Ive been in Abstract Algebra class getting confuse every day untill i meet you Socratica. You are pretty Good. I give you five Star. Thank you so much.
Thank you SO SO SO much for this! I shouldn't admit this, but... ...I went through entire courses on Galois Theory & Lie Algebras... ...all without ever really realising this most basic fact. The curiosity was there, of course...but...I just assumed it was an artefact of abstraction. Instead, ends up it was the very method itself, Shamelessly waving it's self-styled raison d'être in front of our faces. This should have been obvious from the start! Always appreciate a (not-so-)subtle reminder to look up from the granular minutia on occasion, and take step back to appreciate what all of this is actually for. Seriously; Thank you a million, million ways.
Isn't Liliana amazing! She has such a knack for helping everyone understand and become more self-sufficient in math. We think it's because she's a real lifelong learner. 💜🦉
I am a student and have no job but want to donate to this beautiful channel. But have no money, I am sure after I get job I will dinate to this channel.
This is deep, I know the basics of group theory and how it relates to subsets of matrices and rubiks cubes, but I never noticed it's relation to the solvability of equations. This is so simple yet so crazy. Thanks for being on youtube ♡
I love your Explanations, The way you described the group is mind blowing, I am a computer science engineer, and I am from India , lots of love from India, Thank you so much.
Thank you so much for these video's now I don't need to waste data on binge watching series, I can binge watch Abstract Algebra lessons instead. There's hope after all this semester. You summarize everything so eloquently and you make the lessons fun. We're using Pinter Algebra as the set work textbook and my lecturer isn't animated or interactive at all. But when I was reading up on the history of this subject it seemed way cool. You brought that "cool" to life.
Super interesting. My physics lecturer went over this kind of thing during our particle physics lectures. I'm also learning Lisp and Haskell and I figured it was high time to learn this stuff :)
I think that, the real motivation for the definition of a group is that, you can form many groups with a many different sets and operations, but, instead of proving the same with any set and the operation, you prove general statment in the group, and if that set with that operation forms a group, then satisfies every statment you proved before. It's like rationals and integers form an Abelian Group with the Adittion, instead of proving one property with integers and then the same with rationals, you can prove a property of a Abelian Group and that statment is satisfied by rationals and integers, because they form an Abelian Group
Group theory is very beautiful and especially useful for physicists. I don't understand why my university teacher doesn't teach group theory as a fundamental course for Physics major students.
I am a mathematical naif in need of guidance. Noether's work got me very excited since I am performing massive discrete geometric transforms, and what little I have learned is already helping me with breakthroughs. I have a B.S. in physics, so I am not entirely without hope, but the notations are challenging. I've watched several of your explanations, and they are hugely clarifying of material I found opaque before. I do not know if you answer questions here, but if not, can you help steer me to a professional mathematician who could help me develop my own notation for a field of study I am developing from scratch? I enjoyed your Z/nZ explanation. Here is a first question: What is the notation for a random shuffle of an ordered set like Z/nZ? I want to use elements from the ordered list as subscript (index) into the shuffled list. I am willing to work quite hard, but your presentations have been the first glimmer of hope for me.
May I ask for help everyone. Let G be the groups of dates grouped into { M, T, W} where M = all Mondays, T=Tuesday, and W=Wednesdays. Constructa Cayley table to find all groups of G, then make a Cayley graph for the reduce residue class of 12. Write your answers in your activity notebook.
Seems to me you take the universe of elements as a complete set, and restrict the elements for a given operation, then that defines the group. So a group is containment of the elements for a given operation. ( this is an interpretation , not necessarily a definition, so new students do not use this for anything)
Yes, because the group operation is associative, the existence of a right identity and the existence of a right inverse for every element gives a "full" identity and a "full" inverse for every element. (You could similarly get the result from a left identity and a left inverse for every element.) However, I don't think it's harmful to state the "full" identity and "full" inverse as part of the definition of a group.
i was wondering she's has so positive aura with great humour and could also be a good actress & turns out she already is ,which confused me did she act so good that i understood everything or is she ..... poof im out
I have a question, should the group have a single operation or it can have n operations with each of them being satisfying with the formulation of the theory??😊
When talking about a group, you are always talking about a single operation. A set *can* have more than one operation. For example, real numbers have both addition and multiplication. But when talking about them as a group, you are always singling out one of the operations.
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Yes! This channel is pure gold. Professors often don't explain stuff at this level
Yo
4am in the morning and that abstract algebra pun made me burst out a loud laugh haha.. splendid.
Same here
I like the way she explains things. It's hard to be thorough without "talking down" or "dumbing it down," but I think she nails it.
Ive been in Abstract Algebra class getting confuse every day untill i meet you Socratica. You are pretty Good. I give you five Star. Thank you so much.
Very very well done video. I have no words to express the joy.
0:55 that part is just so adorable. Nice video btw
This channel is like a gold mine for Physics and Math students like me! Thank you very much!
Thank you SO SO SO much for this!
I shouldn't admit this, but...
...I went through entire courses on Galois Theory & Lie Algebras...
...all without ever really realising this most basic fact.
The curiosity was there, of course...but...I just assumed it was an artefact of abstraction.
Instead, ends up it was the very method itself,
Shamelessly waving it's self-styled raison d'être in front of our faces.
This should have been obvious from the start!
Always appreciate a (not-so-)subtle reminder to look up from the granular minutia on occasion,
and take step back to appreciate what all of this is actually for.
Seriously;
Thank you a million, million ways.
You do explain everything so charmingly. All interested students will like you very much. THANK YOU ! ❤❤❤
Astounding beauty in the simplicity and power of this group definition. Thank you for demonstrating the motivation for these axioms with such clarity.
Thank you i haven't learnt this much from my whole 2nd year. You and your team are just AWESOME. 👍👍
God bless you🌷
This is very well done on so many levels. Thank you so much.
+sanjursan agreed!
The way you express things is awesome.
what a way for learning mathematics! thanks beyond finite for making things so simple, intuitive and interesting!!!
Whoever that narator is she is the best orator of math i have ever seen in my life. So enthralling
Isn't Liliana amazing! She has such a knack for helping everyone understand and become more self-sufficient in math. We think it's because she's a real lifelong learner. 💜🦉
You are a wonderful teacher....I have seen nobody ( I mean it) explaining such complex things so simply....
I am a student and have no job but want to donate to this beautiful channel. But have no money, I am sure after I get job I will dinate to this channel.
The "impossible easy"!
What a great way of putting it!
THANKS
This is deep, I know the basics of group theory and how it relates to subsets of matrices and rubiks cubes, but I never noticed it's relation to the solvability of equations. This is so simple yet so crazy. Thanks for being on youtube ♡
You make so nice videos. Keep making. Thanks for keeping students like me interested in maths.
We're so glad you're watching! Thanks for your nice message. 💜🦉
Fast + knowledge + that smile in end 💯
Being able to teach abstract subjects like mathematics while smiling is a talent.
2 minute video explains what I have been trying to understand for months.
thank you so much .... you made it easy .. and i wish if i had a teacher like you in my college ..
worlds best definition of group is here. very well done
OMG! I just got it. That sazzyness made it extra fun. Love your channel!
I love your Explanations, The way you described the group is mind blowing, I am a computer science engineer, and I am from India , lots of love from India, Thank you so much.
This was a really wonderful insight thank you!
Simply wonderful videos for teachers and students of Abstract Algebra!!!
Thank you so much for these video's now I don't need to waste data on binge watching series, I can binge watch Abstract Algebra lessons instead. There's hope after all this semester. You summarize everything so eloquently and you make the lessons fun. We're using Pinter Algebra as the set work textbook and my lecturer isn't animated or interactive at all. But when I was reading up on the history of this subject it seemed way cool. You brought that "cool" to life.
Loved the way you teach... Thanks a lot..
Cool! I love your teaching style! ❤ 😊
Hypatia would be proud
+bitofeverythingguy
I know, right?!
Underrated comment
She was in the good place
Thankyou soo much...this is the first tym i really got a helpful introduction of groups and understand its practicality
Super interesting. My physics lecturer went over this kind of thing during our particle physics lectures. I'm also learning Lisp and Haskell and I figured it was high time to learn this stuff :)
Lots of love from India, God bless you guys,
Hatss off !!
REAL Mathematics Teaching
I will surely Become your patreon.
I'm glad I found you guys, your website and set up is amazing and your explanations very easy and enjoyable to follow, thank you.
first I saw my second year book I was shocked and feared . after watched your video I feel really good.
I am here after 8 years and i feel lucky to find this ♥️
Very Clean Explanation!!! May this channel gets more subscribers
Beautiful ,,elegant,, goosebumps
how professional you are
How can you Not listen to her? Soo much passion
Nice explanation and so easy and simple fundamental of the propertys👌👍
Elon musk should also give a donation to this channel, khan academy is great but man this channel is on another level
From your lips to #ElonMusk's ears!! 🙏🙏🙏
Hey Elon, our bitcoin address is
bc1qda47tgfyk67lxa7yqn8y5m02hjcglghsd5c58n
Thanks!
Being mathematician and actress at same time is astonishing
she is really great, she talks with love, you can feel it!!
Excellent keep the good work
Hey, I really liked it. Well explained. So, congrats.
Thank you so much.
Thank you very much
omg, Utube propose this ,and it's awesome
We're so glad you've found us! 💜🦉
I'm mathematically hypnotised 😶
Mostly helpful video , thank you so much 🙏🙏✌️✌️
用心編排的內容，精湛的演譯
amazing explaination mam ,thankyou mam
Astonishing.. really art of scientific literacy.. 😍
Wwwwowww
That equation example was legendery
You're the best 💗
Thanks alot...
Ma'am :) nd Socratica team
you like your way of teaching .
You should teach group theory at my school!!!!!
In theory I should teach to my group at my school...
please keep making vids
on advanced maths
very nice i like it. and i wish she was my teacher
thanks a lot.
"3blue1brown" is also gives wonferfull explanantion on algebra....
I think that, the real motivation for the definition of a group is that, you can form many groups with a many different sets and operations, but, instead of proving the same with any set and the operation, you prove general statment in the group, and if that set with that operation forms a group, then satisfies every statment you proved before.
It's like rationals and integers form an Abelian Group with the Adittion, instead of proving one property with integers and then the same with rationals, you can prove a property of a Abelian Group and that statment is satisfied by rationals and integers, because they form an Abelian Group
Omg, omggggg I am just so delighted cuz I descovered this.. :'(
Group theory is very beautiful and especially useful for physicists. I don't understand why my university teacher doesn't teach group theory as a fundamental course for Physics major students.
I am a mathematical naif in need of guidance. Noether's work got me very excited since I am performing massive discrete geometric transforms, and what little I have learned is already helping me with breakthroughs. I have a B.S. in physics, so I am not entirely without hope, but the notations are challenging. I've watched several of your explanations, and they are hugely clarifying of material I found opaque before. I do not know if you answer questions here, but if not, can you help steer me to a professional mathematician who could help me develop my own notation for a field of study I am developing from scratch? I enjoyed your Z/nZ explanation. Here is a first question: What is the notation for a random shuffle of an ordered set like Z/nZ? I want to use elements from the ordered list as subscript (index) into the shuffled list. I am willing to work quite hard, but your presentations have been the first glimmer of hope for me.
You are great.....
First time i got WTF is a GROUP
Math ASMR. Love it
thank you madam.......
Thank you mam
Thank U Perfect motivación 😉
Awesome!
May I ask for help everyone.
Let G be the groups of dates grouped into { M, T, W} where M = all Mondays, T=Tuesday, and W=Wednesdays. Constructa Cayley table to find all groups of G, then make a Cayley graph for the reduce residue class of 12. Write your answers in your activity notebook.
very helpful!
1:42 you better believe thats goin into our definition!
Thanks
can u plz upload a video about group theory theoremz??specially on infinite groups
this video made my brain get blown.
0:53 holy shit...
Field Axiom 1 and Trichotomy.
Wait so when you solved the problem, why did you go through all the confusing stuff, couldn't you just subtracted 3 from both side and got x=2?
Now i kinda argue with myself. Whether I love abstract algebra more than linear algebra?
great ...
Seems to me you take the universe of elements as a complete set, and restrict the elements for a given operation, then that defines the group. So a group is containment of the elements for a given operation. ( this is an interpretation , not necessarily a definition, so new students do not use this for anything)
Please help with maximals
I think right identity and right inverse is sufficient.
Yes, because the group operation is associative, the existence of a right identity and the existence of a right inverse for every element gives a "full" identity and a "full" inverse for every element. (You could similarly get the result from a left identity and a left inverse for every element.)
However, I don't think it's harmful to state the "full" identity and "full" inverse as part of the definition of a group.
stunned
OMFG; OMFG. The best thing that happened in my life
i was wondering she's has so positive aura with great humour and could also be a good actress & turns out she already is ,which confused me did she act so good that i understood everything or is she ..... poof im out
Done
I have a question, should the group have a single operation or it can have n operations with each of them being satisfying with the formulation of the theory??😊
When talking about a group, you are always talking about a single operation. A set *can* have more than one operation. For example, real numbers have both addition and multiplication. But when talking about them as a group, you are always singling out one of the operations.
Socratica, So you mean that set may have multiple operations but group has only one operation,don't you?😊
@@OmarAhmed-ic4fw no. a group is a set and an operation. so it's always a single operation.
Why are u not making videos in nowadays 😔 😒
I thought groups were introduced from Galois theory.
Bu nası bi şey yaaa :D İlginç ama güzel bir anlatım tekniği