Computer Science 2802, Spring 2019: 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 (Final version): includes a course overview, how to do proofs, a little propositional logic, functions, relations, equivalence relations, transitive closure, bijections, different kinds of infinity

In case you missed the first lecture due to weather, I covered the preliminary slides up to the proof that n^2 is odd if n is (which has 6/40 on the bottom, but doesn't count all the slides I inserted before the slide labeled 1/40).
I'll also talk about course policies, which can be found here
In the first week, I made it up to the slide 80 of 145 (it's labeled "Sets and Propositions")
- But I added slides 66-68, which I'll talk about on Monday, and corrected some typos in the early slides.
In the second week, I made it up to slide 135/145
I expect to finish these slides on Monday, and then continue with induction, which will take the rest of this week and most or all of next week.

Induction (Final version)

In the third week, I finished the first set of slides and made it to slide 46/70 in the induction slides. (There were a few things I left out on slide 34/70 that I'll talk about on Monday.) I expect to finish induction week and start number theory.

Number Theory (Final version)

In the fourth week, I finished the induction slides and made it to slide 7.42 in the number theory slides.
In the fifth week, I made it up to slide 31/42 (Casting out 9s)
In the sixth week, I finished the number theory slides. Next week, on Monday there will be a review session, and on Wednesday we'll start combinatorics.

Combinatorics (Final version)

In the seventh week (ending March 8), we made it to slide 25/39 on the combinatorics slides. Next week we'll finish combinatorics and start probability.

Probability (Final version)

In the eigth week (ending March 15), we finished the combinatorics slides, and made it to slide 9/90 of probability.
In class, I mentioned a case where a mother was convicted of killing her children due to faulty statistics. This was the Sally Clark case. You can check out what happened on Wikipedia. A high-level discussion of the faulty statistics in the case can be found here. An arguably even more famous and controversial case was that of Lucia de Berk, a Dutch nurse who had a lot of children die on her watch. You can check out the details on Wikipdia. A somewhat technical discussion of the statistical errors (with the catchy title "Elementary Statistics on Trial") can be found here. You should be able to follow at least the first 3 pages.
In the ninth week (ending March 22), I made it slide 51/91.
In the tenth week (ending March 29), I finished the probability material, except that I'll spend a few minutes after the break saying a bit more about variance and expectation for independent variables. Then I started automata theory:

Automata Theory (Final version)

In the eleventh week (ending April 12) and twelfth week (ending April 19), I covered automata theory. I ended up on Friday discussing work on which recent work of mine is based, trying to explain apparently "irrational" human behavior as the outcome of computational limitations. For those interested, here is an overview of some of my work in this area (which also includes what I discussed Friday). The paper was actually invited to a cognitive science journal, although the original papers appeared in CS conferences. The technical details are all omitted, so you shouldn't have any trouble reading it :-). The paper also has pointers to the original papers and other related work. The reason I brought it up at this point in the course is that probabilistic automata are used to model computational limitations. (The formal analysis also involves probability.)
Next week we will do graph theory.

Graph Theory (Final version)

In the twelfth week (ending April 26), we just about finished the graph theory material (except for the last two slides). Next week we'll do some logic.

Logic (Final version)

Here are the slides for the final lecture. (I covered only up to slide 11, and then said a few words about slides 14 and 15. If you're interested in this material, it's what I cover in my graduate course "Reasoning about Knowledge", although I suspect that I won't teach it again until academic year 2020-21 or 2021-22.)