Set theory | Abstract algebra | Closure operators
In mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction: 1 − 2 is not a natural number, although both 1 and 2 are. Similarly, a subset is said to be closed under a collection of operations if it is closed under each of the operations individually. The closure of a subset is the result of a closure operator applied to the subset. The closure of a subset under some operations is the smallest subset that is closed under these operations. It is often called the span (for example linear span) or the generated set. (Wikipedia).
Closed Intervals, Open Intervals, Half Open, Half Closed
00:00 Intro to intervals 00:09 What is a closed interval? 02:03 What is an open interval? 02:49 Half closed / Half open interval 05:58 Writing in interval notation
From playlist Calculus
Galois theory: Algebraic closure
This lecture is part of an online graduate course on Galois theory. We define the algebraic closure of a field as a sort of splitting field of all polynomials, and check that it is algebraically closed. We hen give a topological proof that the field C of complex numbers is algebraically
From playlist Galois theory
Javascript Closures Tutorial - What makes Javascript Weird...and Awesome Pt 3
What is a closure? In this Javascript Tutorial, we're going to be learning about closures - our 3rd most misunderstood concept of Javascript. Watch the full playlist: https://www.youtube.com/playlist?list=PLoYCgNOIyGABI011EYc-avPOsk1YsMUe_ Hopefully, we're going to break it down enough t
From playlist Javascript Tutorial For Beginners
Closure of Sets (Allegra's Question)
clarifying the idea of closure of a set under an operation
From playlist Middle School This Year
All About Closed Sets and Closures of Sets (and Clopen Sets) | Real Analysis
We introduced closed sets and clopen sets. We'll visit two definitions of closed sets. First, a set is closed if it is the complement of some open set, and second, a set is closed if it contains all of its limit points. We see examples of sets both closed and open (called "clopen sets") an
From playlist Real Analysis
Commutative Algebra - Integral Closures - part 01 - Basics
This is a video for a second semester graduate algebra class.
From playlist Integral Closures
Understanding the basic principles of closure for natural numbers
From playlist Geometry
Reconsidering `functions' in modern mathematics | Arithmetic and Geometry Math Foundations 43
The general notion of `function' does not work in mathematics, just as the general notions of `number' or `sequence' don't work. This video explains the distinction between `closed' and `open' systems, and suggests that mathematical definitions should respect the open aspect of mathemat
From playlist Math Foundations
Clojure Conj 2012 - Clojure Data Science
Clojure Data Science by: Edmund Jackson Data science / big data exists at the overlap of traditional analytics and large scale computation. As such, neither the traditional tools of analytics (R, Mathematica, Matlab) nor mainstreams languages (Java, C++, C#) supply its requirements well a
From playlist Clojure Conf 2012
DDPS | Large Eddy Simulation Reduced Order Models
Talk Abstract Large eddy simulation (LES) is one of the most popular methods for the numerical simulation of turbulent flows. In this talk, we survey our group's efforts over the last decade to develop a large eddy simulation reduced order modeling (LES-ROM) framework for the numerical s
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
In this Wolfram Technology Conference presentation, Seth Chandler explores the practicalities of using J/Link to establish Mathematica as a communications hub among code developed in Clojure, Scala, and Jython. For more information about Mathematica, please visit: http://www.wolfram.com/m
From playlist Wolfram Technology Conference 2012
Stochastic and Deterministic Models for Tropical Convection - Boualem Khouider
Stochastic and Deterministic Models for Tropical Convection Boualem Khouider, U.Victoria, Canada. DISCUSSION MEETING: MATHEMATICAL PERSPECTIVES ON CLOUDS, CLIMATE, AND TROPICAL METEOROLOGY MONDAY, 21 JANUARY, 2013 (PART 4)
From playlist Mathematical Perspectives on Clouds, Climate, and Tropical Meteorology
Upscaling and Automation: New Opportunities for Multiscale Systems Modeling
SIAM Geosciences Webinar Series Date and Time: Wednesday, March 8, 2023, 12:00pm Eastern time zone Speaker: Ilenia Battiato, Stanford University Abstract: The accurate modeling of energy and geologic systems has challenged generations of computational physicists due to the mathematical an
From playlist SIAM Geosciences Webinar Series
Metric Spaces - Lectures 11 & 12: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 6th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
The Essence of Functional Programming
This talk dives into the origins of functional programming, going all the way back to where the term was first introduced, to see how it evolved over time into our modern understanding of what FP essentially involves. PUBLICATION PERMISSIONS: Original video was published with the Creative
From playlist Functional Programming
Gary Gordon and Liz McMahon: Generalizations of Crapo's Beta Invariant
Abstract: Crapo's beta invariant was defined by Henry Crapo in the 1960s. For a matroid M, the invariant β(M) is the non-negative integer that is the coefficient of the x term of the Tutte polynomial. Crapo proved that β(M) is greater than 0 if and only if M is connected and M is not a loo
From playlist Combinatorics
Super-approximation I - Alireza Salehi Golsefidy
Speaker: Alireza Salehi Golsefidy (UCSD) Title: Super-approximation I Abstract: Let Γ be a finitely generated subgroup of a compact group G. 1. I will recall what it means to say the action of Γ on G by left translation has spectral gap, and mention some examples and applications, e.g. Ban
From playlist Mathematics
Calculus: Absolute Maximum and Minimum Values
In this video, we discuss how to find the absolute maximum and minimum values of a function on a closed interval.
From playlist Calculus
Yoshinori Namikawa: Symplectic singularities and nilpotent orbits
Abstract: I will characterzize, among conical symplectic varieties, the nilpotent orbit closures of a complex semisimple Lie algebra and their finite coverings. Recording during the meeting "Symplectic Representation Theory" the April 3, 2019 at the Centre International de Rencontres Math
From playlist Algebraic and Complex Geometry