In mathematics, the transcendental law of homogeneity (TLH) is a heuristic principle enunciated by Gottfried Wilhelm Leibniz most clearly in a 1710 text entitled Symbolismus memorabilis calculi algebraici et infinitesimalis in comparatione potentiarum et differentiarum, et de lege homogeneorum transcendentali. Henk J. M. Bos describes it as the principle to the effect that in a sum involving infinitesimals of different orders, only the lowest-order term must be retained, and the remainder discarded. Thus, if is finite and is infinitesimal, then one sets Similarly, where the higher-order term du dv is discarded in accordance with the TLH. A recent study argues that Leibniz's TLH was a precursor of the standard part function over the hyperreals. (Wikipedia).
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory
Transcendental numbers powered by Cantor's infinities
In today's video the Mathologer sets out to give an introduction to the notoriously hard topic of transcendental numbers that is both in depth and accessible to anybody with a bit of common sense. Find out how Georg Cantor's infinities can be used in a very simple and off the beaten track
From playlist Recent videos
Homotopy Group - (1)Dan Licata, (2)Guillaume Brunerie, (3)Peter Lumsdaine
(1)Carnegie Mellon Univ.; Member, School of Math, (2)School of Math., IAS, (3)Dalhousie Univ.; Member, School of Math April 11, 2013 In this general survey talk, we will describe an approach to doing homotopy theory within Univalent Foundations. Whereas classical homotopy theory may be des
From playlist Mathematics
Maxim Kazarian - 1/3 Mathematical Physics of Hurwitz numbers
Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num
From playlist Physique mathématique des nombres de Hurwitz pour débutants
Introduction to Homotopy Theory- Part 5- Transition to Abstract Homotopy Theory
Credits: nLab: https://ncatlab.org/nlab/show/Introdu... Animation library: https://github.com/3b1b/manim Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remember (Extended Mix)" • YouTube Track Link: https://bit.ly/31Ma5s0 • Spotify Track Link: https://spoti.fi/
From playlist Introduction to Homotopy Theory
Maxim Kazarian - 2/3 Mathematical Physics of Hurwitz numbers
Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num
From playlist Physique mathématique des nombres de Hurwitz pour débutants
https://www.math.ias.edu/files/media/agenda.pdf More videos on http://video.ias.edu
From playlist Mathematics
U. Brehm: A Universality Theorem for Realization Spaces of Polyhedral Maps
U. Brehms lecture was held within the framework of the Hausdorff Trimester Program Universality and Homogeneity during the special seminar "Universality of moduli spaces and geometry" (06.11.2013) Due to an error with the recording, there is no video available for this lecture.
From playlist HIM Lectures: Trimester Program "Universality and Homogeneity"
Greg Pavliotis (DDMCS@Turing): Phase transitions for mean field limits of noisy interacting agents
Complex models in all areas of science and engineering, and in the social sciences, must be reduced to a relatively small number of variables for practical computation and accurate prediction. In general, it is difficult to identify and parameterize the crucial features that must be incorp
From playlist Data driven modelling of complex systems
Homotopy elements in the homotopy group π₂(S²) ≅ ℤ. Roman Gassmann and Tabea Méndez suggested some improvements to my original ideas.
From playlist Algebraic Topology
03/22/19 Varadharaj Ravi Srinivasan
Integration in Finite Terms: Error Functions, Logarithmic Integrals and Polylogarithmic Integrals
From playlist Spring 2019 Kolchin Seminar
Calculus 17.3 Applications of Second-Order Differential Equations
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Charlotte Hardouin: Galois theory and walks in the quarter plane
Abstract: In the recent years, the nature of the generating series of walks in the quarter plane has attracted the attention of many authors in combinatorics and probability. The main questions are: are they algebraic, holonomic (solutions of linear differential equations) or at least hype
From playlist Combinatorics
Yuri Manin - Numbers as functions
Numbers as functions
From playlist 28ème Journées Arithmétiques 2013
CTNT 2020 - Elliptic curves and the local-global principle for quadratic forms - Asher Auel
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
Rational Methods in Euclidean and Non-Euclidean Geometries
Presenter: Norman Wildberger, UNSW.
From playlist UNSW Mini Workshop: From Novosibirsk to Sydney
Thieu Vo, Ton Duc Thang University
April 2, Thieu Vo, Ton Duc Thang University Rational solutions of first-order algebraic difference equations
From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra
What is a Group Homomorphism? Definition and Example (Abstract Algebra)
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys What is a Group Homomorphism? Definition and Example (Abstract Algebra)
From playlist Abstract Algebra