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PROFESSOR: This is Mathematics
for Computer Science,

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6.042J/18.062J, a joint subject
between electrical engineering

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and computer science
and mathematics.

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Welcome.

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The instructors are
Professor Adam Chlipala

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and Professor Albert R. Meyer.

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And I'm Albert.

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Hi, ya.

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Quickly summarizing what
this course is about,

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it's about the math that
computer scientists almost all

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need regularly and
which you're not

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likely to have come across in
your standard calculus classes.

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You may have seen some of
this stuff in high school.

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For example, in
calculus courses people

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talk about functions
on the real numbers.

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And sometimes, they'll
talk about functions

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on the complex numbers.

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But computer
scientists are usually

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dealing with much more abstract
functions on data types

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and even functions on functions.

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And I wonder how many of you, if
I ask you to define abstractly

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what a function was, could
give that definition.

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In a couple of
weeks in this class,

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you'll be able to do
that with facility.

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We will also be
talking about a variety

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of standard discrete structures,
starting with the numbers which

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we think of as a
structure, because it's

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the numbers packaged with
the operations on them,

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like plus and times
and exponentiation.

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We'll also talk about various
other standard data structures,

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like graphs and trees.

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And we'll look at
methods for counting

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the numbers of these different
kinds of data structures,

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as a typical fundamental problem
in computer science, where

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you typically want to know
how big is the search space.

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For example, the search space
of passwords had better be large

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or a cracker can just
search through them

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all to find one that works.

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And finally, we'll talk about
discrete probability theory,

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which is simply a version
of probability theory,

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where we can get by
with sums instead

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of getting into the
complications of integrals.

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So here's a quick sanity
check, or vocabulary check.

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Do you know what discrete means?

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And I'll give you a hint.

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It doesn't mean discreet.

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If you don't know, this is a
good moment to stop the video

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and look it up.