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
Induction (Final version)
- 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
- 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.
Number Theory (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.
Combinatorics (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.
Probability (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.
Automata Theory (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
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
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:
Graph 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,
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.
Logic (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.
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.)