and the way these are gonna work is I'm going to have...
a table of contents here.
Roughly every bullet will be approximately one minute.
So clearly this is gonna be very very quick.
It's not, you know, you're meant to pause it, and go back, and review it,
it's not meant to replace lectures. It's meant to be a complement to the lectures to say,
“Oh okay, these are the important things we did this week
and these are what I should be focusing on
in order to to develop mastery of mathematics.”
So we're gonna start off with, “What is Math 135?”,
what we cover in it, what's the importance of it.
We’ll talk about truth tables as a definition.
So we talked about truth tables this week and we’d like to
talk about how we can use them to define things.
We'll talk about DeMorgan’s Law and how
truth tables can also be used to prove things.
We talked about chains of equivalences, so using
logical equivalences to show that
statements are equivalent to each other.
Then we talked about direct proofs,
so we just talked about a normal direct proof,
we talked about direct proofs from true statements,
we talked about direct proofs when you break into cases,
and then we finished off the week with the divisibilities and bounds by divisibility.
I should mention that
at this point, before we continue,
don't be alarmed if you didn't cover all of these things.
You'll eventually cover all of these topics, that's perfectly fine.
Some instructors might go in different orders, some instructors
might not have gotten to everything this week, not a big deal.
It's definitely not a big deal; don't take this as like the
gospel to teaching Math 135,
or what you should have done this week, or what you didn't do this week.
Again, these are the topics that I've covered this week,
and so that's what I based this lecture series on.