Let A be a set (of the elements of an algebra ), and let E be an equivalence relation on the set A. The relation E is said to be compatible with (or have the substitution property with respect to) an n-ary operation f if for all whenever implies . An equivalence relation compatible with all the operations of an algebra is called a congruence.
Quotient algebras and homomorphisms
A set A can be partitioned in equivalence classes given by an equivalence relation E, and usually called a quotient set, and denoted A/E. For an algebra , it is straightforward to define the operations induced on A/E if E is a congruence. Specifically, for any operation of arity in (where the superscript simply denotes that it's an operation in ) define as , where denotes the equivalence class of a modulo E.
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term abstract algebra was coined in the early 20th century to distinguish this area of study from the other parts of algebra.
Universal algebra is a related subject that studies the nature and theories of various types of algebraic structures as a whole. For example, universal algebra studies the overall theory of groups, as distinguished from studying particular groups.
History
As in other parts of mathematics, concrete problems and examples have played important roles in the development of abstract algebra. Through the end of the nineteenth century, many -- perhaps most -- of these problems were in some way related to the theory of algebraic equations. Major themes include:
Chapter 5: Quotient groups | Essence of Group Theory
Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory!
In fact, the concept of quotient groups is one way to define modular arithmetic formally, which allows us to prove a lot of number theory theorems once we draw parallels between group theory and number theory. For example, Fermat's little theorem and Euler's totient theorem are just corollaries of the Lagrange's theorem introduced in Chapter 3 of the video series.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for yo...
published: 01 Apr 2020
Powers of Quotients | Expressions & Equations | Grade 8
#MathIsSimple #Grade8 #Exponents #Expressions #Algebra
Powers of Quotients | Expressions & Equations | Grade 8
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published: 05 May 2020
Normal Subgroups and Quotient Groups (aka Factor Groups) - Abstract Algebra
Normal subgroups are a powerful tool for creating factor groups (also called quotient groups). In this video we introduce the concept of a coset, talk about which subgroups are “normal” subgroups, and show when the collection of cosets can be treated as a group of their own. As a motivation, we will begin by discussing congruences.
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published: 15 Dec 2018
Algebra - Quotient rule for exponents
This video show how to use the quotient rule for exponents. Remember that when using the quotient rule we can subtract the exponents. For more videos visit http://www.mysecretmathtutor.com
published: 30 Aug 2011
Quotient Groups and Homomorphic Images | Abstract Algebra
We introduce quotient groups/factor groups. The quotient group of a group G by a normal subgroup H is the set of all cosets of H in G with the operation of coset multiplication. We prove the quotient group construction is indeed a group, and that it is a homomorphic image of the containing group. Thus, quotient groups give us a way to construct homomorphic images of a group. #abstractalgebra #grouptheory
Normal Subgroups: https://youtu.be/kbT5SyF3H60
Left and Right Cosets in Normal Subgroups: https://youtu.be/XOu1zFutrMY
Coset Multiplication on Normal Subgroups: https://youtu.be/DJyOdMBUdnM
Fundamental Homomorphism Theorem: https://youtu.be/wtK1h9TIDCY
Abstract Algebra Course: https://www.youtube.com/playlist?list=PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN
Abstract Algebra Exercises: https://ww...
published: 23 Jun 2023
01 - Simplify Expressions w/ Exponents in Algebra (Quotients of Monomials) - Part 1
View more at http://www.MathTutorDVD.com.
In this lesson, we will learn how to simplify exponent expressions in algebra. Simplifying expressions is a crucial skill because it is used when solving equations, solving and graphing inequalities, radical expressions, factoring, and more.
First, you will learn that this type of problem is also called finding the quotient of two monomials. Next, you will learn how to cancel exponent terms from the numerator and denominator in the algebraic expression. Lastly, we will simplify any numbers present to get the final answer.
published: 21 Mar 2019
Which expression represent the quotient [Algebra | Division of Fraction]
#CollegeEntranceTest
published: 13 Sep 2020
How to find the quotient between two polynomials
👉 Learn how to divide polynomials by quadratic divisors using the long division algorithm. Before dividing a polynomial, it is usually important to arrange the divisor in the descending order of powers of the variable(s). To divide a polynomial by a quadratic divisor using the long division algorithm, we divide the polynomial (dividend) with the quadratic term of the divisor to get a term of the quotient. We will then multiply all the terms of the divisor by the term of the quotient and subtract the result from the dividend. The result is divided again by the quadratic term of the divisor to get another term of the quotient. This process is repeated until the quadratic term of the divisor can no longer divide into the dividend.
The result after subtracting the product of the last term of t...
published: 15 Nov 2016
Factoring Trinomials #maths #ai
This video provides a straightforward, step-by-step guide on factoring trinomials. You’ll discover how to identify two numbers that sum to the middle term and multiply to the product of the first and last coefficients. We’ll walk you through breaking down the middle term, grouping the terms, and completing the factorization process. Perfect for students or anyone wanting to improve their algebra skills.
Music by Vincent Rubinetti
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published: 04 Nov 2024
What is...a quotient vector space?
Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...a quotient vector space? Or: Identifying information.
Slides.
http://www.dtubbenhauer.com/youtube.html
#linearalgebra
#algebra
#mathematics
Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem...
Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory!
In fact, the concept of quotient groups is one way to define modular arithmetic formally, which allows us to prove a lot of number theory theorems once we draw parallels between group theory and number theory. For example, Fermat's little theorem and Euler's totient theorem are just corollaries of the Lagrange's theorem introduced in Chapter 3 of the video series.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
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Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory!
In fact, the concept of quotient groups is one way to define modular arithmetic formally, which allows us to prove a lot of number theory theorems once we draw parallels between group theory and number theory. For example, Fermat's little theorem and Euler's totient theorem are just corollaries of the Lagrange's theorem introduced in Chapter 3 of the video series.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
SUBSCRIBE and see you in the next video!
#mathemanic #grouptheory #abstractalgebra #quotientgroup #intuition
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Facebook: https://www.facebook.com/mathemaniacyt
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#MathIsSimple #Grade8 #Exponents #Expressions #Algebra
Powers of Quotients | Expressions & Equations | Grade 8
Like to learn more math problems from Middle Sch...
#MathIsSimple #Grade8 #Exponents #Expressions #Algebra
Powers of Quotients | Expressions & Equations | Grade 8
Like to learn more math problems from Middle School to Algebra on Math is Simple!,
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#8EEA1 #Math #PowersofQuotient #TakingThePainOutOfMath
#MathIsSimple #Grade8 #Exponents #Expressions #Algebra
Powers of Quotients | Expressions & Equations | Grade 8
Like to learn more math problems from Middle School to Algebra on Math is Simple!,
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#8EEA1 #Math #PowersofQuotient #TakingThePainOutOfMath
Normal subgroups are a powerful tool for creating factor groups (also called quotient groups). In this video we introduce the concept of a coset, talk about wh...
Normal subgroups are a powerful tool for creating factor groups (also called quotient groups). In this video we introduce the concept of a coset, talk about which subgroups are “normal” subgroups, and show when the collection of cosets can be treated as a group of their own. As a motivation, we will begin by discussing congruences.
Our Abstract Algebra playlist is here:
http://bit.ly/AbstractAlgebraSocratica
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Dummit & Foote, Abstract Algebra 3rd Edition
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Produced by Kimberly Hatch Harrison
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Normal subgroups are a powerful tool for creating factor groups (also called quotient groups). In this video we introduce the concept of a coset, talk about which subgroups are “normal” subgroups, and show when the collection of cosets can be treated as a group of their own. As a motivation, we will begin by discussing congruences.
Our Abstract Algebra playlist is here:
http://bit.ly/AbstractAlgebraSocratica
Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W
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Thank you!
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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
http://www.jmilne.org/math/CourseNotes/index.html
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Connect with us!
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Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
♦♦♦♦♦♦♦♦♦♦
This video show how to use the quotient rule for exponents. Remember that when using the quotient rule we can subtract the exponents. For more videos visit htt...
This video show how to use the quotient rule for exponents. Remember that when using the quotient rule we can subtract the exponents. For more videos visit http://www.mysecretmathtutor.com
This video show how to use the quotient rule for exponents. Remember that when using the quotient rule we can subtract the exponents. For more videos visit http://www.mysecretmathtutor.com
We introduce quotient groups/factor groups. The quotient group of a group G by a normal subgroup H is the set of all cosets of H in G with the operation of cose...
We introduce quotient groups/factor groups. The quotient group of a group G by a normal subgroup H is the set of all cosets of H in G with the operation of coset multiplication. We prove the quotient group construction is indeed a group, and that it is a homomorphic image of the containing group. Thus, quotient groups give us a way to construct homomorphic images of a group. #abstractalgebra #grouptheory
Normal Subgroups: https://youtu.be/kbT5SyF3H60
Left and Right Cosets in Normal Subgroups: https://youtu.be/XOu1zFutrMY
Coset Multiplication on Normal Subgroups: https://youtu.be/DJyOdMBUdnM
Fundamental Homomorphism Theorem: https://youtu.be/wtK1h9TIDCY
Abstract Algebra Course: https://www.youtube.com/playlist?list=PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN
Abstract Algebra Exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVQNtNnXeHB_1yquKUY98Xz
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Graph Theory: https://amzn.to/3JHQtZj
Real Analysis: https://amzn.to/3CMdgjI
Abstract Algebra: https://amzn.to/3IjoZaO
Linear Algebra: https://amzn.to/43xAWEz
Calculus: https://amzn.to/3PieD1M
Proofs and Set Theory: https://amzn.to/367VBXP (available for free online)
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We introduce quotient groups/factor groups. The quotient group of a group G by a normal subgroup H is the set of all cosets of H in G with the operation of coset multiplication. We prove the quotient group construction is indeed a group, and that it is a homomorphic image of the containing group. Thus, quotient groups give us a way to construct homomorphic images of a group. #abstractalgebra #grouptheory
Normal Subgroups: https://youtu.be/kbT5SyF3H60
Left and Right Cosets in Normal Subgroups: https://youtu.be/XOu1zFutrMY
Coset Multiplication on Normal Subgroups: https://youtu.be/DJyOdMBUdnM
Fundamental Homomorphism Theorem: https://youtu.be/wtK1h9TIDCY
Abstract Algebra Course: https://www.youtube.com/playlist?list=PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN
Abstract Algebra Exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVQNtNnXeHB_1yquKUY98Xz
◉Textbooks I Like◉
Graph Theory: https://amzn.to/3JHQtZj
Real Analysis: https://amzn.to/3CMdgjI
Abstract Algebra: https://amzn.to/3IjoZaO
Linear Algebra: https://amzn.to/43xAWEz
Calculus: https://amzn.to/3PieD1M
Proofs and Set Theory: https://amzn.to/367VBXP (available for free online)
Statistics: https://amzn.to/3tsaEER
Discrete Math: https://amzn.to/3qfhoUn
Number Theory: https://amzn.to/3JqpOQd
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Thanks to Loke Tan, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Roslyn Goddard, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon!
Outro music is mine. You cannot find it anywhere, for now.
Follow Wrath of Math on...
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View more at http://www.MathTutorDVD.com.
In this lesson, we will learn how to simplify exponent expressions in algebra. Simplifying expressions is a crucial s...
View more at http://www.MathTutorDVD.com.
In this lesson, we will learn how to simplify exponent expressions in algebra. Simplifying expressions is a crucial skill because it is used when solving equations, solving and graphing inequalities, radical expressions, factoring, and more.
First, you will learn that this type of problem is also called finding the quotient of two monomials. Next, you will learn how to cancel exponent terms from the numerator and denominator in the algebraic expression. Lastly, we will simplify any numbers present to get the final answer.
View more at http://www.MathTutorDVD.com.
In this lesson, we will learn how to simplify exponent expressions in algebra. Simplifying expressions is a crucial skill because it is used when solving equations, solving and graphing inequalities, radical expressions, factoring, and more.
First, you will learn that this type of problem is also called finding the quotient of two monomials. Next, you will learn how to cancel exponent terms from the numerator and denominator in the algebraic expression. Lastly, we will simplify any numbers present to get the final answer.
👉 Learn how to divide polynomials by quadratic divisors using the long division algorithm. Before dividing a polynomial, it is usually important to arrange the ...
👉 Learn how to divide polynomials by quadratic divisors using the long division algorithm. Before dividing a polynomial, it is usually important to arrange the divisor in the descending order of powers of the variable(s). To divide a polynomial by a quadratic divisor using the long division algorithm, we divide the polynomial (dividend) with the quadratic term of the divisor to get a term of the quotient. We will then multiply all the terms of the divisor by the term of the quotient and subtract the result from the dividend. The result is divided again by the quadratic term of the divisor to get another term of the quotient. This process is repeated until the quadratic term of the divisor can no longer divide into the dividend.
The result after subtracting the product of the last term of the quotient and the divisor is the remainder when the divisor divides the original polynomial. If the remainder is zero, then the divisor is a factor of the original polynomial.
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Organized Videos:
✅Divide Polynomials using Long Division
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpEqXegKF4X1ZvfIfR3ZRhb
✅Divide Polynomials using Long Division with four terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrl38sUsvo6Povp9Sgv6xzp
✅Divide Polynomials using Long Division with five terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMo5ksA4plaC3kiz05KifyA7
✅Divide Polynomials using Long Division with missing terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMopA0IFtxgKsp3Z5zQbjhKV
✅Divide Polynomials using Long Division with monomial divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqD3NA8bc8uwMxLqwke4gpZ
✅Divide Polynomials using Long Division with quadratic divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp-Mhid4_Ow29RhmP5sOLMX
✅Divide Polynomials using Long Division with linear binomial divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp0lX4rL-EDwao_ZhVkm-Th
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#polynomials #brianmclogan
👉 Learn how to divide polynomials by quadratic divisors using the long division algorithm. Before dividing a polynomial, it is usually important to arrange the divisor in the descending order of powers of the variable(s). To divide a polynomial by a quadratic divisor using the long division algorithm, we divide the polynomial (dividend) with the quadratic term of the divisor to get a term of the quotient. We will then multiply all the terms of the divisor by the term of the quotient and subtract the result from the dividend. The result is divided again by the quadratic term of the divisor to get another term of the quotient. This process is repeated until the quadratic term of the divisor can no longer divide into the dividend.
The result after subtracting the product of the last term of the quotient and the divisor is the remainder when the divisor divides the original polynomial. If the remainder is zero, then the divisor is a factor of the original polynomial.
👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1
❤️Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/join
🙋♂️Have questions? Ask here: https://forms.gle/dfR9HbCu6qpWbJdo7
🎉Follow the Community: https://www.youtube.com/user/MrBrianMcLogan/community
Organized Videos:
✅Divide Polynomials using Long Division
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpEqXegKF4X1ZvfIfR3ZRhb
✅Divide Polynomials using Long Division with four terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrl38sUsvo6Povp9Sgv6xzp
✅Divide Polynomials using Long Division with five terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMo5ksA4plaC3kiz05KifyA7
✅Divide Polynomials using Long Division with missing terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMopA0IFtxgKsp3Z5zQbjhKV
✅Divide Polynomials using Long Division with monomial divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqD3NA8bc8uwMxLqwke4gpZ
✅Divide Polynomials using Long Division with quadratic divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp-Mhid4_Ow29RhmP5sOLMX
✅Divide Polynomials using Long Division with linear binomial divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp0lX4rL-EDwao_ZhVkm-Th
🗂️ Organized playlists by classes here: https://www.youtube.com/user/MrBrianMcLogan/playlists
🌐 My Website - http://www.freemathvideos.com
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👨👩👧👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: https://www.freemathvideos.com/about-me/
#polynomials #brianmclogan
This video provides a straightforward, step-by-step guide on factoring trinomials. You’ll discover how to identify two numbers that sum to the middle term and m...
This video provides a straightforward, step-by-step guide on factoring trinomials. You’ll discover how to identify two numbers that sum to the middle term and multiply to the product of the first and last coefficients. We’ll walk you through breaking down the middle term, grouping the terms, and completing the factorization process. Perfect for students or anyone wanting to improve their algebra skills.
Music by Vincent Rubinetti
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/playlist/3zNK20qC96mVSww60lVi1k
This video provides a straightforward, step-by-step guide on factoring trinomials. You’ll discover how to identify two numbers that sum to the middle term and multiply to the product of the first and last coefficients. We’ll walk you through breaking down the middle term, grouping the terms, and completing the factorization process. Perfect for students or anyone wanting to improve their algebra skills.
Music by Vincent Rubinetti
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/playlist/3zNK20qC96mVSww60lVi1k
Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...a quotient vector space? Or: Identifying information.
Slides.
h...
Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...a quotient vector space? Or: Identifying information.
Slides.
http://www.dtubbenhauer.com/youtube.html
#linearalgebra
#algebra
#mathematics
Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...a quotient vector space? Or: Identifying information.
Slides.
http://www.dtubbenhauer.com/youtube.html
#linearalgebra
#algebra
#mathematics
Quotient groups is a very important concept in group theory, because it has paramount importance in group homomorphisms (connection with the isomorphism theorem(s)). With this video series, abstract algebra needs not be abstract - one can easily develop intuitions for group theory!
In fact, the concept of quotient groups is one way to define modular arithmetic formally, which allows us to prove a lot of number theory theorems once we draw parallels between group theory and number theory. For example, Fermat's little theorem and Euler's totient theorem are just corollaries of the Lagrange's theorem introduced in Chapter 3 of the video series.
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
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If you want to know more interesting Mathematics, stay tuned for the next video!
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#mathemanic #grouptheory #abstractalgebra #quotientgroup #intuition
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#MathIsSimple #Grade8 #Exponents #Expressions #Algebra
Powers of Quotients | Expressions & Equations | Grade 8
Like to learn more math problems from Middle School to Algebra on Math is Simple!,
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Normal subgroups are a powerful tool for creating factor groups (also called quotient groups). In this video we introduce the concept of a coset, talk about which subgroups are “normal” subgroups, and show when the collection of cosets can be treated as a group of their own. As a motivation, we will begin by discussing congruences.
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This video show how to use the quotient rule for exponents. Remember that when using the quotient rule we can subtract the exponents. For more videos visit http://www.mysecretmathtutor.com
We introduce quotient groups/factor groups. The quotient group of a group G by a normal subgroup H is the set of all cosets of H in G with the operation of coset multiplication. We prove the quotient group construction is indeed a group, and that it is a homomorphic image of the containing group. Thus, quotient groups give us a way to construct homomorphic images of a group. #abstractalgebra #grouptheory
Normal Subgroups: https://youtu.be/kbT5SyF3H60
Left and Right Cosets in Normal Subgroups: https://youtu.be/XOu1zFutrMY
Coset Multiplication on Normal Subgroups: https://youtu.be/DJyOdMBUdnM
Fundamental Homomorphism Theorem: https://youtu.be/wtK1h9TIDCY
Abstract Algebra Course: https://www.youtube.com/playlist?list=PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN
Abstract Algebra Exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVQNtNnXeHB_1yquKUY98Xz
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In this lesson, we will learn how to simplify exponent expressions in algebra. Simplifying expressions is a crucial skill because it is used when solving equations, solving and graphing inequalities, radical expressions, factoring, and more.
First, you will learn that this type of problem is also called finding the quotient of two monomials. Next, you will learn how to cancel exponent terms from the numerator and denominator in the algebraic expression. Lastly, we will simplify any numbers present to get the final answer.
👉 Learn how to divide polynomials by quadratic divisors using the long division algorithm. Before dividing a polynomial, it is usually important to arrange the divisor in the descending order of powers of the variable(s). To divide a polynomial by a quadratic divisor using the long division algorithm, we divide the polynomial (dividend) with the quadratic term of the divisor to get a term of the quotient. We will then multiply all the terms of the divisor by the term of the quotient and subtract the result from the dividend. The result is divided again by the quadratic term of the divisor to get another term of the quotient. This process is repeated until the quadratic term of the divisor can no longer divide into the dividend.
The result after subtracting the product of the last term of the quotient and the divisor is the remainder when the divisor divides the original polynomial. If the remainder is zero, then the divisor is a factor of the original polynomial.
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Organized Videos:
✅Divide Polynomials using Long Division
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpEqXegKF4X1ZvfIfR3ZRhb
✅Divide Polynomials using Long Division with four terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrl38sUsvo6Povp9Sgv6xzp
✅Divide Polynomials using Long Division with five terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMo5ksA4plaC3kiz05KifyA7
✅Divide Polynomials using Long Division with missing terms
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMopA0IFtxgKsp3Z5zQbjhKV
✅Divide Polynomials using Long Division with monomial divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqD3NA8bc8uwMxLqwke4gpZ
✅Divide Polynomials using Long Division with quadratic divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp-Mhid4_Ow29RhmP5sOLMX
✅Divide Polynomials using Long Division with linear binomial divisor
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp0lX4rL-EDwao_ZhVkm-Th
🗂️ Organized playlists by classes here: https://www.youtube.com/user/MrBrianMcLogan/playlists
🌐 My Website - http://www.freemathvideos.com
🎯Survive Math Class Checklist: Ten Steps to a Better Year: https://www.brianmclogan.com/email-capture-fdea604e-9ee8-433f-aa93-c6fefdfe4d57
Connect with me:
⚡️Facebook - https://www.facebook.com/freemathvideos
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👨🏫 Current Courses on Udemy: https://www.udemy.com/user/brianmclogan2/
👨👩👧👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: https://www.freemathvideos.com/about-me/
#polynomials #brianmclogan
This video provides a straightforward, step-by-step guide on factoring trinomials. You’ll discover how to identify two numbers that sum to the middle term and multiply to the product of the first and last coefficients. We’ll walk you through breaking down the middle term, grouping the terms, and completing the factorization process. Perfect for students or anyone wanting to improve their algebra skills.
Music by Vincent Rubinetti
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/playlist/3zNK20qC96mVSww60lVi1k
Goal.
Explaining basic concepts of linear algebra in an intuitive way.
This time.
What is...a quotient vector space? Or: Identifying information.
Slides.
http://www.dtubbenhauer.com/youtube.html
#linearalgebra
#algebra
#mathematics
Let A be a set (of the elements of an algebra ), and let E be an equivalence relation on the set A. The relation E is said to be compatible with (or have the substitution property with respect to) an n-ary operation f if for all whenever implies . An equivalence relation compatible with all the operations of an algebra is called a congruence.
Quotient algebras and homomorphisms
A set A can be partitioned in equivalence classes given by an equivalence relation E, and usually called a quotient set, and denoted A/E. For an algebra , it is straightforward to define the operations induced on A/E if E is a congruence. Specifically, for any operation of arity in (where the superscript simply denotes that it's an operation in ) define as , where denotes the equivalence class of a modulo E.