RNT2.6.2. Eisenstein's Criterion

Ring Theory: Continuing with Gauss' Lemma, we prove Eisenstein's Criterion for Irreducibility and that R UFD implies R[x] UFD. As an example of EC, we show that f(x) = x^4+x^3+x^2+x+1 is irreducible over the integers using substitution.

[jimmybroomfield]

I think that there is a typo around 3:47.  Correct me if I'm wrong but I believe that the polynomial in the numerator should be x^4+5x^3+10x^2+10x+5.  Other than that, thanks for the videos.

[cmdstraker]

I guess I should be watching the whole list in order to make sense of all of this, but you deserve a lot more views than you get

[znhait]

Sometimes, I wish the day could have 48 hours so I could divide my life into two parts.  This is because I want to learn upper level math just for the sake of it.  I am just fascinated by mathematicians in general like Gauss, Euclid, Euler, Galois, Abel, etc.  I guess I can ask you this Bob.  Do you think at this level, it's about genius or hard work?  My point is do you think it's possible for someone to be great at math solely through hard work?  I think I am mathematically inclined but yet sometimes I think it takes a bit of an extra gift to get to a certain level.

[MathDoctorBob]

Thanks! No complaints here; advanced math videos are going to have a limited audience.

[AlexHGong]

I think if p doesn't divide a_n, f is irreducible over Q. It also holds over Z, since Guass' Lemma holds. Right?

[SumanKumar-iqoe]

I am from india.
I am watching your video

[linkVIII]

I started a video in the playlist for help on cryptography and then it kept playing