23 Algebraic system isomorphism
Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.
From playlist Abstract algebra
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra
Ch02n2: Aitken-Neville Interpolation
Aitken-Neville Interpolation Numerical Methods, chapter 2, additional video no 2. To be viewed after the video ch2.5. Wen Shen, Penn State University, 2018.
From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University
Put all three properties of binary relations together and you have an equivalence relation.
From playlist Abstract algebra
Creating a Calorimeter: Using Mathematica to Measure Dielectric Loss
As a researcher at the Electrical Engineering Lab of Grenoble, Frederic Aitken studies discharge in insulating liquids in order to understand the defects associated with high-voltage transformers. This requires the ability to quickly analyze experimental data and compare it to theoretical
From playlist Customer Stories
Successive Parabolic Interpolation - Jarratt's Method
Optimization method for finding extrema of functions using three points to create a parabola that is then used to find the next approximation to the solution. This lesson visualizes the behavior of the method with numeric examples as well as its convergence through fractals. Based off the
From playlist Numerical Methods
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Complex Numbers Explained | An Introduction to Complex Numbers
In this video, we look at an introduction to complex numbers. We show why it is necessary to consider i = sqrt(-1) and complex numbers, based on Gauss' fundamental theorem of algebra. We work through examples of adding complex numbers, multiplying complex numbers, dividing complex numbers,
From playlist Complex Numbers
Generalized Aitken-Steffensen Method
Generalized Aitken's delta-squared method and Generalized Steffensen's Method applying Fixed Point Iteration to Systems of Nonlinear Equations. Video goes step-by-step to derive Generalized Aitken-Steffensen and discusses induced and accelerated convergence behavior as well as quadratic or
From playlist Solving Systems of Nonlinear Equations
Steffensen's Method with Aitken's Δ²
Discussion of Steffensen's Method and Aitken's Delta-Squared Method with their relation to Fixed Point Iteration including examples, convergence acceleration, order, and code. GitHub: https://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:08 Aitken's Δ² Method History 0:23 Deriv
From playlist Root Finding
Ex: Evaluate a Combination and a Permutation - (n,r)
This video explains how to evaluate a combination and a permutation with the same value of n and r. Site: http://mathispower4u.com
From playlist Permutations and Combinations
The Massive Chunk of Metal Hiding in the Moon
The moon's South Pole-Aitken basin is the largest known crater in existence, and there's something big hidden underneath. Hosted By: Reid Reimers SciShow is on TikTok! Check us out at https://www.tiktok.com/@scishow ---------- Support SciShow Space by becoming a patron on Patreon: https
From playlist SciShow Space
Equivalence Relations Definition and Examples
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.
From playlist Abstract Algebra
Fixed Point Iteration method for finding roots of functions. Frequently Asked Questions: Where did 1.618 come from? If you keep iterating the example will eventually converge on 1.61803398875... which is (1+sqrt(5))/2. Why not use x = x^2 -1? Generally you try to reduce the degree of the
From playlist Root Finding
Permutation Groups and Symmetric Groups | Abstract Algebra
We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory We will see the
From playlist Abstract Algebra
Steffensen's Method for Systems of Nonlinear Equations
Generalized Steffensen's Method for Simultaneous Nonlinear Systems originally credited to J. F. Traub. Video shows how to solve nonlinear systems by approximating the Jacobian. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Prerequisites 0:20 Intro 0:
From playlist Solving Systems of Nonlinear Equations
Isomorphisms (Abstract Algebra)
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same. Be sure to subscribe s
From playlist Abstract Algebra
Fixed Point Iteration System of Equations with Banach
Fixed Point Iteration Method to solve Systems of Nonlinear Equations with discussion of Banach Fixed Point Theorem, finding the Jacobian, convergence, and order. Example code on GitHub: http://github.com/osveliz/numerical-veliz Chapters: 00:00 Intro 00:25 Systems of Equations 00:33 Solvin
From playlist Solving Systems of Nonlinear Equations
Tutorial - Dividing complex numbers ex 17, (-2 - 5i)/3i
http://www.freemathvideos.com In this video series I will show you how divide complex numbers. We do this by eliminating the imaginary number on the denominator by producing equivalent fractions. We do this by multiplying i if we have an imaginary number on the denominator and multiplyin
From playlist Complex Numbers
What We Know, And Still Don’t Know, About the Dark Side of the Moon | Compilation
More than a classic rock album that'll change your life, this classic space rock has a dark side that has mystified scientists for centuries. Hosted by: Hank Green ---------- Huge thanks go to the following Patreon supporter for helping us keep SciShow Space free for everyone forever: Jas
From playlist SciShow Space