Again, the idea behind this slide is meant to be sort of a
timestamp thing if you want to try to find this,
you can go to this approximate minute stamp.
What are we going to talk about in this video?
We're going to talk about the Principle Mathematical Induction, that was the
main topic of the week.
We'll see an example and we'll highlight the base case,
the inductive hypothesis, and the inductive step.
We're going to talk about when induction isn't enough, so a situation where…
what do I want to say…
the usual or the
typical induction statement’s not going to work,
and that's where we would like to use something called strong induction,
which will help us out so we'll talk with that in slide 7.
I'm going suppress from this video an example of strong induction,
You can go on the Math 135 Resources Page
and check out an example of strong induction there.
Then we're going to talk about the Fibonacci sequence. We'll just
or just remind ourselves what it is, and that's all we'll say about that,
and then the last four bullets, so this is where
my course might differ from your course substantially.
I decided to do the Fundamental Theorem of Arithmetic
as the last lecture of the induction week.
t turns out that we can't actually do it. We
actually need something called Euclid's Lemma that we don't have yet,
but we will prove that next week,
but assuming that we can actually do the Fundamental Theorem of Arithmetic,
particularly see the proof. I think it's one of the
most difficult proofs in this course to do formally,
so in class I did it formally. Here I'm going to…
well okay I should say in class in January 2016,
I did it formally.
But in this video, I’m going to do it informally.
I'm going to do an existence proof formally, and I'm going to do
an informal uniqueness proof just to kind of get the idea down.
The formal proof kind of takes away from
what's really going on, and I think the informal proof
is good to see once.
So this is the outline for this week.