For solving the Bring-Jerrard quintic, some parts I couldn't fully explain, but in this new video I have generalized the process to any arbitrary trinomial and it is much clearer what to do to get the finite sum of hypergeometric functions (TLDR - screw Gauss' multiplication theorem, just split indices mod 4): kzitem.info/news/bejne/1mp-02ePgHdel44
@joeldewitt4138
Жыл бұрын
I'm having unclean thoughts of writing a Fortran program to do this.
@ZXD121
7 ай бұрын
I didn’t even know this was possible until I saw the video.
@samueldeandrade8535
5 ай бұрын
I know an algebraic solution is not possible. Meaning a formula involving sums, differences, multiplications, division, roots.
@angelosterizakis7635
7 ай бұрын
This is truly a work of art.
@mihaiadamescu9861
Жыл бұрын
This is insane 😧
@angelosterizakis7635
7 ай бұрын
It would be interesting to see how the Lagrange Reversion Theorem for implicit functions is derived.
@captainchicky3744
Ай бұрын
this is a good video, i genuinly always wondered how mathematica spits out the 4f3 hypergeometrics for quintics lol, and the scattered MSE posts never really helped much :p
@samuelogunsina9191
Жыл бұрын
My greatest respect for you for making this content accessible for all. I'm an EE major heading into my sophomore year. I just finished Calc 2 and about taking Calc 3 this fall. Even though I have complete understanding of the steps to solving a cubic and quartic. I dont understand most of the techniques used in the videos. My question is what level of Math class do I need to have completed to understand the techniques used. In a related fashion, I'm taking a math minor, starting with Bridge to Abstract Math and Linear Algebra this fall. Will they help?
@MichaelMaths_
Жыл бұрын
Thank you for the kind words! It really is bothersome to me how hidden away most of this stuff is, and I wanted to do a treatment of the content in a way that I would love to see if I was trying to learn it all over again for the first time. Yeah for cubics and quartics this stuff mainly stays within the realm of algebra (like high school algebra), just really clever ways of using it. However for higher degrees, analysis enters the mix for solutions and the transformations to get there borrow a lot more from number theory and some abstract algebra (including the unsolvability in radicals as you may have heard), as well as the theory of elliptic functions and other special functions if you really want to go deeper. Your choice of courses are very good and I would say well in-line with this. I've just worked on gettiing a general understanding of these techniques, mainly looking at the clever steps of algebra and my personal curiosity leading me to learn about special functions given their rarer coverage, but one can definitely go a lot more in-depth.
@samuelogunsina9191
Жыл бұрын
@@MichaelMaths_ I see, so that's why I couldn't understand most of the techniques used, cause by the time I finally learnt of the solutions to the Cubic and Quartic without much understanding of Abstract Algebra and Galois Theory, my next line of action was researching on the solutions to Quintic. However most of the resources I found about the Bring-Jerrad method involved complex math I couldn't understand yet. Regardless, I won't give up on trying to understand the methodology, and I hope someday I finally develop the intuition to understanding the techniques used here. Nevertheless, thank you very much for putting this out 👏.
@TitoTheThird
Жыл бұрын
Good work!. You got the method to transform the general quintic to Bring-Jerrard form from Math StackExchange, did you? Edit: I see from the "Sources and other tidbits" that indeed it is from MSE. :)
@MichaelMaths_
Жыл бұрын
That was the only source which I could properly understand lol. A bunch of papers stated what to do and what transformation is used, but no mention on how to specifically compute/perform it. Thank you for your MSE answer 🙏
@TitoTheThird
Жыл бұрын
@@MichaelMaths_ Your're welcome. Yeah, those papers sometimes make things overly complicated.
@ElwalidAbderahman1
6 ай бұрын
Good 👍
@isaakyhsialf4369
Жыл бұрын
nice, i mean the idea of solving a quintic is solving a quintic
@mihaiadamescu9861
Жыл бұрын
What does this mean
@belgagrave
4 ай бұрын
@@mihaiadamescu9861it means that the idea of solving a quintic is solving a quintic
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