# 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 second week.
• 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 here.
• 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.