Lecture Schedule

Note that the final exam is on the last day of lecture, not during finals week. It is not comprehensive, but only covers material since the midterm (also given during lecture).

This schedule is tentative and may change as the quarter progresses. I will try not to change scheduled days of quizzes and the midterm, however.  The topics listed for each lecture are an estimate. After the lecture, I will alter the topics to reflect what we actually covered. In particular, I originally designed this for a MWF lecture, but now it's TR, so although the weekly topics are not likely to change, I'm guessing a bit how it will be distributed between the days.

Any section/subsection in the lecture notes labeled "Optional" is something we will not cover. Topics from those sections will not appear on homework, quizzes, or exams.

Lecture 0 is not covered in class when teaching in person. It is a review of prerequisite discrete math concepts that will be used in the course. It will be covered in discussion the first week.

Pre-recorded lectures

I pre-recorded lectures the first time I taught this course online during the COVID-19 pandemic. The recorded lectures cover the same material that we will cover in live lecture. I've made them available through links below for students who wish to have a recorded version of what is covered in lecture that they can watch on their own time.

Generally I've tried to break up each video into smaller chunks than a long 50-minute thing (although without interaction, most of these are 30-40 minutes instead of the full 50). A few of the videos have errors, which are noted as "errata" in the text Details below the video, for example: this video.

The day of week (e.g., 1b, 2a) might be off since the quarter I recorded these has a different schedule than the current quarter.

The AggieVideo site provides automatic transcription of my voice in the lectures, which you can see by clicking on "Show transcript" at the bottom of the video. Since they are automatic, they are not completely accurate, especially for mathematical terms, but they can hopefully help you follow along if English is not your native language.

There's a some errata in a few of the videos, which are explained at the pages at the links below with the individual videos.

lecture	date	videos	reading assignment
0	discrete math review; not covered in lecture, but covered in discussion the first week	sets sequences functions and relations equivalence relations graphs and trees Boolean logic pigeonhole principle combinatorics	1.1 1.2 1.3 1.4
1a	1/9	introduction to course course policies (watch on your own) string theory intuitive overview of DFAs formal models of computation formal definition of DFA syntax intuitive overview of DFA semantics	syllabus intro-slides.pdf on "Lecture Notes" page 2.1 2.2 2.3 3.1 3.2 3.3
1b	1/11	examples of DFA state diagrams example DFAs deciding input length congruence example DFA deciding binary number congruence formal definition of DFA semantics	3.4 3.5
2a	1/16	regex introduction regex formal definition conventions and the tree view of regex's small examples example of regex matching double literals CFG introduction formal definition of CFG syntax	4.1 4.2
2b	1/18	formal definition of CFG semantics right-regular grammars NFA introduction formal definition of NFA syntax example NFA and states it could reach listing transitions versus defining transition function formal definition of NFA semantics	4.3
3a	1/23	automatic transformation of regex's, NFAs, DFAs roadmap for next two chapters DFA union (product construction) example DFA union proof DFA intersection (two ways) gotchas: multiple union or intersection, closure only goes one way, and difficulty of showing closure for concatenation and Kleene star	5.1 5.2
3b	1/25	NFA Kleene star example NFA union proof NFA concatenation proof NFA Kleene star proof introduction to computational equivalence, NFAs can simulate DFAs example of DFA simulating NFA (subset construction)	5.3
4a	1/30	proof DFAs can simulate NFAs with no ε-transitions handling ε-transitions alternative choices in subset construction RRGs can simulate DFAs example RRGs can simulate DFAs proof NFAs can simulate RRGs proof right-regular versus left-regular grammars NFAs can simulate regex's proof NFAs can simulate regex's example	6.1 6.2
4b	2/1	NFAs with "isolated" start and accept state expression automata regex's can simulate NFAs why we need rigor to argue that a language is not regular definition of separating extension and L-equivalence example of separating extension statement of Myhill-Nerode Theorem corollary of Myhill-Nerode theorem we use and its proof	6.3 7.1
5a	2/6	examples of using the Myhill-Nerode Theorem proof of non-regularity using closure properties more examples of using Myhill-Nerode Theorem a non-regular unary language introduction to Turing machines (TM) example TM formal definition of TM syntax formal definition of TM semantics	7.2 7.3
5b	2/8	languages decided/recognized by TMs multitape TM transition function single-tape TMs can simulate multitape TMs other variants of TMs TMs versus code	8.1 8.2 8.3 8.5 8.6
6a	2/13	measuring running time asymptotic analysis, definition of O() and o() rules-of-thumb for comparing function growth rates definition of Ω(), ω(), and Θ()	Appendix A 9.1
6b	2/15	time complexity classes and the Time Hierarchy Theorem definition of P, encoding of data structures P is the same for most encodings and programming languages example problem in P: EulerianGraph example problem in P: RelPrime example problem in P: Connected (note: this assumes Path is in P, discussed in the optional video on that problem) (Optional) example problem in P: Path polynomial-time verifier for HamPath polynomial-time verifier for Composites definition of NP decision vs. search vs. optimization	9.2 9.4 9.5 10.1 10.2
7a	2/20	midterm
7b	2/22	example problem in NP: Clique example problem in NP: SubsetSum the P vs. NP question exponential-time algorithms for NP problems P versus NP versus EXP	10.3 10.4
8a	2/27	introduction to NP-completeness and Boolean formulas implementation in Python and the Boolean satisfiability problem ranking the hardness of problems reducing IndSet to Clique definition of polynomial-time reducibility using reductions to bound hardness of problems how to remember which direction reductions go definition of the 3SAT problem	10.5 10.6
8b	2/29	3SAT is reducible to IndSet reduction between two problems is an algorithm, but it doesn't solve either problem definition of NP-completeness Cook-Levin Theorem: if P≠NP, then no NP-complete problem is in P	10.7 10.8
9a	3/5	halting problem definition and Turing-recognizability reducibility no-input halting problem is undecidable recipe for showing undecidability acceptance problem is undecidable empty language problem is undecidable rejecting problem is undecidable how to spot undecidability	11.1 11.3 11.4
9b	3/7	comparing sizes of sets ℕ vs. ℤ ℕ vs. ℚ+ ℕ vs. ℚ ℕ vs. {0,1}* ℝ vs. (0,1)	11.5
10a	3/12	diagonalization to show a set is smaller than its power set the real numbers are uncountable and the Continuum Hypothesis diagonalization to show the halting problem is undecidable	11.6
10b	3/14	final exam