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and the way these are gonna 
work is I'm going to have...

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and the way these are gonna 
work is I'm going to have...

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a table of
contents here.

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Roughly every bullet will be 
approximately one minute.

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So clearly this is gonna 
be very very quick.

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It's not, you know, you're meant
to pause it, and go back, and review it,

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it's not meant to replace lectures. It's 
meant to be a complement to the 
lectures to say,

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“Oh okay, these are the important 
things we did this week

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and these are what I
should be focusing on

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in order to to develop 
mastery of mathematics.”

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So we're gonna start off 
with, “What is Math 135?”,

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what we cover in it, what's 
the importance of it.

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We’ll talk about truth
tables as a definition.

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So we talked about truth tables 
this week and we’d like to

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talk about how we can 
use them to define things.

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We'll talk about DeMorgan’s 
Law and how

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truth tables can also be
used to prove things.

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We talked about chains of
equivalences, so using

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logical equivalences 
to show that

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statements are
equivalent to each other.

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Then we talked 
about direct proofs,

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so we just talked about 
a normal direct proof,

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we talked about direct 
proofs from true statements,

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we talked about direct proofs
when you break into cases,

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and then we finished off the week 
with the divisibilities and bounds by
divisibility.

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I should mention that

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at this point, before 
we continue,

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don't be alarmed if you didn't 
cover all of these things.

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You'll eventually cover all of
these topics, that's perfectly fine.

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Some instructors might go in 
different orders, some instructors

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might not have gotten to everything 
this week, not a big deal.

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It's definitely not a big deal; 
don't take this as like the

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gospel to teaching 
Math 135,

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or what you should have done this 
week, or what you didn't do this week.

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Again, these are the topics 
that I've covered this week,

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and so that's what I based 
this lecture series on.