So here are the topics that I'm going to talk about this week.
Again each one roughly covers 2 minutes, so if you want to
skip forward to that part in the talk, you can.
We're going to start with a couple of polynomial statements
that I'm not going to prove but that are pretty important,
and then as you can see here, we have - what is this, 6 named theorems.
So Remainder Theorem, Factor Theorem,
Roots Over a Field which arguably is
just as important as some of these other theorems
but doesn't have a name, Fundamental Theorem of Algebra,
Complex Polynomials of Degree n Have n Roots,
then the proof of that, the Rational Roots Theorem, and the Conjugate Roots Theorem.
So notice in the middle here, I've kind of glossed over this
but Fundamental Theorem of Algebra is one of the more important statements
in mathematics. Fundamental - anything Fundamental Theorem of
blah, that's probably a pretty important theorem and you should know it.
That's all I really have to say. Here we'll talk a little bit more about the
Fundamental Theorem of Algebra in a minute.
We won't talk about the proof. The proof is just a little bit beyond what
we want to do in this course.