I haven't come across this way of thinking of the derivative before, but it makes perfect sense now, this was really well-explained. I watched this video without having seen any of the previous material, it just popped up in my feed, so I'll have to check out the back catalog now.
Since every Group is nonempty, Every nonempty set can be first viewed as a copy of a subset of all bijections onto itself. Since ∀ n ≥ 1 n ≤ n!, We are trying to carry the Second Inequality over to Groups with these Cardinalities. ( G ≤ Perm (G) ) Since n always divides n! we still have to resist the temptation for a converse of Fermat Theorem, since n may not be a prime. Our Group of n elements can be buried deep anywhere within a huge Group of Size n!, requiring some finesse
This is cool work, but do you actually have an image which is the result of un-doing Escher's transformation pixel-by-pixel from the original art directly? I don't want to see a diagram of the result, I want to see the actual result!
Hi Dr. Salomone. I just came across your channel, and look forward to my next math adventure! My favorite topics are General Stokes, SVD (singular value decomposition), and most of all, Fourier decomposition, specifically using complex exponentials to represent curves. You seemed to have taken this to the next levels with your 3D work. Thank you so much for sharing your love of math. I wonder if you might share your views, and maybe make a series on Fourier epicycles, ala RU-vid GoldPlatedGoof ‘Fourier for the rest of us’ Thank you!
Thank you for your explaination! That question of what else adds when multiplied was one I never heard and really added insight for me. I had been always taught to memorize these equations, but thinking about the “why” is much more fun and interesting.
It always bothers me when a lecturer pulls out a "guess" that magically ends up being the right one. Like... how can I learn from that if I don't see where that guess might have come from?!
big fan of you videos a learned a lot from it if my math teacher would that been like you i would has done much better in math they don't explain anything and the class is a bureaucratic process for them to get pay and for you to get a job it is that ??? i^4=(e^(pi I/2))^4=(e^(pi I/2))^2*(e^(pi I/2))^2=(e^pi I)(e^pi I)=(-1)(-1)=1
10:06 May I ask what software you are using to write your notes for this lecture? I think that the drop down menus are very cool and helpful for those of use teaching online. Thanks.
This format is really helpful in helping me design a better more discovery based classroom. The interaction between investigation and discovery via tools like geogebra are so essential in the discovery aspect , which is lacking in so many high schools. Thanks for the inspiration!
Love that! I'm sure if high school teachers had 2x as much time to be with their students, we would see more of these discovery-oriented approaches in use... but it's hard to find the space for them sometimes when teachers (and administrators) are worried about depth of basic skills.
Great video! I just found out about short exact sequences and was struggling to get a feeling of why they are useful. Most written sources online also weren’t helpful. With your videos it’s much clearer, thank you!
I agree that these videos are amazing and I've learned a lot from them. I would say that they are some of the best videos on group/field theory and galois theory. However, I also want to give you sincere constructive feedback. I would suggest a slower talking speed. Just as an example, check out videos by Gilbert Strang in his MIT lectures on linear algebra and note the slowness of his cadence. I think it's ideal for first time learners. One can always speed up the videos for those that want to go faster but slowing down videos makes them sound odd. Another example of good cadence is Erik Demaine's video on Divide & Conquer: FFT. There is something to be said of chalk lectures that forces the instructor to slow down and give time for first time learners to absorb material. Again not trying to diminish what you've done here but I think these tips might just take your videos to an even higher level in the future.
You have annotations within your videos that don't work. RU-vid got rid of annotations back in 2019 I believe. Therefore, if you want to link to other videos in your series then you have to include those within the description.
