Seriously, i wish I’m one of the algebra students you’re producing. Oh my goodness, you’re one of the great professors in algebra I’ve seen so far. Thanks so much for these videos
These videos are amazing! I first fell in love with Group Theory in my first undergraduate year - 1969-70. I have spent most of the intervening years teaching secondary school maths and latterly (up to my retirement in 2010) as headteacher. Since retiring I have turned back to some of the maths I so enjoyed over 40 years ago - including completing my Masters in maths, which included a great amount of Number Theory. These lectures are snappy, well focussed, pacy and yet very clearly argued and so entertaining. Brilliant. Thank you so much!
Your videos are very helpful. The quick speed helps me pull the ideas together to get the big picture before I get lost and stuck in the calculations details. Usually within the first 2 minutes of your video, I have an "aha" moment about something that I have been trying to study for many hours :) Very time-saving and nice explanations. And, the videos are very interactive and cleverly, well put-together. Please keep them coming!
0:300:46 What, how did tearing the paper automatically factor the polynomial like that!? 😮😆 4:54 It's been awhile since I used Mathematica, and I never knew you could try factoring polynomials over different fields like that!
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. RUclips 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.
...a subfield of ℂ that contains ∜2 and i will always contain ∜-2 ; (1+i)/∜2 = ∜-2, after all. (In general, it's slightly weird to talk about a splitting field of t⁴+2 (over ℚ) containing elements of ℂ; such a splitting field ≈exists separately from its embeddings into ℂ. Still, any such embedding must always have ∜-2 in the image: this splitting field has 4 distinct roots of t⁴+2, which must map to 4 distinct roots of t⁴+2 in ℂ, of which ∜-2 is one.)
Seriously, i wish I’m one of the algebra students you’re producing. Oh my goodness, you’re one of the great professors in algebra I’ve seen so far. Thanks so much for these videos
I think Matt still teaches at Bridgewater State University. You could always apply to be a BSU Bear! 🐻
These videos are amazing! I first fell in love with Group Theory in my first undergraduate year - 1969-70. I have spent most of the intervening years teaching secondary school maths and latterly (up to my retirement in 2010) as headteacher. Since retiring I have turned back to some of the maths I so enjoyed over 40 years ago - including completing my Masters in maths, which included a great amount of Number Theory.
These lectures are snappy, well focussed, pacy and yet very clearly argued and so entertaining. Brilliant.
Thank you so much!
very good material. you helped me a lot. thank you teacher
Your videos are very helpful. The quick speed helps me pull the ideas together to get the big picture before I get lost and stuck in the calculations details. Usually within the first 2 minutes of your video, I have an "aha" moment about something that I have been trying to study for many hours :) Very time-saving and nice explanations. And, the videos are very interactive and cleverly, well put-together. Please keep them coming!
What a brilliant teacher. Congrats Matt!!! By the way, I am volunteering to help you online, depending on the amount of hours.
0:30 0:46 What, how did tearing the paper automatically factor the polynomial like that!? 😮😆
4:54 It's been awhile since I used Mathematica, and I never knew you could try factoring polynomials over different fields like that!
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.
Great lecture! But there doesn't seem to be a link for "Why not Q(i)?" around 9:20.
You've been click baited! My guess is this video wasn't originally released for YTube, and wherever the video's home was before it did have some link.
You have annotations within your videos that don't work. RUclips 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.
t^4+2=(t^2+8^1/4t+2^1/2)(t^2-8^1/4t+2^1/2). Isn’t it? 13:20.
This is correct. And it makes the discriminant of each factor the same, as he said.
Sir how to find splitting field and it's degree
Sir please some examples of splitting fields
I like your ripping paper
He certainly helps tear down walls of confusion to help us understand things better 👍
...a subfield of ℂ that contains ∜2 and i will always contain ∜-2 ; (1+i)/∜2 = ∜-2, after all.
(In general, it's slightly weird to talk about a splitting field of t⁴+2 (over ℚ) containing elements of ℂ; such a splitting field ≈exists separately from its embeddings into ℂ. Still, any such embedding must always have ∜-2 in the image: this splitting field has 4 distinct roots of t⁴+2, which must map to 4 distinct roots of t⁴+2 in ℂ, of which ∜-2 is one.)