex

The counting function associated to the moduli space of stable pairs on a 3-fold X is conjectured to give the Laurent expansion of a rational function. For toric X, this conjecture can be proven by a careful grouping of the box con gurations appearing in the stable pairs equivariant descen

From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten

Related pages

Linear independence | Dehn invariant | Linear flow on the torus | Lindemann–Weierstrass theorem | Gelfond–Schneider theorem | Vector space | Mathematics | Rational number | Schanuel's conjecture | Real number | Baker's theorem | Hodge conjecture