Computer Science 2802, Spring 2020: Lecture Notes

• 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 the first week, I made it up to the discussion of the semantics of implication (slide 14/51). I'll keep going from there. I expect to finish most of these slides by the end of the second week.
  • In the second week, I made it up to the beginning of the discussion of cardinality for infinite sets (slide 44/52). I'll keep going from there. I expect to finish these slides by Monday or Wednesday.
  • In the third week, I finished the first set of slides, and did the first few slides on induction, but then class was canceled on Friday, so I didn't get as far as I expected.
• Induction (Final version)
• In the fourth week, we just about finished the induction section, except that I'll be talking about fun problems involving induction on Monday (Feb. 17). The rest of the week we'll do number theory.
• Here are Meir Friedenberg's notes from Friday's class.
• Number theory (Final version)
• In the sixth week we'll do number theory, which I expect to finish the following Monday (March 2), just in time for the prelim (March 5).
• In the seventh week, I'll do RSA and other fun stuff on Monday, and then start combinatoriccs on Wednesday
• Combinatorics (Final version)
• We'll spend about two weeks on probability starting April 6:
• Probability (Final version)
• The week of April 6-10, I made it up to slide 31. (I also updated the slides to reflect some points made in class.)
• In class, I mentioned the case 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. 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. Another somewhat similar case is one 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.
• The week of April 13-17, I made it up to slide 65. I should finish the probability material sometime on Wednesday, and then will start on finite automata.
• Finite Automata (Final version)
• The week 20-24, I finished off the discussion of probability on Monday and Wednesday, and started on finite automata on Friday; I made it slide 12. Next week I should finish most of the material on finite automata.
• The week April 27, I did more on automata theory. (Note that I've updated the slides, making lots of minor changes.) I should finish it on Monday. The last 3 lectures will focus on logic. We have one more homework
• Logic (Final version)
• I taught an optinal class on May 13 on graph theory (the video is on Canvas). Below are my complete notes on graph theory. I didn't cover all the notes in my class (this material normally takes 3 classes). I covered Eulerian paths and graph coloring.
• Graph Theory