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:
More precisely, * is required to satisfy the following properties:
(x + y)* = x* + y*
(x y)* = y* x*
1* = 1
(x*)* = x
for all x, y in A.
This is also called an involutive ring, involutory ring, and ring with involution. Note that the third axiom is actually redundant, because the second and fourth axioms imply 1* is also a multiplicative identity, and identities are unique.
Ring(リング,Ringu) is a Japanese mystery horror novel by Koji Suzuki, first published in 1991, and set in modern-day Japan. It was the basis for a 1995 television film (Ring: Kanzenban),a television series (Ring: The Final Chapter), a film of the same name (1998's Ring), and two remakes of the 1998 film: a South Korean version (The Ring Virus) and an American version (The Ring).
Plot synopsis
After four teenagers mysteriously die simultaneously in Tokyo, Kazuyuki Asakawa, a reporter and uncle to one of the deceased, decides to launch his own personal investigation. His search leads him to "Hakone Pacific Land", a holiday resort where the youths were last seen together exactly one week before their deaths. Once there he happens upon a mysterious unmarked videotape. Watching the tape, he witnesses a strange sequence of both abstract and realistic footage, including an image of an injured man, that ends with a warning revealing the viewer has a week to live. Giving a single means of avoiding death, the tape's explanation ends suddenly having been overwritten by an advertisement. The tape has a horrible mental effect on Asakawa, and he doesn't doubt for a second that its warning is true.
Production took approximately 9 months.Ring and its sequel Rasen were released in Japan at the same time.
After release, Ring inspired numerous follow-ups within the Ring franchise and triggered a trend of Western remakes.
Plot
Two teenagers, Masami (Hitomi Satō) and Tomoko (Yūko Takeuchi), talk about a videotape recorded by a boy in Izu which is fabled to bear a curse that kills the viewer seven days after watching. Tomoko reveals that a week ago, she and three of her friends watched a weird tape and received a call after watching. Tomoko is killed by an unseen force as Masami watches, horrified.
From kindergarten through high school, the mathematics education in public schools in the United States has historically varied widely from state to state, and often even varies considerably within individual states. With the recent adoption of the Common Core Standards by 45 states, mathematics content across the country is moving into closer agreement for each grade level.
Curricular content
Each state sets its own curricular standards and details are usually set by each local school district. Although there are no federal standards, 45 states have agreed to base their curricula on the Common Core State Standards in mathematics beginning in 2015. The National Council of Teachers of Mathematics(NCTM) published educational recommendations in mathematics education in 1991 and 2000 which have been highly influential, describing mathematical knowledge, skills and pedagogical emphases from kindergarten through high school. The 2006 NCTM Curriculum Focal Points have also been influential for its recommendations of the most important mathematical topics for each grade level through grade 8.
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in the sciences, too.
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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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published: 07 Jul 2016
Teaching myself abstract algebra
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published: 03 May 2021
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to continue your study of abstract algebra be learning about rings, fields, modules and vector spaces.
Our sincere thanks go out to our VIP Patron, Matt Peters. Matt supported us on Patreon, and thanks to his generous donation, we were able to make this video. Thank you for helping make this video happen, Matt!
Be sure to subscribe so you don't miss new lessons from Socratica:
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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
http://amzn.to/...
published: 06 Nov 2017
Abstract Algebra is Impossible Without These 8 Things
Important note: for the Descartes rule of signs, there are actually 3, not 2, sign changes. But in the summary document below the error is fixed.
PDF Summary
https://drive.google.com/file/d/1d_Xgjhnd5ttdQ2exkjmfvP7ZWRYXQ3sX/view?usp=sharing
This video was made with the help of this Abstract Algebra book
https://amzn.to/3z3S9fy
--
Al-Khwarizmi Video (it's from awhile ago but it explains that concept well!)
https://youtu.be/q0I8ffMbkWs?si=29xJfkLnAGjlXlJV
Galois Theory Video
https://youtu.be/lkvkUT3Qdw4?si=TDjLw7KVHHBPUtYa
---
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published: 31 Aug 2024
Group theory, abstraction, and the 196,883-dimensional monster
An introduction to group theory (Minor error corrections below)
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: https://3b1b.co/monster-thanks
Timestamps:
0:00 - The size of the monster
0:50 - What is a group?
7:06 - What is an abstract group?
13:27 - Classifying groups
18:31 - About the monster
Errors:
*Typo on the "hard problem" at 14:11, it should be a/(b+c) + b/(a+c) + c/(a+b) = 4
*Typo-turned-speako: The classification of quasithin groups is 1221 pages long, not 12,000. The full collection of papers proving the CFSG theorem do comprise tens of thousands of pages, but no one paper was quite that crazy.
Thanks to Richard Borcherds for his helpful comments ...
published: 19 Aug 2020
Lec 1 | Abstract Algebra
Week 1: Review of linear algebra. Groups. Examples of groups.
Basic properties and constructions.
This video:
Introduction to the course; Review: Linear algebra; Definition of groups
Notes for this lecture: http://www.extension.harvard.edu/sites/default/files/openlearning/math222/files/notes/L1-N.pdf
These lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School.
View Complete course (Syllabus, Notes, Problem Sets, etc) at: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra
published: 06 Sep 2013
Abstract Algebra Book with TONS of Content
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published: 02 May 2023
(Abstract Algebra 1) Definition of a Group
The definition of a group is given, along with several examples.
published: 30 Dec 2013
Abstract Algebra || Properties of Symmetric Groups || Lecture 32
Recorded Video of the Online Session on Abstract Algebra Course by K. Selvakumar, MSU
published: 10 Nov 2024
Learn Abstract Algebra from START to FINISH
In this video I talk about how to learn abstract algebra from start to finish. I go over some books which you can use to help you learn abstract algebra from the very basics all the way to graduate level abstract algebra.
My Udemy Course on Abstract Algebra
https://www.udemy.com/course/abstract-algebra-group-theory-with-the-math-sorcerer/?referralCode=B04607DA7A7D0E29272A
Here are links to the books in these videos.
Abstract Algebra by Saracino https://amzn.to/3bF8Dwp
Contemporary Abstract Algebra by Gallian https://amzn.to/39xmRg3
Modern Algebra by Durbin https://amzn.to/2Kg1eZf
Abstract Algebra by Beachy and Blair https://amzn.to/3qs7EE9
A Concrete Approach to Abstract Algebra by Sawyer https://amzn.to/3oXSJBj
Introduction to Abstract Algebra by Dubisch https://amzn.to/3suliIK
Abstrac...
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, ...
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in the sciences, too.
Be sure to subscribe so you don't miss new lessons from Socratica:
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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
How to Be a Great Student
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Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in the sciences, too.
Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W
♦♦♦♦♦♦♦♦♦♦
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
How to Be a Great Student
ebook: https://amzn.to/2Lh3XSP
Paperback: https://amzn.to/3t5jeH3
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The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of...
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to continue your study of abstract algebra be learning about rings, fields, modules and vector spaces.
Our sincere thanks go out to our VIP Patron, Matt Peters. Matt supported us on Patreon, and thanks to his generous donation, we were able to make this video. Thank you for helping make this video happen, Matt!
Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W
♦♦♦♦♦♦♦♦♦♦
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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► Join our Patreon : https://www.patreon.com/socratica
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Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
♦♦♦♦♦♦♦♦♦♦
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to continue your study of abstract algebra be learning about rings, fields, modules and vector spaces.
Our sincere thanks go out to our VIP Patron, Matt Peters. Matt supported us on Patreon, and thanks to his generous donation, we were able to make this video. Thank you for helping make this video happen, Matt!
Be sure to subscribe so you don't miss new lessons from Socratica:
http://bit.ly/1ixuu9W
♦♦♦♦♦♦♦♦♦♦
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
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : https://www.patreon.com/socratica
► Make a one-time PayPal donation: https://www.paypal.me/socratica
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Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
♦♦♦♦♦♦♦♦♦♦
Important note: for the Descartes rule of signs, there are actually 3, not 2, sign changes. But in the summary document below the error is fixed.
PDF Summary
...
Important note: for the Descartes rule of signs, there are actually 3, not 2, sign changes. But in the summary document below the error is fixed.
PDF Summary
https://drive.google.com/file/d/1d_Xgjhnd5ttdQ2exkjmfvP7ZWRYXQ3sX/view?usp=sharing
This video was made with the help of this Abstract Algebra book
https://amzn.to/3z3S9fy
--
Al-Khwarizmi Video (it's from awhile ago but it explains that concept well!)
https://youtu.be/q0I8ffMbkWs?si=29xJfkLnAGjlXlJV
Galois Theory Video
https://youtu.be/lkvkUT3Qdw4?si=TDjLw7KVHHBPUtYa
---
🐦 Follow me on X: https://x.com/dibeoluca
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📊 Do you need Private Classes or a Consultation on Math & Physics, or do you know somebody who does? I might be helpful! Our email: [email protected]
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🥹 Consider supporting us on Patreon:
https://www.patreon.com/user?u=86646021
Important note: for the Descartes rule of signs, there are actually 3, not 2, sign changes. But in the summary document below the error is fixed.
PDF Summary
https://drive.google.com/file/d/1d_Xgjhnd5ttdQ2exkjmfvP7ZWRYXQ3sX/view?usp=sharing
This video was made with the help of this Abstract Algebra book
https://amzn.to/3z3S9fy
--
Al-Khwarizmi Video (it's from awhile ago but it explains that concept well!)
https://youtu.be/q0I8ffMbkWs?si=29xJfkLnAGjlXlJV
Galois Theory Video
https://youtu.be/lkvkUT3Qdw4?si=TDjLw7KVHHBPUtYa
---
🐦 Follow me on X: https://x.com/dibeoluca
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📈 Check out my Udemy courses (you may find something that interests you 😉): https://www.udemy.com/user/luca-di-beo/
📊 Do you need Private Classes or a Consultation on Math & Physics, or do you know somebody who does? I might be helpful! Our email: [email protected]
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An introduction to group theory (Minor error corrections below)
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of suppo...
An introduction to group theory (Minor error corrections below)
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: https://3b1b.co/monster-thanks
Timestamps:
0:00 - The size of the monster
0:50 - What is a group?
7:06 - What is an abstract group?
13:27 - Classifying groups
18:31 - About the monster
Errors:
*Typo on the "hard problem" at 14:11, it should be a/(b+c) + b/(a+c) + c/(a+b) = 4
*Typo-turned-speako: The classification of quasithin groups is 1221 pages long, not 12,000. The full collection of papers proving the CFSG theorem do comprise tens of thousands of pages, but no one paper was quite that crazy.
Thanks to Richard Borcherds for his helpful comments while putting this video together. He has a wonderful hidden gem of a channel: https://youtu.be/a9k_QmZbwX8
You may also enjoy this brief article giving an overview of this monster:
http://www.ams.org/notices/200209/what-is.pdf
If you want to learn more about group theory, check out the expository papers here:
https://kconrad.math.uconn.edu/blurbs/
Videos with John Conway talking about the Monster:
https://youtu.be/jsSeoGpiWsw
https://youtu.be/lbN8EMcOH5o
More on Noether's Theorem:
https://youtu.be/CxlHLqJ9I0A
https://youtu.be/04ERSb06dOg
The symmetry ambigram was designed by Punya Mishra:
https://punyamishra.com/2013/05/31/symmetry-new-ambigram/
The Monster image comes from the Noun Project, via Nicky Knicky
This video is part of the #MegaFavNumbers project: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo
To join the gang, upload your own video on your own favorite number over 1,000,000 with the hashtag #MegaFavNumbers, and the word MegaFavNumbers in the title by September 2nd, 2020, and it'll be added to the playlist above.
Thanks to these viewers for their contributions to translations
German: dlatikaynen
Hebrew: Omer Tuchfeld
Italian: mulstato
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
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/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
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An introduction to group theory (Minor error corrections below)
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: https://3b1b.co/monster-thanks
Timestamps:
0:00 - The size of the monster
0:50 - What is a group?
7:06 - What is an abstract group?
13:27 - Classifying groups
18:31 - About the monster
Errors:
*Typo on the "hard problem" at 14:11, it should be a/(b+c) + b/(a+c) + c/(a+b) = 4
*Typo-turned-speako: The classification of quasithin groups is 1221 pages long, not 12,000. The full collection of papers proving the CFSG theorem do comprise tens of thousands of pages, but no one paper was quite that crazy.
Thanks to Richard Borcherds for his helpful comments while putting this video together. He has a wonderful hidden gem of a channel: https://youtu.be/a9k_QmZbwX8
You may also enjoy this brief article giving an overview of this monster:
http://www.ams.org/notices/200209/what-is.pdf
If you want to learn more about group theory, check out the expository papers here:
https://kconrad.math.uconn.edu/blurbs/
Videos with John Conway talking about the Monster:
https://youtu.be/jsSeoGpiWsw
https://youtu.be/lbN8EMcOH5o
More on Noether's Theorem:
https://youtu.be/CxlHLqJ9I0A
https://youtu.be/04ERSb06dOg
The symmetry ambigram was designed by Punya Mishra:
https://punyamishra.com/2013/05/31/symmetry-new-ambigram/
The Monster image comes from the Noun Project, via Nicky Knicky
This video is part of the #MegaFavNumbers project: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo
To join the gang, upload your own video on your own favorite number over 1,000,000 with the hashtag #MegaFavNumbers, and the word MegaFavNumbers in the title by September 2nd, 2020, and it'll be added to the playlist above.
Thanks to these viewers for their contributions to translations
German: dlatikaynen
Hebrew: Omer Tuchfeld
Italian: mulstato
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
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If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
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Week 1: Review of linear algebra. Groups. Examples of groups.
Basic properties and constructions.
This video:
Introduction to the course; Review...
Week 1: Review of linear algebra. Groups. Examples of groups.
Basic properties and constructions.
This video:
Introduction to the course; Review: Linear algebra; Definition of groups
Notes for this lecture: http://www.extension.harvard.edu/sites/default/files/openlearning/math222/files/notes/L1-N.pdf
These lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School.
View Complete course (Syllabus, Notes, Problem Sets, etc) at: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra
Week 1: Review of linear algebra. Groups. Examples of groups.
Basic properties and constructions.
This video:
Introduction to the course; Review: Linear algebra; Definition of groups
Notes for this lecture: http://www.extension.harvard.edu/sites/default/files/openlearning/math222/files/notes/L1-N.pdf
These lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School.
View Complete course (Syllabus, Notes, Problem Sets, etc) at: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra
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Here is the legendary book: https://amzn.to/3ALXWDG
Useful Math Supplies https://amzn.to/3Y5TGcv
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***********Math, Physics, and Computer Science Books***********
Epic Math Book List https://amzn.to/3F98vT1
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In this video I talk about how to learn abstract algebra from start to finish. I go over some books which you can use to help you learn abstract algebra from th...
In this video I talk about how to learn abstract algebra from start to finish. I go over some books which you can use to help you learn abstract algebra from the very basics all the way to graduate level abstract algebra.
My Udemy Course on Abstract Algebra
https://www.udemy.com/course/abstract-algebra-group-theory-with-the-math-sorcerer/?referralCode=B04607DA7A7D0E29272A
Here are links to the books in these videos.
Abstract Algebra by Saracino https://amzn.to/3bF8Dwp
Contemporary Abstract Algebra by Gallian https://amzn.to/39xmRg3
Modern Algebra by Durbin https://amzn.to/2Kg1eZf
Abstract Algebra by Beachy and Blair https://amzn.to/3qs7EE9
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Introduction to Abstract Algebra by Dubisch https://amzn.to/3suliIK
Abstract Algebra an Introduction by Hungerford https://amzn.to/3sulqIe
Elements of Abstract Algebra by Clark https://amzn.to/3ihbLA2
Algebraic Structures(note the name is updated now) by Lang https://amzn.to/2N7tM8n
A First Course in Abstract Algebra by Paley and Weischel (can't find it, here is another one) https://amzn.to/3iHfuLx
A First Course in Abstract Algebra by Fraleigh https://amzn.to/3nE7dEQ
Lectures in Abstract Algebra by Jacobson(this all 3 actually) https://amzn.to/3sqibBg
Concepts in Abstract by Lanski https://amzn.to/3nM9Rbs
Algebra by Artin https://amzn.to/39BIWKD
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Algebra by Lang https://amzn.to/2N5X3jL
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Ring Theory by Behrens https://amzn.to/3oOHRoY
The Theory of Rings by McCoy https://amzn.to/2XFS2QX
Note all of the links above are my affiliate links.
If you enjoyed this video please consider liking, sharing, and subscribing.
Udemy Courses Via My Website: https://mathsorcerer.com
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Advanced Calculus Course
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Thank you:)
In this video I talk about how to learn abstract algebra from start to finish. I go over some books which you can use to help you learn abstract algebra from the very basics all the way to graduate level abstract algebra.
My Udemy Course on Abstract Algebra
https://www.udemy.com/course/abstract-algebra-group-theory-with-the-math-sorcerer/?referralCode=B04607DA7A7D0E29272A
Here are links to the books in these videos.
Abstract Algebra by Saracino https://amzn.to/3bF8Dwp
Contemporary Abstract Algebra by Gallian https://amzn.to/39xmRg3
Modern Algebra by Durbin https://amzn.to/2Kg1eZf
Abstract Algebra by Beachy and Blair https://amzn.to/3qs7EE9
A Concrete Approach to Abstract Algebra by Sawyer https://amzn.to/3oXSJBj
Introduction to Abstract Algebra by Dubisch https://amzn.to/3suliIK
Abstract Algebra an Introduction by Hungerford https://amzn.to/3sulqIe
Elements of Abstract Algebra by Clark https://amzn.to/3ihbLA2
Algebraic Structures(note the name is updated now) by Lang https://amzn.to/2N7tM8n
A First Course in Abstract Algebra by Paley and Weischel (can't find it, here is another one) https://amzn.to/3iHfuLx
A First Course in Abstract Algebra by Fraleigh https://amzn.to/3nE7dEQ
Lectures in Abstract Algebra by Jacobson(this all 3 actually) https://amzn.to/3sqibBg
Concepts in Abstract by Lanski https://amzn.to/3nM9Rbs
Algebra by Artin https://amzn.to/39BIWKD
Galois Theory by Artin https://amzn.to/38H9fzN
Algebra Through Practice: Rings, Fields, and Modules https://amzn.to/38KmIXK
Algebra Through Practice: Groups https://amzn.to/3oMfKXJ
Algebra by Van Der Waerden Volume 1 and 2 https://amzn.to/3oMg5tt and https://amzn.to/2LQc5JI
Basic Algebra by Knapp https://amzn.to/3icgaEh
Algebra by Lang https://amzn.to/2N5X3jL
Abstract Algebra by Dummit and Foote https://amzn.to/3oLfyrG
Exercises in Classical Ring Theory by Lam https://amzn.to/3qleYRJ
Topics in Ring Theory of Barshay https://amzn.to/2LxAaFr
Ring Theory by Behrens https://amzn.to/3oOHRoY
The Theory of Rings by McCoy https://amzn.to/2XFS2QX
Note all of the links above are my affiliate links.
If you enjoyed this video please consider liking, sharing, and subscribing.
Udemy Courses Via My Website: https://mathsorcerer.com
My FaceBook Page: https://www.facebook.com/themathsorcerer
There are several ways that you can help support my channel:)
Consider becoming a member of the channel: https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join
My GoFundMe Page: https://www.gofundme.com/f/support-math-education-for-the-world
My Patreon Page: https://www.patreon.com/themathsorcerer
Donate via PayPal: https://paypal.com/donate/?cmd=_s-xclick&hosted_button_id=7XNKUGJUENSYU
************Udemy Courses(Please Use These Links If You Sign Up!)*************
Abstract Algebra Course
https://www.udemy.com/course/abstract-algebra-group-theory-with-the-math-sorcerer/?referralCode=B04607DA7A7D0E29272A
Advanced Calculus Course
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Calculus 1 Course
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Calculus Integration Insanity
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Differential Equations Course
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College Algebra Course
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How to Write Proofs with Sets Course
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How to Write Proofs with Functions Course
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Statistics with StatCrunch Course
https://www.udemy.com/course/statistics-with-statcrunch-by-the-math-sorcerer/?referralCode=69B27AF43D10924FF63B
Math Graduate Programs, Applying, Advice, Motivation
https://www.udemy.com/course/math-graduate-programs-applying-advice-motivation/?referralCode=70A1CED973D7910E9161
Daily Devotionals for Motivation with The Math Sorcerer
https://www.udemy.com/course/daily-math-devotionals-for-motivation-with-the-math-sorcerer/?referralCode=2653144E315A37A94B8C
Thank you:)
How The Ring Book Compares to the Film: Book vs Movie Review
Have you ever wondered how Koji Suzuki's Ring compares to the films Ringu and The Ring? In this video, I'm reviewing the book, comparing it to the movies, and detailing why The Ring book is better than the movie. Have you read the book? Please let me know your thoughts below!
DISCLAIMER: I apologize for pronouncing any names incorrectly in this video. I tried my best!
Let's become spooky besties~
Instagram: instagram.com/mandymorgue87/
Twitter: https://twitter.com/LivnDeadGrl87
TikTok: https://www.tiktok.com/@mandymorgue87?
Goodreads: https://www.goodreads.com/user/show/44648215-mandymorgue87
Letterboxd: https://letterboxd.com/mandymorgue87/
Business Inquiries: [email protected]
PO Box
339 Medfield, MA 02052
published: 23 Aug 2021
Ring by Koji Suzuki, Chapter One Audiobook
published: 19 Jan 2021
This Japanese Horror Film Was Actually Real.
ON THE CASE - The Ring
PATREON: https://www.patreon.com/akidearest
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-New Users "Akidearest" for $5 off your first purchase
For Business Inquiries, reach me at [email protected]
▽CREDITS▽
This video was edited by MudanTV
https://www.youtube.com/channel/UCNAvv1fuKQyuqkHc0wnzViw
Outro animation:
Cursed Mark
https://t.co/CoxwDYI5NQ
Outro Song:
Super G@mer Boy
HiLi
http://conte-de-fees.com/?p=468
FTC: This video is not sponsored
published: 19 Dec 2020
REVIEW: Ring by Koji Suzuki
SEVEN DAYS.
here are my thoughts on the English translation of the thriller/mystery novel, Ring!
// article i mentioned: http://horror.dreamdawn.com/?p=54891
// find me over at these places:
- goodreads: http://www.goodreads.com/user/show/19618894-selina
- twitter: http://www.twitter.com/selinas_shelf
- instagram: http://www.instagram.com/moon__mirror/
- art instagram: http://www.instagram.com/moonmirrorart
published: 19 Jun 2017
Ring (Ringu) by Koji Suzuki (spoilers!)
Hakone, Island Baby! The source novel behind the Japanese horror phenomenon of the late nineties and our initial introduction to beautiful, baleful Sadako Yamamura - haunter of the empty channels. Dark, dark themes here, even if you're already familiar with the film. Play it at your friends. Preferably within the week.
Unfortunately a bit of traffic noise (and light) has leaked in in parts. And, that bit of fibre on my top at the beginning is not a white pubic hair. It just looks like one.
published: 09 Sep 2020
Ring by Koji Suzuki review in a minute
This was such a hard book to talk about because I REALLY enjoyed parts of it but I was constantly uncomfortable with the misogyny and r@pe culture so like??????
published: 18 Sep 2021
Talking about Ring by Koji Suzuki with a spoiler see descripiton
Honestly, I feel like I could have done this review a little better, however there is a lot to unpack that would contain a lot of spoilers about the book.
published: 23 Oct 2021
Horror Novels that Actually Scare Me
The first 1000 people to use the link will get a free trial of Skillshare Premium Membership: https://skl.sh/rgsdevilship10201
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🌙 Last Video 🔮 Gothic Horror Book Recommendations
https://youtu.be/pDH5f2a7efk
💀 Books...
published: 30 Oct 2020
Loop by Koji Suzuki, Chapter One Audiobook [Ring, Book 3]
published: 10 Sep 2021
Ring by Koji Suzuki Book Review
Ring by Koji Suzuki Book Review
Part of the #365100books
Buy the book: https://www.waterstones.com/book/ring/koji-suzuki/robert-b-rohmer/9780007240135
https://www.artelino.com/articles/ghost_story_okiku.asp
Have you ever wondered how Koji Suzuki's Ring compares to the films Ringu and The Ring? In this video, I'm reviewing the book, comparing it to the movies, and d...
Have you ever wondered how Koji Suzuki's Ring compares to the films Ringu and The Ring? In this video, I'm reviewing the book, comparing it to the movies, and detailing why The Ring book is better than the movie. Have you read the book? Please let me know your thoughts below!
DISCLAIMER: I apologize for pronouncing any names incorrectly in this video. I tried my best!
Let's become spooky besties~
Instagram: instagram.com/mandymorgue87/
Twitter: https://twitter.com/LivnDeadGrl87
TikTok: https://www.tiktok.com/@mandymorgue87?
Goodreads: https://www.goodreads.com/user/show/44648215-mandymorgue87
Letterboxd: https://letterboxd.com/mandymorgue87/
Business Inquiries: [email protected]
PO Box
339 Medfield, MA 02052
Have you ever wondered how Koji Suzuki's Ring compares to the films Ringu and The Ring? In this video, I'm reviewing the book, comparing it to the movies, and detailing why The Ring book is better than the movie. Have you read the book? Please let me know your thoughts below!
DISCLAIMER: I apologize for pronouncing any names incorrectly in this video. I tried my best!
Let's become spooky besties~
Instagram: instagram.com/mandymorgue87/
Twitter: https://twitter.com/LivnDeadGrl87
TikTok: https://www.tiktok.com/@mandymorgue87?
Goodreads: https://www.goodreads.com/user/show/44648215-mandymorgue87
Letterboxd: https://letterboxd.com/mandymorgue87/
Business Inquiries: [email protected]
PO Box
339 Medfield, MA 02052
ON THE CASE - The Ring
PATREON: https://www.patreon.com/akidearest
//LINKS AND STUFF//
➣TENTACLE MERCH: http://sharkrobot.com/collections/akidearest
➣ANIME M...
ON THE CASE - The Ring
PATREON: https://www.patreon.com/akidearest
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For Business Inquiries, reach me at [email protected]
▽CREDITS▽
This video was edited by MudanTV
https://www.youtube.com/channel/UCNAvv1fuKQyuqkHc0wnzViw
Outro animation:
Cursed Mark
https://t.co/CoxwDYI5NQ
Outro Song:
Super G@mer Boy
HiLi
http://conte-de-fees.com/?p=468
FTC: This video is not sponsored
ON THE CASE - The Ring
PATREON: https://www.patreon.com/akidearest
//LINKS AND STUFF//
➣TENTACLE MERCH: http://sharkrobot.com/collections/akidearest
➣ANIME MERCH (Use code, Akidearest for $5 Off)
https://aitaikuji.com/akidearest
➣MANGA: https://global.bookwalker.jp/collections/5447/?adpcnt=7qM_Vsha
-New Users "Akidearest" for $5 off your first purchase
For Business Inquiries, reach me at [email protected]
▽CREDITS▽
This video was edited by MudanTV
https://www.youtube.com/channel/UCNAvv1fuKQyuqkHc0wnzViw
Outro animation:
Cursed Mark
https://t.co/CoxwDYI5NQ
Outro Song:
Super G@mer Boy
HiLi
http://conte-de-fees.com/?p=468
FTC: This video is not sponsored
SEVEN DAYS.
here are my thoughts on the English translation of the thriller/mystery novel, Ring!
// article i mentioned: http://horror.dreamdawn.com/?p=54891...
SEVEN DAYS.
here are my thoughts on the English translation of the thriller/mystery novel, Ring!
// article i mentioned: http://horror.dreamdawn.com/?p=54891
// find me over at these places:
- goodreads: http://www.goodreads.com/user/show/19618894-selina
- twitter: http://www.twitter.com/selinas_shelf
- instagram: http://www.instagram.com/moon__mirror/
- art instagram: http://www.instagram.com/moonmirrorart
SEVEN DAYS.
here are my thoughts on the English translation of the thriller/mystery novel, Ring!
// article i mentioned: http://horror.dreamdawn.com/?p=54891
// find me over at these places:
- goodreads: http://www.goodreads.com/user/show/19618894-selina
- twitter: http://www.twitter.com/selinas_shelf
- instagram: http://www.instagram.com/moon__mirror/
- art instagram: http://www.instagram.com/moonmirrorart
Hakone, Island Baby! The source novel behind the Japanese horror phenomenon of the late nineties and our initial introduction to beautiful, baleful Sadako Yamam...
Hakone, Island Baby! The source novel behind the Japanese horror phenomenon of the late nineties and our initial introduction to beautiful, baleful Sadako Yamamura - haunter of the empty channels. Dark, dark themes here, even if you're already familiar with the film. Play it at your friends. Preferably within the week.
Unfortunately a bit of traffic noise (and light) has leaked in in parts. And, that bit of fibre on my top at the beginning is not a white pubic hair. It just looks like one.
Hakone, Island Baby! The source novel behind the Japanese horror phenomenon of the late nineties and our initial introduction to beautiful, baleful Sadako Yamamura - haunter of the empty channels. Dark, dark themes here, even if you're already familiar with the film. Play it at your friends. Preferably within the week.
Unfortunately a bit of traffic noise (and light) has leaked in in parts. And, that bit of fibre on my top at the beginning is not a white pubic hair. It just looks like one.
This was such a hard book to talk about because I REALLY enjoyed parts of it but I was constantly uncomfortable with the misogyny and r@pe culture so like??????...
This was such a hard book to talk about because I REALLY enjoyed parts of it but I was constantly uncomfortable with the misogyny and r@pe culture so like??????
This was such a hard book to talk about because I REALLY enjoyed parts of it but I was constantly uncomfortable with the misogyny and r@pe culture so like??????
Honestly, I feel like I could have done this review a little better, however there is a lot to unpack that would contain a lot of spoilers about the book.
Honestly, I feel like I could have done this review a little better, however there is a lot to unpack that would contain a lot of spoilers about the book.
Honestly, I feel like I could have done this review a little better, however there is a lot to unpack that would contain a lot of spoilers about the book.
The first 1000 people to use the link will get a free trial of Skillshare Premium Membership: https://skl.sh/rgsdevilship10201
Thank you for liking & subscrib...
The first 1000 people to use the link will get a free trial of Skillshare Premium Membership: https://skl.sh/rgsdevilship10201
Thank you for liking & subscribing 🖤
CONTACT ME & SOCIALS
💌 Email | [email protected]
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👾 Lifestyle Channel | https://www.youtube.com/@R0YA.
FILMING EQUIPMENT 🎬
Camera | Panasonic Lumix DMC-FZ1000
Mic | Rode NT1-A
Interface | Yamaha Audiogram 3
Editor | Final Cut Pro
🌙 Last Video 🔮 Gothic Horror Book Recommendations
https://youtu.be/pDH5f2a7efk
💀 Books Mentioned 🩸
The Exorcist - William Peter Blatty
The Case Against Satan - Ray Russell
The Ring - Koji Suzuki
The Haunting of Hill House - Shirley Jackson
Pet Sematary - Stephen King
Thomas Ligotti - Songs of a Dead Dreamer & Grimscribe
I am Legend - Richard Matheson
The War of the Worlds - H. G. Wells
House of Leaves - Mark Z. Danielewski
Disclaimer: This video was sponsored by Skillshare
The first 1000 people to use the link will get a free trial of Skillshare Premium Membership: https://skl.sh/rgsdevilship10201
Thank you for liking & subscribing 🖤
CONTACT ME & SOCIALS
💌 Email | [email protected]
🔥 Instagram | https://www.instagram.com/rgsdevilship
🔮 Twitter | https://twitter.com/RGsDevilship
📖 Goodreads | https://www.goodreads.com/user/show/6263420-r-g
🍄 Storygraph | https://app.thestorygraph.com/profile/roya
⚡️ Ko-Fi | https://ko-fi.com/rgsdevilship
🥀 Tiktok | https://www.tiktok.com/@rgsdevilship
👾 Lifestyle Channel | https://www.youtube.com/@R0YA.
FILMING EQUIPMENT 🎬
Camera | Panasonic Lumix DMC-FZ1000
Mic | Rode NT1-A
Interface | Yamaha Audiogram 3
Editor | Final Cut Pro
🌙 Last Video 🔮 Gothic Horror Book Recommendations
https://youtu.be/pDH5f2a7efk
💀 Books Mentioned 🩸
The Exorcist - William Peter Blatty
The Case Against Satan - Ray Russell
The Ring - Koji Suzuki
The Haunting of Hill House - Shirley Jackson
Pet Sematary - Stephen King
Thomas Ligotti - Songs of a Dead Dreamer & Grimscribe
I am Legend - Richard Matheson
The War of the Worlds - H. G. Wells
House of Leaves - Mark Z. Danielewski
Disclaimer: This video was sponsored by Skillshare
Ring by Koji Suzuki Book Review
Part of the #365100books
Buy the book: https://www.waterstones.com/book/ring/koji-suzuki/robert-b-rohmer/9780007240135
https://w...
Ring by Koji Suzuki Book Review
Part of the #365100books
Buy the book: https://www.waterstones.com/book/ring/koji-suzuki/robert-b-rohmer/9780007240135
https://www.artelino.com/articles/ghost_story_okiku.asp
Ring by Koji Suzuki Book Review
Part of the #365100books
Buy the book: https://www.waterstones.com/book/ring/koji-suzuki/robert-b-rohmer/9780007240135
https://www.artelino.com/articles/ghost_story_okiku.asp
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in the sciences, too.
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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
How to Be a Great Student
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The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to continue your study of abstract algebra be learning about rings, fields, modules and vector spaces.
Our sincere thanks go out to our VIP Patron, Matt Peters. Matt supported us on Patreon, and thanks to his generous donation, we were able to make this video. Thank you for helping make this video happen, Matt!
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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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Important note: for the Descartes rule of signs, there are actually 3, not 2, sign changes. But in the summary document below the error is fixed.
PDF Summary
https://drive.google.com/file/d/1d_Xgjhnd5ttdQ2exkjmfvP7ZWRYXQ3sX/view?usp=sharing
This video was made with the help of this Abstract Algebra book
https://amzn.to/3z3S9fy
--
Al-Khwarizmi Video (it's from awhile ago but it explains that concept well!)
https://youtu.be/q0I8ffMbkWs?si=29xJfkLnAGjlXlJV
Galois Theory Video
https://youtu.be/lkvkUT3Qdw4?si=TDjLw7KVHHBPUtYa
---
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An introduction to group theory (Minor error corrections below)
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: https://3b1b.co/monster-thanks
Timestamps:
0:00 - The size of the monster
0:50 - What is a group?
7:06 - What is an abstract group?
13:27 - Classifying groups
18:31 - About the monster
Errors:
*Typo on the "hard problem" at 14:11, it should be a/(b+c) + b/(a+c) + c/(a+b) = 4
*Typo-turned-speako: The classification of quasithin groups is 1221 pages long, not 12,000. The full collection of papers proving the CFSG theorem do comprise tens of thousands of pages, but no one paper was quite that crazy.
Thanks to Richard Borcherds for his helpful comments while putting this video together. He has a wonderful hidden gem of a channel: https://youtu.be/a9k_QmZbwX8
You may also enjoy this brief article giving an overview of this monster:
http://www.ams.org/notices/200209/what-is.pdf
If you want to learn more about group theory, check out the expository papers here:
https://kconrad.math.uconn.edu/blurbs/
Videos with John Conway talking about the Monster:
https://youtu.be/jsSeoGpiWsw
https://youtu.be/lbN8EMcOH5o
More on Noether's Theorem:
https://youtu.be/CxlHLqJ9I0A
https://youtu.be/04ERSb06dOg
The symmetry ambigram was designed by Punya Mishra:
https://punyamishra.com/2013/05/31/symmetry-new-ambigram/
The Monster image comes from the Noun Project, via Nicky Knicky
This video is part of the #MegaFavNumbers project: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo
To join the gang, upload your own video on your own favorite number over 1,000,000 with the hashtag #MegaFavNumbers, and the word MegaFavNumbers in the title by September 2nd, 2020, and it'll be added to the playlist above.
Thanks to these viewers for their contributions to translations
German: dlatikaynen
Hebrew: Omer Tuchfeld
Italian: mulstato
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
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Download the music on Bandcamp:
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If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
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Week 1: Review of linear algebra. Groups. Examples of groups.
Basic properties and constructions.
This video:
Introduction to the course; Review: Linear algebra; Definition of groups
Notes for this lecture: http://www.extension.harvard.edu/sites/default/files/openlearning/math222/files/notes/L1-N.pdf
These lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School.
View Complete course (Syllabus, Notes, Problem Sets, etc) at: http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra
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In this video I talk about how to learn abstract algebra from start to finish. I go over some books which you can use to help you learn abstract algebra from the very basics all the way to graduate level abstract algebra.
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Abstract Algebra by Saracino https://amzn.to/3bF8Dwp
Contemporary Abstract Algebra by Gallian https://amzn.to/39xmRg3
Modern Algebra by Durbin https://amzn.to/2Kg1eZf
Abstract Algebra by Beachy and Blair https://amzn.to/3qs7EE9
A Concrete Approach to Abstract Algebra by Sawyer https://amzn.to/3oXSJBj
Introduction to Abstract Algebra by Dubisch https://amzn.to/3suliIK
Abstract Algebra an Introduction by Hungerford https://amzn.to/3sulqIe
Elements of Abstract Algebra by Clark https://amzn.to/3ihbLA2
Algebraic Structures(note the name is updated now) by Lang https://amzn.to/2N7tM8n
A First Course in Abstract Algebra by Paley and Weischel (can't find it, here is another one) https://amzn.to/3iHfuLx
A First Course in Abstract Algebra by Fraleigh https://amzn.to/3nE7dEQ
Lectures in Abstract Algebra by Jacobson(this all 3 actually) https://amzn.to/3sqibBg
Concepts in Abstract by Lanski https://amzn.to/3nM9Rbs
Algebra by Artin https://amzn.to/39BIWKD
Galois Theory by Artin https://amzn.to/38H9fzN
Algebra Through Practice: Rings, Fields, and Modules https://amzn.to/38KmIXK
Algebra Through Practice: Groups https://amzn.to/3oMfKXJ
Algebra by Van Der Waerden Volume 1 and 2 https://amzn.to/3oMg5tt and https://amzn.to/2LQc5JI
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Algebra by Lang https://amzn.to/2N5X3jL
Abstract Algebra by Dummit and Foote https://amzn.to/3oLfyrG
Exercises in Classical Ring Theory by Lam https://amzn.to/3qleYRJ
Topics in Ring Theory of Barshay https://amzn.to/2LxAaFr
Ring Theory by Behrens https://amzn.to/3oOHRoY
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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:
Have you ever wondered how Koji Suzuki's Ring compares to the films Ringu and The Ring? In this video, I'm reviewing the book, comparing it to the movies, and detailing why The Ring book is better than the movie. Have you read the book? Please let me know your thoughts below!
DISCLAIMER: I apologize for pronouncing any names incorrectly in this video. I tried my best!
Let's become spooky besties~
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ON THE CASE - The Ring
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SEVEN DAYS.
here are my thoughts on the English translation of the thriller/mystery novel, Ring!
// article i mentioned: http://horror.dreamdawn.com/?p=54891
// find me over at these places:
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Hakone, Island Baby! The source novel behind the Japanese horror phenomenon of the late nineties and our initial introduction to beautiful, baleful Sadako Yamamura - haunter of the empty channels. Dark, dark themes here, even if you're already familiar with the film. Play it at your friends. Preferably within the week.
Unfortunately a bit of traffic noise (and light) has leaked in in parts. And, that bit of fibre on my top at the beginning is not a white pubic hair. It just looks like one.
This was such a hard book to talk about because I REALLY enjoyed parts of it but I was constantly uncomfortable with the misogyny and r@pe culture so like??????
Honestly, I feel like I could have done this review a little better, however there is a lot to unpack that would contain a lot of spoilers about the book.
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🌙 Last Video 🔮 Gothic Horror Book Recommendations
https://youtu.be/pDH5f2a7efk
💀 Books Mentioned 🩸
The Exorcist - William Peter Blatty
The Case Against Satan - Ray Russell
The Ring - Koji Suzuki
The Haunting of Hill House - Shirley Jackson
Pet Sematary - Stephen King
Thomas Ligotti - Songs of a Dead Dreamer & Grimscribe
I am Legend - Richard Matheson
The War of the Worlds - H. G. Wells
House of Leaves - Mark Z. Danielewski
Disclaimer: This video was sponsored by Skillshare
Ring by Koji Suzuki Book Review
Part of the #365100books
Buy the book: https://www.waterstones.com/book/ring/koji-suzuki/robert-b-rohmer/9780007240135
https://www.artelino.com/articles/ghost_story_okiku.asp