- Видео 8
- Просмотров 122 980
Martin Trifonov
Добавлен 26 апр 2017
Prelude to Galois Theory: Exploring Symmetric Polynomials
A short lecture explaining the fundamental theorem on symmetric polynomials and its relationship to Galois theory.
Reference book: Harold M Edwards - Galois Theory
Chapters:
00:00 Introduction
05:00 Definition 1 - Polynomial
07:36 Definition 2 - Symmetric Polynomial
08:28 Definition 3 - Elementary Symmetric Polynomials
10:01 Power Sum Theorem - Preamble
12:08 Power Sum Theorem - Proof
17:39 Fundamental Theorem on Symmetric Polynomials - Preamble
20:04 Fundamental Theorem on Symmetric Polynomials - Proof
28:00 Outlook to Galois Theory
30:32 Outro
Reference book: Harold M Edwards - Galois Theory
Chapters:
00:00 Introduction
05:00 Definition 1 - Polynomial
07:36 Definition 2 - Symmetric Polynomial
08:28 Definition 3 - Elementary Symmetric Polynomials
10:01 Power Sum Theorem - Preamble
12:08 Power Sum Theorem - Proof
17:39 Fundamental Theorem on Symmetric Polynomials - Preamble
20:04 Fundamental Theorem on Symmetric Polynomials - Proof
28:00 Outlook to Galois Theory
30:32 Outro
Просмотров: 43 551
Видео
Rotation + Translation = Rotation. Animated proof | #SoME3
Просмотров 77 тыс.Год назад
Every orientation-preserving rigid motion is either a translation or a rotation. This video shows an animated, geometric proof of this fact. Submitted to Summer of Math Exposition #SoME3 Illustrations by Aleks Pankratova. aleks-pankratova.com/.
Walls or Bridges? - #WirVsVirusHack #1 008 corona tracking
Просмотров 9354 года назад
Try out the simulation here: wallsbridges.appspot.com/ Submitted to the #WirVsVirusHack Drei Studenten, ein Ziel. Johann Ioannou-Nikolaides, Martin Trifonov, Julian Wykowski devpost.com/software/walls-not-bridges
Amazing!!!
Davis Richard Perez Betty Hernandez Kimberly
Thanks a lot. Really inspiring
So clear! I love the video!
Great content. Thank you. I'm just stepping into this level of math, and you have deepened my understanding. There is an annoying echo on the audio though. I don't mind replaying parts to be sure of understanding the math; but having to replay six times just to catch the word "norm" was truly annoying.
Wonderful!
Thank you
17:18 unmatched parenthesis on the second line
What an awesome video. You deserve many more views!
Very nice presentation. ⭐️
Cannot wait for the next part.. This has been an elusive topic for me and for the first time ever it has made any sense to me after watching this video. I had to subscribe immediately.. Please keep making more of these...❤
Thank you, thats such a nice comment, its really encouraging :) I have some more planned, stay tuned!
Hey, this is a brilliant introduction, easily missed or overlooked, but more and more enlightening the more you listen to it. The fog is lifting and the relationship between the Galois theory and the Representation / Group theory is becoming apparent. I think I am going to revisit this intro a couple of times more. Thanks!
Thanks, that’s really encouraging! Glad you found it useful!
Hogwarts math!
👍
Excellent use of exposition (telling the story of it) to illuminate a frustratingly slippery path towards Galois Theory. At least now we can see where we are stepping, and place our feet more firmly on the ground before us! Thank you! PS: Great idea using a 'green board' to present your formulas! A nice compromise between the slow-but-friendly blackboard/whiteboard, and the fast-but-impersonal use of math-formula animations! Very innovative!
Fire video my man keep it coming
that drip
Fantastic video. Very clearly presented and motivated. Thanks.
This was such a wonderful watch. I can't wait to see what else you are planning to make.
does this generalize to higher dimensions?
I love how you highlight the essence of galois theory and hence demystify it. Best video so far on symmetric polynomial . Incredible work !!! I'm eagerly looking forward to what comes next in group theory
Amazing video! I learned briefly about Galois Theory in a history of math class, and I couldn’t understand the motivation for so many concepts that were introduced. This video was engaging the whole way through and I have so much more appreciation for symmetric polynomials! Really hoping for a follow up video!
Excellent.
Bob ross style 😂😂😂😂 nice ❤❤❤❤❤
Hello Martin! Algebraist here. I would like to stretch out a hand and say that you did this presentation on symmetrical polynomials very wonderfully. Very clear. Very insightful. I’m looking forward to more of your videos! I might even have a thing or two to learn from you… 😉 Greetings from Sweden! 🇸🇪
Hey! Thank you for your kind words, I'm just starting out, so it means a lot. Greetings from Berlin!
Love your work! Thoroughly enjoyable.
Loved your intro. Decided to stay. Thank you for this.
Thats very kind, thank you! :)
Learning math is way easier with this kind of content, thank you!!
Suggestion: check out the semirings of polynomials, they're pretty cool too.
Will do!
How did you move from quadratic to quintic without explainig cubic and quartic? :)
If this becomes a series the quintic would be the next chapter! :)
I am in love with you. And I am a guy.. I am questioning my sexuality..
Thank you for a lucid presentation of how to develop theories.
Glad it was helpful!
Will try again later. Great presentation.
Made it to 10:22 then I got lost.
That's valuable feedback, it's good to know which moments might be hard to follow, so thanks!
As a highschooler with an interest in cryptology, Galois Theory has been a puzzle I've been poking at for a while. Though we have not quite gotten to Galois Fields yet, this is definitely the clearest explanation I've seen of such concepts. Really hoping this will be a series
If you haven't done so already you'll need to familiarize your self with abstract algebra and a decent understanding of proofs beforehand.
this inspired me to finish my linear algebra pset -- awesome content
Fatnastic stuff! I love the way you explain and summarize. The positively-biased board (black-on-white) really helps me a lot. The audio could get a little bit better, but hey, couldn't it always 😆 Thanks for the ride 🤗
Thanks, that’s very kind :) will work on the audio!
Sincerely thank you for trying to make this topic more approachable, I know from experience that it's not easy, and I cherish every resource I have that can show some insight on it. Edit: 31:00 This resonates with me a lot, I have asked myself many times with Galois Theory why anything shown was thought of, or how any of it follows from the axioms. Most of what I've seen was either too vague to actually show the specifics, or too technical to clearly explain the underlying material, so you're doing a great service by laying this out fully.
Thank you, that’s very kind - I’m glad you enjoyed it :)
Dude, I am not a math type, and I am only a few minutes in, and already I am extremely imptessed with every aspect of you presentation. Congratulations from an educated leyman on your project, which is first rate as far as I am concerned. EDIT. Wow, I got through to 27 minutes before brain called Time-Out !! Superb work Dude.
Thank you, that’s very nice - I’m glad you enjoyed it :)
Audio quality is not great. That makes it hard to focus upon your lecture, which I want to hear. You will well serve your viewers by attending this niggling issue.
Noted, working on it. Thanks for the feedback!
Impossible not to be humbled how a 20 years old guy from the early 1800s could come out with such a deep and abstract insight into algebra. Excellent job presenting the fundamentals of that insight, Martin, so concise and clear. Congrats!!
Humbling indeed. Thank you for the kind words!
Great job. Well done. Better in terms of didactic value than many university lecturers!
Thank you, I'm glad you enjoyed it! :)
Great video! My only suggestion would be a differently colored background as your hair blends in and is a bit distracting. Looking forward to more.
You're right, that didn't quite turn out how I hoped it would. Will be working on the production quality (the audio too) in future videos. Thanks for the feedback!
This presentation, undoubtedly, stands as the quintessence of introductory discourse on this subject matter. The presenter undoubtedly possesses a prodigious intellect akin to that of Galois. Remarkably exceptional!
What video software are you using? It is excellent.
Thanks! Mostly DaVinci Resolve, and additionally I wrote some code that allows me to create the whiteboard animations easily
Мавроди?
This video is an eye opener. Back in the day I built Reed-Solomon encoder and decoders and struggled to get the key ideas of Galois theory. I didn’t understand it. Now I am feeling hopeful with your video. I must understand this so I hope you will make follow up videos on this topic. Thank you, thank you!
I must admit I have no clue what Reed-Solomon encoders are, but it is intriguing to hear they have something to do with Galois theory. Might look into that. Thank you so much for your kind words, I'm glad you enjoyed it!
Masterpiece in all aspects - title, artful ambient space composition, scrupulous deliberate manner of presentation, deliberately stylish outfit and haircut (English artistic sophistication a la Oscar Wild? 😅 ),.. and of course fine math
Such a kind comment, you're being very nice - thank you :)
Wonderful video! I've already taken a galois theory class, but I had the same frustration you described at the end: I didn't understand where all these definitions and proofs were coming from. This video reignited my intrigue for it. I especially liked your proofs. You gave just enough detail to give a full understanding without being slowed down, and you placed emphasis on the magical moments. It was really enjoyable!
I'm glad you enjoyed the proofs, it means a lot to hear that - thank you :)
I am here because the whiteboard is magical... writes himself on!