Hello, can you please tell me how to translate equations like (x^2+5x+6=0) into a math field? I tried looking up that in ANY way, but I've been having no luck finding a way. 😓😣😢
My problem with abstract algebra has always been intuition, which most professors and videos on the internet skip. I've been through many videos of Socratica's abstract algebra playlist and my basics are so much better! You've given me a simple intuitive approach that I can easily build upon with my textbooks. Special mention to this video, it's eye opening. Thanks for clearing the fog and making abstract ideas so comprehensible. This is rare, keep going, lots of love and gratitude 🙌🏻❤️✨
Totally true. So many resources won't even through a single bone to help intuition. It's definition/proof, barely alluding to novel examples. Throwing in integers mod P in this video really turbo-charged the intuition factor.
Two days of reading books trying to understand this topic, and this video helps to break down and clear up any misunderstandings in less than 10 minutes. Thank you so much and please never stop making these explanation videos. :)
I like that your teaching videos are short and snappy. I’m extending my maths beyond the applied stuff I learned when studying electronic engineering decades ago. Purely out of whimsical interest and I get a bit addicted to it.
I'm building a computer and get to choose what instructions it will perform. While watching this video, I realised that I could free up 'space' for one extra instruction (a useful one that previously could not be included) by deleting all of the subtraction-based instructions and instead implementing negation-based instructions to go along with the pre-existing addition-based ones. In effect, I can do everything I could do before, and also got a bonus instruction into the bargain! I just have to perform subtractions in 2 steps instead of 1: 1) negate B 2) add A,B Credit where it's due: I had the thought to do this when you spoke about additive inverses, so thank you :)
I thought I found some very good resources over the years, but I am amazed at how I didn't come across Socratica until now. This is the first video of theirs that I have ever seen, and everything from the clear explanation and clean presentation to the really satisfying sound effects is top-notch. I am thinking I may have just started another binge-watch tonight...
Great video and really appreciated work. To provide great video without any cost is a noble work. Be with us and provide more videos on real-analysis :)
Excellent topic overview for those of us trying to get started with this and already the door is opening to a much more expansive beautiful intellectual view.
It's worth noting that "division rings" do exist and aren't necessarily fields. As long as the multiplication is noncommutative, it will not be a field. But also commutative rings without multiplicative inverses aren't fields either. So really, they are both the distinguishing features between rings and fields.
I just binge watched all of Abstract Algebra. I started trying to makes sense of GCSE math (its unstructured memorization). Between here and numberphile we have what makes sense and interesting.
Hey socratica, can you do a series about Galois Theory and Polynomials? since that would be a nice follow up from your abstract algebra series and a nice refresher for the audience who may have done it in the past. Great videos :)
Can anyone please explain why at 6:31 it is mentioned that any field F contains exactly one prime field as a subfield? If it were so then the field Q contains all integer mod p subfields which are prime fields.
Keep in mind that the operations in a subfield must be the same as that in the original field. For instance, in Z/2Z, we have 1+1 = 0, but in Q, we have 1+1 = 2, which is not 0. So they don't have the same addition. (And this generalizes to every prime field.)
I started to get inspired by physics through Stephen Hawking in 2018 so I started to self teach myself I started on math and I became good at in understanding the math more than ever but I haven't done any of the differential equations and multiavariable calculus so not trying to be like anyone I took a strong interest in it and physics, now im 39yr old I said to myself how well I am foing in math the past 3 or 4 yrs after in hightschool I used to be crap at math its amazing what self-teaching yourself can do.
Very good explanation. I lost you in what exactly is the Char(F). Maybe it needed a little bit more explanation. Or maybe I should study Galois Theory xD
I'd like to emphasize more on Monoids here. They are semigroups with an associative [a*(b*c) = (a*b)*c for a binary operation *] binary operation (+, -, ×, or ÷), with identity (1×a = a×1 = a, 0+a = a+0 = a)
You should do a collab with Grant from 3blue1brown :D He is in deed very interested in collaborating with high quality education channels, he will be surprised, when he looks at your content 👍
Sign up to our email list to be notified when we release more Abstract Algebra content: snu.socratica.com/abstract-algebra
Can you please add videos on Linear algebra.
Moomomomoommoommo
must not a field have a propert that x*y means adding x+x+x...x y - times, or it can be different?
Hello, can you please tell me how to translate equations like (x^2+5x+6=0) into a math field? I tried looking up that in ANY way, but I've been having no luck finding a way. 😓😣😢
This might have been the clearest explanation of rings and fields I've seen. Great vid!
+ Groups
when i took abstract we did not study rings, integral domains or fields in class, were just given 3 pdfs that we were to study before the final exam
Agree - Books require memorization of ~250 pages to likely fully understand what was presented here.
Best companion to self learning mathematicians.
Along with Khan Academy, sure.
My problem with abstract algebra has always been intuition, which most professors and videos on the internet skip. I've been through many videos of Socratica's abstract algebra playlist and my basics are so much better! You've given me a simple intuitive approach that I can easily build upon with my textbooks. Special mention to this video, it's eye opening. Thanks for clearing the fog and making abstract ideas so comprehensible. This is rare, keep going, lots of love and gratitude 🙌🏻❤️✨
Totally true. So many resources won't even through a single bone to help intuition. It's definition/proof, barely alluding to novel examples. Throwing in integers mod P in this video really turbo-charged the intuition factor.
Two days of reading books trying to understand this topic, and this video helps to break down and clear up any misunderstandings in less than 10 minutes. Thank you so much and please never stop making these explanation videos. :)
Thanks! Great explanation of Fields!
Thank you so much for your kind support! It makes a huge difference!! 💜🦉
The quality of your teaching is way beyond the average
I like that your teaching videos are short and snappy. I’m extending my maths beyond the applied stuff I learned when studying electronic engineering decades ago. Purely out of whimsical interest and I get a bit addicted to it.
I love Socratica too.. it is everything that a good channel should be.
You guys closed a black hole in my math knowledge, keep up the good work
Yeay math. Please do videos on topology, real analysis and just any pure math subject you like.
Yes!!! Please do videos on real analysis!
This is amazing. It took me 30 seconds of watching this video to understand what i have been taking for granted in high school
I'm building a computer and get to choose what instructions it will perform. While watching this video, I realised that I could free up 'space' for one extra instruction (a useful one that previously could not be included) by deleting all of the subtraction-based instructions and instead implementing negation-based instructions to go along with the pre-existing addition-based ones. In effect, I can do everything I could do before, and also got a bonus instruction into the bargain! I just have to perform subtractions in 2 steps instead of 1:
1) negate B
2) add A,B
Credit where it's due: I had the thought to do this when you spoke about additive inverses, so thank you :)
you have explained one of the most difficult math topics and made it look easy. I wish you were my prof in University
No this is not one of the most difficult math topics
I thought I found some very good resources over the years, but I am amazed at how I didn't come across Socratica until now. This is the first video of theirs that I have ever seen, and everything from the clear explanation and clean presentation to the really satisfying sound effects is top-notch. I am thinking I may have just started another binge-watch tonight...
Your work I highly valued by myself, I can easily read through a textbook after watching your videos. You are so good!
"Additive inverse" = "opposé" in french
and "multiplicative inverse" is simply "inverse"
Great video and really appreciated work. To provide great video without any cost is a noble work. Be with us and provide more videos on real-analysis :)
Videos like these make me fell in love with Mathematics more and more.................. This is the best channel to learn mathematics!!!!!!!
Thanks Socoratica
from Somalia
Excellent topic overview for those of us trying to get started with this and already the door is opening to a much more expansive beautiful intellectual view.
I always love the math videos on this channel
Socratica is a companion indeed, you make me feel safe. God bless you, and I hope to be a Patreon soon
A good and fun video that we can watch smiling from beginning to end
I was waiting for Field videos when I was taking Abstract Algebra in my junior year. Now, I have even completed my bachelors. Lol
Thank you Socratica, very cool
Thanks!
I can't stop falling in love with maths because of ur way of teaching mam
Thanks
This is the most easy way to understand mathematics you are have a simple and deep understanding of mathematics thanks
I became fan of this Channel ❤. I loved the way you explained harder concepet in simpler terms.
Yess!! Socratica We love to watch your videos because these build best concepts...Thank you so much
You are the best at explaining these concepts which are somehow complicated. Thanks for making these video
I am amazed by your explanation, it seem much easier now, thanks a lot!
Such a clear explanation even highschooler could understand. Very good, thanks
Great video. This is my current course so I greatly appreciate the clarity
Thank you for your kind words! Good luck in your course this term!! 💜🦉
wish this was there when I was preparing for the exam ! GREAT VIDEO !!!
It's worth noting that "division rings" do exist and aren't necessarily fields. As long as the multiplication is noncommutative, it will not be a field. But also commutative rings without multiplicative inverses aren't fields either. So really, they are both the distinguishing features between rings and fields.
Cool! For example?
@@valeriobertoncello1809 Quaternions.
Thanks for making ideas of fields more clear.
Hope you will make video on Galois fields and their applications.
thank you so much. I am studying for a quiz and doing homework and this helped so much
I just binge watched all of Abstract Algebra. I started trying to makes sense of GCSE math (its unstructured memorization). Between here and numberphile we have what makes sense and interesting.
I love the way you explain things...JUST BEAUTIFUL
Hey socratica, can you do a series about Galois Theory and Polynomials? since that would be a nice follow up from your abstract algebra series and a nice refresher for the audience who may have done it in the past. Great videos :)
The beats at 1:56 ! I thought it was my heart thumping really fast because of enlightenment 😂😅
You are doing a great job SOCRATICA...please carry-on...Cover some topics of Differential Geometry if possible...
i love her. the only good explanation i found among all the yb bs
I was able to understand our lesson because of your videos. Next content please about Quasigroup. Thank you in advance!
Just discovered this channel. Instant subscription! I LOVE the style of your exposition!
You are doing good for the whole mankind. Thank you.
The best explanation in the internet.
Thank you this's video very amazing and powerful content.
No doubt these teachings are class apart!
you and your team are so great, i do really appreciate your work! i understand more now , thank you
good comment I like you , i live in India
We look forward to more new videos, please. great contribution.
She is a best teacher ..In my thinking ...
Great explanation! Covered in less than 10 minutes what I spent an hour searching for. Sub and like 👍🏼
Thanks for the video, pretty straight. The educational approach is awesome, good work !
Can anyone please explain why at 6:31 it is mentioned that any field F contains exactly one prime field as a subfield? If it were so then the field Q contains all integer mod p subfields which are prime fields.
Keep in mind that the operations in a subfield must be the same as that in the original field.
For instance, in Z/2Z, we have 1+1 = 0, but in Q, we have 1+1 = 2, which is not 0. So they don't have the same addition. (And this generalizes to every prime field.)
Auto-subscribed, don't even need to look at content of the channel, you already deserve it with this video.
You explained all of this in best possible way ....you should go more then that would ne reallllly helpful .
Thanks for uploading these valuable videos. Please also upload videos on functional analysis and complex analysis
You sure make the mathematics understanding a quite easier
Such sweetness in the end can't donate now surely in future 🙂
Very nice video to learn abstract algebra in simple manner with simple english. Excellent work my teachers.... Thank you so much....
This person is a genius - thx so much
Wowwww. Just Wowww.
Can't even explain how good it is.
Really it is high quality explanation.
Watching from Indian occupied Kashmir.
Mind blowing clear definition of field awesome 👌
best explanation for self learners. thank you
Just to the point that's what make wonderful lectures ... Thank you Ma'am 😊
I prefer to write: (fog)(x):= f(g(x)) instead of fog(x)= (f(g(x)) ...as written at 0:04... nevertheless, congratulations for clarity of presentation
I started to get inspired by physics through Stephen Hawking in 2018 so I started to self teach myself I started on math and I became good at in understanding the math more than ever but I haven't done any of the differential equations and multiavariable calculus so not trying to be like anyone I took a strong interest in it and physics, now im 39yr old I said to myself how well I am foing in math the past 3 or 4 yrs after in hightschool I used to be crap at math its amazing what self-teaching yourself can do.
Lifelong learning FTW!!! Thank you for sharing your story - it inspires us to keep making videos!! 💜🦉
Man I love this Channel
Thank you. This video was perfect and helped me a lot.
Nice description of fields
Very good explanation. I lost you in what exactly is the Char(F). Maybe it needed a little bit more explanation. Or maybe I should study Galois Theory xD
Char(F) is the smallest number of ones to be added in order for it to be zero. In Z/5Z, 1+1+1+1+1 (5 times) = 0
Legendary explanation❤🙏🏻✌🏻
Ojala pronto vuelva Socrática en Español . Felicitaciones por sus videos
Beautiful explanation✨
Great Video. Thanks for making this.
Great explanation. However, as a scientist and not a mathematician I would have loved an example of using a field to address a problem.
Awesome as usual.
I love these videos. Thank you!
Perfectly explained, thanks
Loose Definitions
+ Monoid (no inverses)
+ - Group
+ - x Ring
+ - x ÷ Field
I'd like to emphasize more on Monoids here.
They are semigroups with an associative [a*(b*c) = (a*b)*c for a binary operation *] binary operation (+, -, ×, or ÷), with identity (1×a = a×1 = a, 0+a = a+0 = a)
She teaches more concisely than my teacher at school
thank you so much! for explaning group/ring/fields.
Great Work🔥
Finally I understood what is a field, thank you!
I hated abstract when i took it, but it helped me understand mathematics more than any other class I took in undergrad
wonderful work!!
You should do a collab with Grant from 3blue1brown :D
He is in deed very interested in collaborating with high quality education channels, he will be surprised, when he looks at your content 👍
It's been a while I've been dreaming of a Socratica-like definition of a Function Field. I wonder if that will come true someday.
I mean wow 😲,what an explanation,just amazing❤
My God. I never heard the things this way... All are so stupid in talking about abstract algebra. You nailed it....
This is very helpful keep up the good work. I will donate when I can.
Is 0 the additive identity, not the additive inverse? Great video anyways, I love how clearly everything is explained.
Great Jop 👍👍... Thank You Soooooo Much for these wonderful lectures 🙏🙏🙏
Love this! More topology and the like (maybe even do a video on non-orientable surfaces)!
You are the best teacher I have ever come across.