In mathematics, the notion of a germ of an object in/on a topological space is an equivalence class of that object and others of the same kind that captures their shared local properties. In particular, the objects in question are mostly functions (or maps) and subsets. In specific implementations of this idea, the functions or subsets in question will have some property, such as being analytic or smooth, but in general this is not needed (the functions in question need not even be continuous); it is however necessary that the space on/in which the object is defined is a topological space, in order that the word local has some meaning. (Wikipedia).
Integers – Easy, Clear and Understandable Definition
TabletClass Math: https://tcmathacademy.com/ Math help with integers and real numbers. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes: https://ta
From playlist GED Prep Videos
Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
Analyzing Sets of Data: Range, Mean, Median, and Mode
What does the word "average" mean to you? There are a lot ways we use that word, and even in math, it can imply a few different things. If we want to summarize a set of data in a meaningful way, we can talk about the mean, the median, or the mode, and one might be more useful than another
From playlist Mathematics (All Of It)
Finding Eigenvalues and Eigenvectors
In studying linear algebra, we will inevitably stumble upon the concept of eigenvalues and eigenvectors. These sound very exotic, but they are very important not just in math, but also physics. Let's learn what they are, and how to find them! Script by Howard Whittle Watch the whole Math
From playlist Mathematics (All Of It)
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
Geometry: Ch 5 - Proofs in Geometry (2 of 58) Definitions
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give examples of definitions. Next video in this series can be seen at: https://youtu.be/-Pmkhgec704
From playlist GEOMETRY 5 - PROOFS IN GEOMETRY
Quantum Mechanics -- a Primer for Mathematicians
Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w
From playlist Mathematics
Walter Neumann: Lipschitz embedding of complex surfaces
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Volodymyr Nekrashevych: Contracting self-similar groups and conformal dimension
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 20, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM'
From playlist Dynamical Systems and Ordinary Differential Equations
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Connor McCranie and Markus Pflaum (2/25/20): Catastrophe theory
Title: Catastrophe theory Abstract: We given an introduction to catastrophe theory by René Thom. After briefly defining what degenerate and non-degnerate critical points of a smooth function are we introduce the algebra of germs of smooth real-valued functions and describe singular germs
From playlist DELTA (Descriptors of Energy Landscape by Topological Analysis), Webinar 2020
http://www.teachastronomy.com/ Cosmology is the study of the universe, its history, and everything in it. It comes from the Greek root of the word cosmos for order and harmony which reflected the Greek belief that the universe was a harmonious entity where everything worked in concert to
From playlist 22. The Big Bang, Inflation, and General Cosmology
Alex Wilkie: On complex continuations of functions definable in ℝan,exp with a diophantine [...]
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Logic and Foundations
Jean Écalle - Resurgence’s two Main Types and Their Signature Complications...
Resurgence’s two Main Types and Their Signature Complications: Tessellation, Isography, Autarchy Quite specific challenges attend the move from equational resurgence (i.e. resurgence in a singular variable –the main type in frequency and importance) to coequational re
From playlist Resurgence in Mathematics and Physics
13. Contagionism versus Anticontagionsim
Epidemics in Western Society Since 1600 (HIST 234) The debate between contagionists and anticontagionists over the transmission of infectious diseases played a major role in nineteenth-century medical discourse. On the one side were those who believed that diseases could be spread by in
From playlist Epidemics in Western Society Since 1600 with Frank Snowden
2020.06.04 Alison Etheridge - Branching Brownian motion, mean curvature flow and hybrid zones
Hybrid zones are narrow regions in which two genetically distinct populations come together and interbreed, resulting in hybrids. They may be maintained by an abrupt change in the environment or because of natural selection against the hybrids, in which case the location of the zone can ch
From playlist One World Probability Seminar
Aurélien Tellier: Plant ecology influences population genetics: the role of seed banks in [...]
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
Universality of Resurgence in Quantization Theories - 13 June 2018
http://crm.sns.it/event/433 Universality of Resurgence in Quantization Theories Recent mathematical progress in the modern theory of resurgent asymptotic analysis (using trans-series and alien calculus) has recently begun to be applied systematically to many current problems of interest,
From playlist Centro di Ricerca Matematica Ennio De Giorgi
Steven Kleiman - "Equisingularity of germs of isolated singularities"
Steven Kleiman delivers a research lecture at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
The Bridge Between Math and Quantum Field Theory
Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, reveals where math and QFT converge. Read more at Quanta: https://www.quantamagazine.org/nathan-seiberg-on-how-math-might-reveal-quantum-
From playlist Inside the Mind of a Scientist