Computer Science 2802, Fall 2020: Lecture Notes
Note that the final version of the notes may differ from the
preliminary version. I correct typos and add more details.
- Introductory material (Updated final version):
includes a course overview,
how to do proofs, a little propositional logic, functions,
different kinds of infinity
- In the first week, I made it up to the discussion of the
semantics of implication (slide 22/45). I'll keep going from
there. I expect to finish these slides by the end of the
- In the second week, I made it up to the proof that the reals
are uncountable. Because of zoom problems, there was no class on
Monday. I'll prove Schroder-Bernstein next week. On Wednesday
we'll start induction, so you can do this week's homework.
- Induction (Final version)
- In the third week, we started induction. I expect to
finish induction by Wednesday of the fourth week (the Wednesday
class should be particularly fun, since I'll be talking about
puzzles and paradoxes from other fields). Then the rest of
Wednesday (if there's time) and Friday, I'll be doing relations and graphs.
- Relations and graphs (Final version)
- Number theory (Final version)
- In the fifth week I made it up to the discussion of linear
congruential method for generating pseudorandom sequences. (I added
a little bit more on that to the slides.) Next week I'll start with a
mindreading trick (it's fun; come to class for details!) and then do
RSA. I expect to finish number theory and do the Schroder-Bernstein
proof (which I had deferred) next week.
- In the sixth week, I finished number theory and the
Schroder-Bernstein proof. Next week I'll start combinatorics.
Combinatorics (Final version)
- In the seventh week, we started combinatorics; I expect to finish
it by Wednesday, at which point we'll start probability.
- Probability (Final version)
- In the eighth week, we finished combinatorics, and started probability
- In the ninth week, we did more probability. One of the things I
discussed was the fact that if you toss a coin that has a
probability p of landing n times, the expected number of heads is
np. I gave three proofs, one of which was an intuitive proof by
induction. Ambrose asked for details. They can be found
- In the tenth week, I'll finish probability (probably by
Wednesday) and start on finite automata.
- Finite automata (Final version)
- I finished finite automata in the tenth week; next week I'll do
a little on graph theory and start probability.
- Graph theory (Final version)
- Logic (Final version)
- Here are the slides that I
used in the final class when discussing my research.