Singularity theory | Differential geometry | Contact geometry | Multivariable calculus
In mathematics, two functions have a contact of order k if, at a point P, they have the same value and k equal derivatives. This is an equivalence relation, whose equivalence classes are generally called jets. The point of osculation is also called the double cusp. Contact is a geometric notion; it can be defined algebraically as a valuation. One speaks also of curves and geometric objects having k-th order contact at a point: this is also called osculation (i.e. kissing), generalising the property of being tangent. (Here the derivatives are considered with respect to arc length.) An osculating curve from a given family of curves is a curve that has the highest possible order of contact with a given curve at a given point; for instance a tangent line is an osculating curve from the family of lines, and has first-order contact with the given curve; an osculating circle is an osculating curve from the family of circles, and has second-order contact (same tangent angle and curvature), etc. (Wikipedia).
10 Relations (still with the not-so-exciting-stuff)
This video introduces relations between pairs of elements.
From playlist Abstract algebra
Ask me any math questions you'd like, over the chat or the discord.
From playlist Ask Me Math!
Breakthrough Prize in Mathematics 2014
Breakthrough Prize in Mathematics 2014 recipients talking about mathematics
From playlist Actualités
Tangent Line of Curve Parallel to A Line Calculus 1 AB
I work through an example to explain how to find tangent lines to a function that are parallel to a given line. Find free review test, useful notes and more at http://www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channe
From playlist Calculus
From playlist Help! I'm Teaching Math (Series)
Abstract Algebra: The definition of a Ring
Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend th
From playlist Abstract Algebra
In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
#2 Idenitfying Irrational numbers
An example that helps in identifying irrational numbers and understanding the basic concepts of irrational numbers.
From playlist Middle School This Year
How do mathematicians model infectious disease outbreaks?
Models. They are dictating our Lockdown lives. But what is a mathematical model? We hear about the end result, but how is it put together? What are the assumptions? And how accurate can it be? In our first online only Oxford Mathematics Public Lecture Robin Thompson, Research Fellow in M
From playlist Oxford Mathematics Public Lectures
Further reading: Razak F. A & Expert P. Modelling the Spread of Covid-19 on Malaysian Contact Networks for Practical Reopening Strategies in an Institutional Setting, Sains Malaysiana (2021) 50(5): 1497-1509 https://arxiv.org/abs/2104.04156 https://www.ukm.my/jsm/pdf_files/SM-PDF-50-5-202
From playlist Summer of Math Exposition Youtube Videos
Smartphones will help save lives in a pandemic. Smartphones' value is exaggerated. Smartphones are compromising our privacy. What is the reality? And, as ever, what is the Maths behind it all? Leading Network Scientist Renaud Lambiotte downloads the facts in this Oxford Mathematics Public
From playlist Oxford Mathematics Public Lectures
RELATIONS - DISCRETE MATHEMATICS
We introduce relations. How to write them, what they are, and properties of relations including reflexivity, symmetry, and transitivity. #DiscreteMath #Mathematics #Relations Support me on Patreon: http://bit.ly/2EUdAl3 Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http:
From playlist Discrete Math 1
Vittoria Colizza: "Chasing the COVID-19 Pandemic through Modeling"
Mathematical Models in Understanding COVID-19 "Chasing the COVID-19 Pandemic through Modeling" Vittoria Colizza - INSERM - French National Institute of Health and Medical Research Institute for Pure and Applied Mathematics, UCLA August 10, 2020 For more information: https://www.ipam.ucl
From playlist Mathematical Models in Understanding COVID-19 2020
IMS Public Lecture : A History of Moving Contact Lines
Stephen H. Davis, Northwestern University, USA
From playlist 2018 Modeling and Simulation of Interface Dynamics in Fluids/Solids and Their Applications
Mathematical Models for Infectious Diseases by Gautam Menon
PROGRAM SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS (ONLINE) ORGANIZERS: Siva Athreya (ISI-Bengaluru, India), Purvi Gupta (IISc, India), Anita Naolekar (ISI-Bengaluru, India) and Dootika Vats (IIT-Kanpur, India) DATE: 14 June 2021 to 25 June 2021 VENUE: ONLINE The summer sch
From playlist Summer School for Women in Mathematics and Statistics (ONLINE) - 2021
Would you like to see some toys? 'Toys' here have a special sense: objects of daily life which you can find or make in minutes, yet which, if played with imaginatively, reveal surprises that keep scientists puzzling for a while. We will see table-top demos of many such toys and visit some
From playlist Mathematics Research Center
Presentation of the T2 2021 : "Symplectic topology, contact topology and interactions"
It has been more than 25 years ago that the previous thematic program on symplectic topology took place at Institut Henri Poincaré. Since then, the field has undergone a spectacular transformation earning itself a central position in the mathematical landscape. It interacts strongly with o
From playlist Centre Émile Borel - program presentations
Field Definition (expanded) - Abstract Algebra
The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They
From playlist Abstract Algebra
Eddie interviews Po-Shen Loh (3 of 3: Fighting a pandemic with mathematics)
Find out more about the NOVID app: https://www.novid.org Watch part 1, "Discovering a love for mathematics": https://youtu.be/B2Z19_M_v9M Watch part 2, "Life as a mathematician": https://youtu.be/xXs2eXnnGmI More resources available at www.misterwootube.com
From playlist Interviews & Media