Hamiltonian mechanics | Dynamical systems
In classical mechanics, a physical system is termed a monogenic system if the force acting on the system can be modelled in a particular, especially convenient mathematical form. The systems that are typically studied in physics are monogenic. The term was introduced by Cornelius Lanczos in his book The Variational Principles of Mechanics (1970). In Lagrangian mechanics, the property of being monogenic is a necessary condition for certain different formulations to be mathematically equivalent. If a physical system is both a holonomic system and a monogenic system, then it is possible to derive Lagrange's equations from d'Alembert's principle; it is also possible to derive Lagrange's equations from Hamilton's principle. (Wikipedia).
What is the definition of a monomial and polynomials with examples
👉 Learn how to classify polynomials based on the number of terms as well as the leading coefficient and the degree. When we are classifying polynomials by the number of terms we will focus on monomials, binomials, and trinomials, whereas classifying polynomials by the degree will focus on
From playlist Classify Polynomials
Linear systems: 2 equations, 2 unknowns
Basic introduction on how to solve linear systems of equations. Several examples are discussed and geometrically depicted through Geogebra.
From playlist Intro to Linear Systems of Simultaneous Equations
Clustering 2: Monothetic vs polythetic
From playlist Clustering Algorithms
Voting Theory: Monotonicity Criterion Using Instant Runoff Voting
This video explains the Monotonicity Criterion and how it can affect the outcome of an election when using instant runoff voting. Site: http://mathispower4u.com
From playlist Voting Theory
Polynomials - Classifying Monomials, Binomials & Trinomials - Degree & Leading Coefficient
This algebra video tutorial provides a basic introduction into polynomials. It explains how to identify a monomial, binomial, and a trinomial according to the number of terms present in an algebraic expression. it also explains how to identify all of the terms in a polynomial as well as
From playlist New Algebra Playlist
Intro to Linear Systems: 2 Equations, 2 Unknowns - Dr Chris Tisdell Live Stream
Free ebook http://tinyurl.com/EngMathYT Basic introduction to linear systems. We discuss the case with 2 equations and 2 unknowns. A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that ar
From playlist Intro to Linear Systems
Non-monogenic Division Fields of Elliptic Curves, Hanson Smith
Abstract: This talk will serve as an exposition of a recent preprint investigating the division fields of elliptic curves. In this work we show that for various positive integers n there exist of infinite families of elliptic curves over Q with n-division fields, Q(E[n]), that are not mono
From playlist My Students
Ari Shnidman: Monogenic cubic fields and local obstructions
Recording during the meeting "Zeta Functions" the December 05, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http:
From playlist Number Theory
On Class Groups of Monogenic Fields
Short Talks by Postdoctoral Members Topic: On Class Groups of Monogenic Fields Speaker: Artane Jeremie Siad Affiliation: Member, School of Mathematics September 30, 2022
From playlist Short Talks by Postdoctoral Members
Kristin Lauter, Microsoft Research Redmond The Mathematics of Modern Cryptography http://simons.berkeley.edu/talks/kristin-lauter-2015-07-07
From playlist My Collaborators
Monogenic fields with odd class number - Artane Jeremie Siad
Joint IAS/Princeton University Number Theory Seminar Topic: Monogenic fields with odd class number Speaker: Artane Jeremie Siad Affiliation: Princeton University; Visitor, School of Mathematics Date: November 4, 2021 In this talk, we prove an upper bound on the average number of 2-torsi
From playlist Mathematics
Linear Algebra - Lecture 10 - Homogeneous Linear Systems
In this lecture, we define "homogeneous" linear systems, and discuss how to find the solutions to these systems in parametric vector form.
From playlist Linear Algebra Lectures
Affine symmetric spaces and 2-torsion in the class group of unit-monogenized cubic... - Artane Siad
Spring Opportunities Workshop 2023 Topic: Affine symmetric spaces and 2-torsion in the class group of unit-monogenized cubic fields Speaker:Artane Siad Affiliation: IAS Date: January 13, 2023 Davenport’s lemma has been a crucial ingredient in recent applications of geometry of numbers
From playlist Spring Opportunities Workshop 2023
Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
Arul Shankar, Ordering elliptic curves by conductor
VaNTAGe seminar, on Oct 27, 2020 License: CC-BY-NC-SA. Closed captions provided by Rachana Madhukara.
From playlist Rational points on elliptic curves
Do Your Genes Make You Fat? - with Giles Yeo
Are your genes to blame when your jeans don't fit? Giles Yeo explores the role of genetics in appetite control and obesity. Subscribe for regular science videos: http://bit.ly/RiSubscRibe Giles' book "Gene Eating" is available now - https://geni.us/jnNxw0p Watch the Q&A here: https://you
From playlist Ri Talks
Counting Low Degree Number Fields with Almost Prescribed Successive Minima - Sameera Vemulapalli
Joint IAS/PU Number Theory Seminar Topic: Counting Low Degree Number Fields with Almost Prescribed Successive Minima Speaker: Sameera Vemulapalli Affiliation: Princeton University Date: January 26, 2023 The successive minima of an order in a degree n number field are n real numbers encod
From playlist Mathematics
9.1 - Mental disorders: Explanations
"Evolutionary Medicine" Sinauer Associates (2015) is the textbook that supports these lectures. Instructors can request examination copies and sign up to download figures here: http://www.sinauer.com/catalog/medical/evolutionary-medicine.html
From playlist Evolution and Medicine (2015) with Stephen Stearns
Discrete-Time Dynamical Systems
This video shows how discrete-time dynamical systems may be induced from continuous-time systems. https://www.eigensteve.com/
From playlist Data-Driven Dynamical Systems