What is Abstract Algebra? (Modern Algebra)
Вставка
- Опубліковано 6 лип 2016
- 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:
bit.ly/1ixuu9W
♦♦♦♦♦♦♦♦♦♦
We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
amzn.to/2oOBd5S
Milne, Algebra Course Notes (available free online)
www.jmilne.org/math/CourseNote...
How to Be a Great Student
ebook: amzn.to/2Lh3XSP
Paperback: amzn.to/3t5jeH3
Kindle Unlimited: amzn.to/3atr8TJ
♦♦♦♦♦♦♦♦♦♦
Ways to support our channel:
► Join our Patreon : / socratica
► Make a one-time PayPal donation: www.paypal.me/socratica
► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9
Thank you!
♦♦♦♦♦♦♦♦♦♦
Connect with us!
Facebook: / socraticastudios
Instagram: / socraticastudios
Twitter: / socratica
♦♦♦♦♦♦♦♦♦♦
Teaching Assistant: Liliana de Castro
Written & Directed by Michael Harrison
Produced by Kimberly Hatch Harrison
♦♦♦♦♦♦♦♦♦♦
Sign up to our email list to be notified when we release more Abstract Algebra content: snu.socratica.com/abstract-algebra
Hi teacher I want your number in the WhatsApp plz send me
I have a lot of math work to do and I will pay you for it
People would do better in this class if professors took 10 min at the beginning of the semester to say what's been said here.
Let's hope they share our video at the start of each semester!! 💜🦉
Why take ten minutes, when the video is only 3??
@@Charles.Wright to repeat it hahaha
@@Socratica *BRINGS LUNA, I MEAN... LILIANA'S BACK!!!! Please!! 🙏🏻🙌🤩.*
@@Charles.Wright maybe questions may arise
"If you are ever at a cocktail party full of mathematicians..."
I'm still trying to figure out if this is a joke or if I'm just such a nerd that even the nerds don't invite me to parties.
To be fair, these only happen when all the planets align.
A party of mathematicians would only be attended by imaginary numbers.
If you don't mind a bunch of socially inept maths-nerds, D&D players, coders, and neurotransmission modification connoisseurs ... you're totally welcome to come to our next ... uhm ... "cocktail party".
@@sharonjuniorchess lateral numbers...
@@CreationTribe .
I recall that this series was one of the things that drew me towards pure mathematics when I was in high school. Now I'm doing a master's in algebra, geometry and number theory; thank you for making this!!
How wonderful to hear this, thank you so much for telling us! We're so glad to hear about your progress. 💜🦉
It is hard to find many well done tutorials on higher maths on UA-cam. I really appreciate that you have made this. I would love to see more with topology, analysis, complex analysis and more. I would love to help! Take care and great work.
Thank you Socratica for this series of Abstract Algebra 😃 You made all things easier to understand for me and I felt confident in myself after learning from you 😊
Welcome to Socratica! We're so glad you've found us. We hope you subscribe so you hear about our new videos: bit.ly/SocraticaSubscribe
Here's our Abstract Algebra playlist (more videos coming soon): bit.ly/AA_playlist
thanks
Dear Socratica I have some problems with my Accounts in digitally world when I could get rid of them completely and get control over my Accounts than I would gladly began to subscribe your channel until than I have to get rid of hackers that buddering me.
Your explanation technique is awesome and I liked your channel very much
Thanks for making this series - very helpful 🙏
What is the book used in the video ?
Thanks for the explanation!
I've already done abstract algebra and consider it an easy subject to pick up. What isn't so easy is explaining it to someone who barely remembers high school geometry, but you succeed. Thanks!
This is now a UA-cam textbook for abstract algebra 🤝
To me, this is the most valuable Socratica series of lectures. Subject is usually very dry presented by un-enthusiatic mathematicians with no teaching skills and certainly without any examples that the student recognizes. Ms De Castro presents this series with a sense of humor and her very expressive face makes each lesson quite fun and painless. I don't know if I should congratulate myself for finding this lecture series on these topics that I so seek to learn for so many year...or to congratulate Ms De Castro for her outstanding set of lectures...the recommended textbook by Dummit and Foote is the usual dry, unreadable, and incomprehensible strings of words and symbols...nothing like the lectures. Don't waste your money....just watch the videos over and over again and think about the meaning and implications. Good luck.
Thank you so much, Socratica, for all of your wonderful videos!
You are so kind, thank you so much for watching! :)
Thank you for all the work you've done. I'm really grateful to this course.
I’m not a math major but I’m in love with mathematics and have recently decided to teach myself. Amazing video, a great introduction that left me excited to dive in!
It's pretty amazing that for most subjects, you really do need to spend years and years as an apprentice to other people, in college and beyond, but if you are motivated you can learn SO much math on your own with textbooks and now videos!
Hey Socratica!
You have no idea how much your explanation helped me!
Even though you covered the basics of LA, the playlist is still missing the core of LA, which are the vector spaces. I would really appreciate if you guys can continue making videos of this topic, cuz let's be honest, you explain better than many professors out there! ;) Thanks for the current videos, and looking forward to new ones! Cheers :)
I honestly thought that I teach things pretty simply but Algebra was a part of the course that I would always find too abstract even for mathematics so I never thought I could find anyone who can explain it in an easy way the way you did and for this you deserve all the gratitude lady good luck in your career !! (This is not my main account )
GOD! With this exciting intro I'm going to watch all the series today. Just Perfect!
It worked!!!! Hee hee that's just wonderful to hear. We hope you enjoy! :)
It's a perfect field.
Thanks to the UA-cam algorythm I'm here
We're so glad you've found us!! 💜🦉
My dad sent me this video.
Love ur video ...u made it so easy to understand what abstract algebra is about ...your natural way of expressing things that are complicated makes things easy😊
Our first book is here! How to Be a Great Student
ebook: amzn.to/2Lh3XSP
Paperback: amzn.to/3t5jeH3
Kindle Unlimited (read for free): amzn.to/3atr8TJ
I love to watch Abstract Algebra videos on your channel. It is so fascinating and delightful.
Really great video! Thank you! Keep going!
These videos are dope! Who thinks we need a series on Category Theory from @Socratica?
I remember taking the Group Theory class for my math BA requirements. It was the hardest class I ever took and it took at least 15 - 20 hours per week of my time. I got a B+ in the class and I was the happiest person at the time when I was done with it.
Wait why did you pursue a math degree if you hate group theory so much? That's like if a vegan were to eat steak.
I never knew such a beautiful yt channel of maths existed, thankyou, you people make yt a better place. I wish my fellow countrymen starts studying this way rather than mugging up formulas to get answers, without knowing anything what they're doing
Hello.
I have a request. Please make more videos on abstract algebra such as mappings, permutations, isomorphism, homomorphisms, normal subgroups,factor subgroups,coset and cyclic groups. It would be beneficial for students. I hope you consider my request. Looking forward :)
U guys are doing something that no one ever did keep making these video ur stuff is outstanding
Modern Algebra still remains my favorite math course I've ever taken. I took it junior year of college and it's the only math textbook I made sure to keep instead of selling back to the bookstore. I still revisit it every few years (my friends think I'm nuts when I tell them I'm reading it for pleasure).
Interestingly, the book we used teaches Fields first, then Rings, then Groups.
bless these videos my teacher just goes on and on about the details of groups i dont even know why they are useful until now :')
Thank you for this course! Incredible videos.
mam you have made this video in 2016 but I am watching your video in 2022 and feeling like i am sitting in front of you and you are teaching me live. i really like your way of teaching, way of speaking and everything. before i was thinking that English is not good language for teaching but after listening u my mindset has changed. Thanks for making the video, i will listen you again and again to speaking english like u
Wow this is awesome. My professor never mentioned that group theory was used to solve higher degree polynomials. Of course, after watching this it makes sense, but if I’d known at the time I took the course, I’d have a better appreciation for abstract algebra.
Would be nice if you guys could make a similar series of videos about Category Theory.
Good suggestion! Once we cover topics like continuous functions, diffeomorphisms, and other morphisms, then we'll be ready to make some videos on category theory.
Oh snap. this just got REAL ...as in the Field of the Reals.
I know this is a super old comment but I'm wanting to get into category theory too and if it's possible to make videos of this quality as an introduction, I definitely wanna have that as well.
@@Socratica hello from 2020. Any updates on category theory videos? :p
Category theory is the abstract algebra of abstract algebra.
Very useful information. Thank you very much!
what a great lectures? I love these lectures.......and a bundle of thanks to socratica
"When are you ready to learn Abstract Algebra?"
Starting my Modern Algebra course in a couple weeks when going back to College, so I hope I'm ready? Absolutely glad I found this channel now by the way, I'll make sure to watch many more videos ;)
We're so glad you've found us - keep us posted on your progress!! 💜🦉
Thank you so much!! I will 😉
Amazing....the way u explained... enabled my mind to think...that's really really nice....the world requires more teachers like u ma'am....thanks for such a wonderful UA-cam channel....great work...
here saying "it took years of hard work to find the right definitions of absrct algeb"
..
my teacher : " aight we're gonna finish this chapter this week and i define it now!! "
Thank you, you have explained it well.
It would be great if you could make some videos about Linear Algebra too.
These videos are amazing. please try to cover all the topics of algebra. Videos are making our concept clear and i think, i am falling in love with maths. Thank you so much. :)
Instant subscribe. Interesting channel. Modern Algebra was one of my favorite subjects as an undergrad.
I never heard about abstract algebra, but after this video I'm just really excited to learn it!
That's fantastic!! We're so glad our video got you interested in this important branch of math!! Thanks for watching. :)
Thank for making a video about Abstract Algebra. The song in the end is also nice. :D
my final project was made by a one man group (me), I used only abstract algebra, in fact, I used an extension of abstract algebra for creating cubes using irregular data universes for hypothesis discovery. It may sound fancy, but it is very straightforward and totally can be used in the real world
This kind of videos we all need to make the basic concepts of higher mathematics to be accessible to interested non mathematician public .. thus appreciate it's importance and beauty .. keep the good job!
your lectures are very nice, thank you
You guys just kinda saved my life... :-D Please complete this playlist, please please, Do not abandon this playlist(some do)... A BIIIIG THANKS
It's great to hear our videos have helped. We plan on making many more abstract algebra videos! :) In fact, we just released a new video today. We're working hard to release abstract algebra videos more frequently. Dozens of more videos are on the way!
I've been a proud nerd for several years, watching maths videos for recreation in the evenings, yet I only just found this channel??? You guys need to be wayyyy more famous
We're so glad you've found us!!
It would help us a ton if you'd share our videos (Twitter, Reddit, etc.) so more people can find out about us!
NERDS UNITE!!
Thanks for watching :)
Socratica haha we're an endangered species, gotta look out for each other!!! I've already told 2 of my friends who are trying to learn python to check you guys out, and I recommended this channel on reddit. You guys are my new favourite channel by far: python tutorials and maths, it's like someone read my mind
Hooray!!
More math and python coming soon. :)
Socratica WOOP WOOP WOOP
Really mam l follow you for 24 hours your attitude to teach students is really up of the benchmark. Thank you for your service.
This kind of video helps to learn the concept deeply thanks for it
Love content and presentation!
The videos on group theory are quite helpful. It would be great if some videos on representation theory of groups are made.
Awesome videos, loving it ❤👍
a whole semester of struggling with abstract algebra now i've bumped into this...thank you Socratica!!!
We're so glad you've found us!! 💜🦉
@@Socratica In my opinion, maybe need a Chinese subtitle 🤣🤣
Are u Nigerian sir
@@wisdomemeka6271 I don't know why that is necessary here
This playlist made me believe that it is quite possible for me to learn Abstract Algebra on my own and enjoy it. After watching these videos, I was able to breeze through the first 1/3 of "A Book of Abstract Algebra" by Pinter (on the same difficulty level of this playlist, so I highly recommend it too). I wouldn't have been encouraged enough to do that if it weren't for these vids. Now I have my sights set on getting to Representation Theory, I couldn't have imagined that when I started watching this playlist a month ago. Thank you, Socratica!
Thank you so much, Harold, for your kind comment. We can't tell you how wonderful it was to read your words. This is exactly why we are making these videos! Please keep us posted about your progress - we'd love to hear more about your studies!! :)
At University I loved Abstract Algebra - it was the only subject that 'pushed' me, and seriously hurt my brain.
Abel also had a big role in starting this field. So many talented young mathematicians.
You're glad that I found your channel and I'm glad that I found your channel. Wonderful video.
Thanks for this explanation, like to hear and see more, kind regards
That was helpful. Many thanks!!!!
I like your way of making things easy to understand ♡
Really very helpful.. Apreciate you the way you explaning.
Thank you x 2^2048! I am learning a lot about Abstract Algebra with this series of videos. What a high-quality material! Please, keep up the good work. Looking forward to supporting this project. Want to learn more about the ways of doing this. Amazing! Just amazing!
Thank you so much for your words of encouragement, David!! :)
These are concepts it took me a long time to grasp by myself
You are amazing! Thank you so much.
what book you recommend me to learn abstract algebra.
Great Job. You revolutionized my mind..
VERY MUCH THANKFUL FOR THIS YT Channel. 💙
I have learned so much from this channel in pretty small amount of time, The mathematics' teachers here are definitely God sent. Thank you!
Thank u..Nice explanation...we need it.. Lots of love to the team..
Love the way you explain...
Have you covered Sylow's Theorems yet? Any plans on Lie Groups? I read something about dffeomorphisms and morphisms. Seems like a good topic to bridge into.
Thank you very much. This was what I needed to hear. 👍👍
We're so glad you enjoyed the video!! 💜🦉
What is the book used in the video ?
Hi, I'm an undergraduate student in Electrical Engineering, and I have taken a basic course in linear algebra. I found it really fascinating. I have learned about fields, vectorspaces, matrices, inner product, eigenvalues/vectors, etc. (I have also already received a basic knowledge of calculus and differential equations.) What books would you guys recommend to deepen and expand my knowledge on abstract algebra?
Who ever edits your videos is a genius. The music, background, colours and audio quality remind me of a 90s movie or a 3d shareware video game.
You are so kind! Our videos are really a labor of love. We're self-taught, and we love making our little movies! You can read more about our small team at Socratica here: www.patreon.com/socratica
I'll check it out! thank you for your videos, I really appreciate the effort you all put in to make these amazing videos for us.
omg, i have goosebumps.. i love you..subscribed. done
Same here. This is a beautiful video.
extremly usefull!! thanks
Thank you for the knowledge ma'am❤️
Might be interesting to note that there disciplines outside of the STEM ones mentioned in the video that use abstract algebra. There is a whole subdiscipline of music theory based in abstract algebra! Those interested should look up David Lewin's seminal book "Generalized Musical Intervals and Transformation"
awesome video!!
One of the best channel on mathematics !
So kind, thank you for your appreciation!! 💜🦉
you videos help students who are doing degree courses in mathematics. i highly appreciate your offer. thanks
Thank you so much for your kind words. It makes us so happy to hear our videos are helping people! :D
Could you please cover Fluid Mechanics ? It's a hard subject but you make things so simple to understand !
This is awsome. Very cool and interesting video. Not at all like my boring professors.
Great video, looking forward to learn more.
Fantastic!! We're so glad you've found us. Thanks for watching! :)
thank you, I'm learning from both my son and a text book but to see such videos still helps a lot to better understand!
How fun to be learning with your son! Let us know how you get on. 💜🦉
@@Socratica thanks for the reaction - I'll do my best! It's hard but it's so good to train the brain!
Please update a video can you release that abstract algebra in group action
sister you saved us tommorow is our exams and you saved our asses
thanks a lot
Ótimo vídeo de um ótimo canal. Postem mais vídeos
Your presentation is best ...I clearly understand your classes
amazing videos it actually made my studies sooo easy
Fantástic! Amazing your Algebra explanation
Thank very much
Go ahead !
From India but it took many years to me find best channel. ....
By abstract are you talking about an Aristotelian abstraction where you aggregate the abstracted object across many instances? Or are you doing a more transcendental abstraction, where one tries to see what is logically prior or necessary for x,y, or z?
Amazing!!!
may i know which book is recommended by you for beginners?
Great intro ...thanx!
I am teaching myself abstract algebra (with a book of course). I expect I will be using this site as a tool to guide me. I am excited to take on the challenge!
Im trying to learn it too! good luck :)
@@JP-xn3tj Awesome! If you ever want to compare notes or have a study buddy, let me know! I am at a community college currently, so no one is able to help me at the school.
amazing videos... very helpful...
"If you ever are on a cocktail party with mathematicians, they will just call it algebra" Just this xd.
Not that they don't have different names for its brachches though, from Linear Algebra, Algebra, kommutative Algebra, ... or even universial algebra (yes, this is then the abstractified version of abstract algebra :D)