11_7_1 Potential Function of a Vector Field Part 1
The gradient of a function is a vector. n-Dimensional space can be filled up with countless vectors as values as inserted into a gradient function. This is then referred to as a vector field. Some vector fields have potential functions. In this video we start to look at how to calculat
From playlist Advanced Calculus / Multivariable Calculus
Field Theory - Algebraically Closed Fields - Lecture 9
In this video we define what an algebraically closed field and assert without proof that they exist. We also explain why if you can find a single root for any polynomial, then you can find them all.
From playlist Field Theory
Functions of equations - IS IT A FUNCTION
👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Field Theory: We consider the property of algebraic in terms of finite degree, and we define algebraic numbers as those complex numbers that are algebraic over the rationals. Then we give an overview of algebraic numbers with examples.
From playlist Abstract Algebra
Definition of a Field In this video, I define the concept of a field, which is basically any set where you can add, subtract, add, and divide things. Then I show some neat properties that have to be true in fields. Enjoy! What is an Ordered Field: https://youtu.be/6mc5E6x7FMQ Check out
From playlist Real Numbers
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
algebraic geometry 31 Rational maps
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of rational functions and rational maps, and gives an example of a cubic curve that is not birational to the affine line.
From playlist Algebraic geometry I: Varieties
Determine if a Relation is a Function
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From playlist Intro to Functions
Determine if a Function is a Polynomial Function
This video explains how to determine if a function is a polynomial function. http://mathispower4u.com
From playlist Determining the Characteristics of Polynomial Functions
Alberto Cattaneo: An introduction to the BV-BFV Formalism
Abstract: The BV-BFV formalism unifies the BV formalism (which deals with the problem of fixing the gauge of field theories on closed manifolds) with the BFV formalism (which yields a cohomological resolution of the reduced phase space of a classical field theory). I will explain how this
From playlist Topology
Pre-recorded lecture 16: Frolicher-Nijenhuis bracket and Frolicher-Nijenhuis cohomology
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Galois theory: Transcendental extensions
This lecture is part of an online graduate course on Galois theory. We describe transcendental extension of fields and transcendence bases. As applications we classify algebraically closed fields and show hw to define the dimension of an algebraic variety.
From playlist Galois theory
Elliptic Curves - Lecture 4a - Varieties, function fields, dimension
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Sebastian Eterović, UC Berkeley
April 12, Sebastian Eterović, UC Berkeley Existential Closedness and Differential Algebra
From playlist Spring 2022 Online Kolchin seminar in Differential Algebra
On the notion of genus for division algebras and algebraic groups - Andrei Rapinchu
Joint IAS/Princeton University Number Theory Seminar Topic: On the notion of genus for division algebras and algebraic groups Speaker: Andrei Rapinchu Affiliation: University of Virginia Date: November 2, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
What is a Tensor? Lesson 20: Algebraic Structures II - Modules to Algebras
What is a Tensor? Lesson 20: Algebraic Structures II - Modules to Algebras We complete our survey of the basic algebraic structures that appear in the study of general relativity. Also, we develop the important example of the tensor algebra.
From playlist What is a Tensor?
Determine the Domain of Various Functions
This video explains how to determine the domain of various functions including linear, quadratic, square root, cube root, cubic, absolute value, and rational functions. http://mathispower4u.com
From playlist The Properties of Functions