How to make new fields -- Abstract Algebra 24 

I just want to say I am beyond impressed with your ability to teach virtually ALL undergraduate math major classes. Very few professors boast something similar.

It's worth noting that F=Z_2[x]/(x^8+x^4+x^3+x^2+1) actually has a lot of real world applications. Since computers often work with data transmitted as a sequence of elements of a 256-member set, having a 256-element field means that algorithms that work for arbitrary fields can be applied to any transmission if you use this particular field. This has been widely used for error correction and encryption, for example.

Also, if anyone else is bummed that this series is over and needs something to hold them over until the next one, Dr. Penn's main channel has an old, slightly longer abstract algebra course that I loved watching a few years ago. I am loving all the mathmajor reboots of these series, and absolutely cannot wait for the next one!!

Thank you for all the high quality math content!

When you factor 1/c0····Cn at @19:00 every bi has to be multiplied by c0···cn (not including ci). You can name these c0···cn·bi sumands as bi' and continue anyways, but be careful.

will you do Category theory series?

Fantastic. This was definitely my favourite of the MathMajor series so far. Looking forward to the subsequent Abstract Algebra mini-series. Thank you very much for your efforts. 😀👍🏻

Anyone else find it really cool that the first three irreducible polynomials in Z2 evaluate to the golden, plastic, and supergolden ratios in R?

This course helped me through my abstract algebra course so much...thanks!!

Nooo, don't let this series end :)

Would love to know how abstract algebra develops into other types of algebra such as Clifford Algebras, which seem very relevant to physics. Thanks for the series :)