Singularity theory | Algebraic geometry
In mathematics, properties that hold for "typical" examples are called generic properties. For instance, a generic property of a class of functions is one that is true of "almost all" of those functions, as in the statements, "A generic polynomial does not have a root at zero," or "A generic square matrix is invertible." As another example, a generic property of a space is a property that holds at "almost all" points of the space, as in the statement, "If f : M → N is a smooth function between smooth manifolds, then a generic point of N is not a critical value of f." (This is by Sard's theorem.) There are many different notions of "generic" (what is meant by "almost all") in mathematics, with corresponding dual notions of "almost none" (negligible set); the two main classes are: * In measure theory, a generic property is one that holds almost everywhere, with the dual concept being null set, meaning "with probability 0". * In topology and algebraic geometry, a generic property is one that holds on a dense open set, or more generally on a residual set, with the dual concept being a nowhere dense set, or more generally a meagre set. There are several natural examples where those notions are not equal. For instance, the set of Liouville numbers is generic in the topological sense, but has Lebesgue measure zero. (Wikipedia).
Complete Derivation: Universal Property of the Tensor Product
Previous tensor product video: https://youtu.be/KnSZBjnd_74 The universal property of the tensor product is one of the most important tools for handling tensor products. It gives us a way to define functions on the tensor product using bilinear maps. However, the statement of the universa
From playlist Tensor Products
Identify Multiplication Properties of Real Numbers
This video explains and provides examples of the properties of real numbers. http://mathispower4u.com
From playlist Number Sense - Properties of Real Numbers
Why does the distributive property Where does it come from
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
This video defines the properties of real numbers and then provides examples of the properties by rewriting and simplifying expressions. http://mathispower4u.com
From playlist Number Sense - Properties of Real Numbers
Introduction to the Distributive Property
This video explains the distributive property and provides examples on how to use the distributive property. http://mathispower4u.yolasite.com/
From playlist The Distributive Property and Simplifying Algebraic Expressions
Properties of Real Numbers: Mixed Review
This video explains and provides examples of the properties of real numbers. http://mathispower4u.com
From playlist Sets of Numbers/Properties of Real Numbers
Understanding CSS Custom Properties
Custom Properties are still a relatively new feature of CSS. Let me introduce you to the basics, some of the tricks and then show you how to use custom properties in CSS for maintainable large scale applications. Let's dive into some of the challenges of responsive design, global and local
From playlist Web Design: CSS / SVG
How to Learn the Basics of The Distributive Property
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Live CEOing Ep 681: Language Design in Wolfram Language [Ontologies]
In this episode of Live CEOing, Stephen Wolfram discusses upcoming improvements and features to the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfram
From playlist Behind the Scenes in Real-Life Software Design
Weak and strong ETH from the clustering property by Keiji Saito
PROGRAM THERMALIZATION, MANY BODY LOCALIZATION AND HYDRODYNAMICS ORGANIZERS: Dmitry Abanin, Abhishek Dhar, François Huveneers, Takahiro Sagawa, Keiji Saito, Herbert Spohn and Hal Tasaki DATE : 11 November 2019 to 29 November 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore How do is
From playlist Thermalization, Many Body Localization And Hydrodynamics 2019
[hgraph2graph] Hierarchical Generation of Molecular Graphs using Structural Motifs | AISC Spotlight
For slides and more information on the paper, visit https://aisc.ai.science/events/2020-02-26 Discussion lead: Wengong Jin Discussion facilitator(s): Rouzbeh Afrasiabi
From playlist Machine Learning for Scientific Discovery
What is quantum mechanics? A minimal formulation (Seminar) by Pierre Hohenberg
29 December 2017 VENUE : Ramanujan Lecture Hall, ICTS , Bangalore This talk asks why the interpretation of quantum mechanics, in contrast to classical mechanics is still a subject of controversy, and presents a 'minimal formulation' modeled on a formulation of classical mechanics. In bot
From playlist US-India Advanced Studies Institute: Classical and Quantum Information
MIT 3.60 | Lec 15b: Symmetry, Structure, Tensor Properties of Materials
Part 2: Space Group Notation and Tensors View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material
Lefschetz Without Positivity: An Overview - Karim Alexander Adiprasito
Members' Colloquium Topic: Lefschetz Without Positivity: An Overview Speaker: Karim Alexander Adiprasito Affiliation: Hebrew University of Jerusalem, Member, School of Mathematics Date: February 6, 2023 2:00pm|Simonyi Hall 101 and Remote Access - see Zoom link below The Lefschetz propert
From playlist Mathematics
Geometry of tropical varieties with a view toward applications (Lecture 4) 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 & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
The Distributive Property for Arithmetic
We know about the commutative property and the associative property, but there are more to learn! This next one, the distributive property, is very important in algebra, so let's introduce it now so that when we get there we already have this covered. Watch the whole Mathematics playlist:
From playlist Mathematics (All Of It)
Commutative algebra 38 Survey of module properties
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give a short survey of some of the properties of modules, in particular free, stably free, Zariski locally free, projectiv
From playlist Commutative algebra