This is meant as constructive criticism, but I would add the Fundamental Theorem of Algebra from Gauss stating there are an equal number of roots as the highest order coefficient to the Classical Algebra half.
I agree that it should be stated and used but proving is an exercise in analysis.
18 годин тому
You are right, unfortunately I forgot to mention that. While the core of the proof is analytic in nature the statement is clearly an algebraic one that would have fit in perfectly with the discussion of the n > 4 case.
16 годин тому
Could you please add the word "complex" (roots) to your comment?
It's great that the basic structure is explained and not started straight in!
2 дні тому+2
Thanks to Pinter's book on algebra. It has such an inspiring introduction to the roots of the subject that I thought I should make a video about that before diving right in.
Thanks for the introduction. I've attempted several times to learn abstract algebra. Hopefully, this time, things will click a little better for me.
День тому+1
Especially in the first lessons I'm proceeding extra slow and careful, so hopefully this will help you with things clicking better this time. Keep me posted about your progress.
День тому+1
P.S.: Try to do as much of the exercises on the problem sets as you can - that really helps to get a better grasp of the new concepts.
As much as I would love to understand this upper level of math, the reality is it takes several years of going from elementary algebra/trig/geo, calc i-iii, linear, analysis, and topo.
17 годин тому
That is true. But abstract algebra is a good starting point because you don't need much prerequisites (except for the matrix-stuff) and the new concepts in this course are thoroughly explained.
This is meant as constructive criticism, but I would add the Fundamental Theorem of Algebra from Gauss stating there are an equal number of roots as the highest order coefficient to the Classical Algebra half.
I agree that it should be stated and used but proving is an exercise in analysis.
You are right, unfortunately I forgot to mention that. While the core of the proof is analytic in nature the statement is clearly an algebraic one that would have fit in perfectly with the discussion of the n > 4 case.
Could you please add the word "complex" (roots) to your comment?
It's great that the basic structure is explained and not started straight in!
Thanks to Pinter's book on algebra. It has such an inspiring introduction to the roots of the subject that I thought I should make a video about that before diving right in.
underrated comment. just boosting in hopes more teachers will take notice
sehr schön erklärt und der historische Aspekt ist sehr interessant. Danke
Seems like a very cool course, hopefully I will have time to follow it through! :)
I hope so too. If not at first try, the videos will be waiting for you... :)
Thanks for the introduction. I've attempted several times to learn abstract algebra. Hopefully, this time, things will click a little better for me.
Especially in the first lessons I'm proceeding extra slow and careful, so hopefully this will help you with things clicking better this time. Keep me posted about your progress.
P.S.: Try to do as much of the exercises on the problem sets as you can - that really helps to get a better grasp of the new concepts.
As much as I would love to understand this upper level of math, the reality is it takes several years of going from elementary algebra/trig/geo, calc i-iii, linear, analysis, and topo.
That is true. But abstract algebra is a good starting point because you don't need much prerequisites (except for the matrix-stuff) and the new concepts in this course are thoroughly explained.
Good start
Excellent video. Thanks a lot for the overview of all those algebraic structures!
Thank you, glad you like it.
Many thanks for the "friendly" introduction, Sir! Great vid. In my opinion, there is no need for a German version. Go ahead! 🙂
Thank YOU, sir, for the kind words. 👍😀
we may never know 🤔
😀 ... at least what algebra is going to become in the next decades.
2+x = 9?
Hilarious 🤣 That IS (one aspect of) algebra.