ECS 20 — Fall 2021 — Lecture-by-Lecture Schedule |
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Lecture | Topic |
Week 0 | Notes: Introduction. Example problems: (1) counting paths; (2) R(3,3); (3) shuffling cards |
0W Sep 22 | Introductory remarks and example problem (1) |
0R Sep 23 | Introductory remarks and problems (1), (2), (3) |
0F Sep 24 | Example problems (2), (3) |
0U Sep 26 | Sunday@4 Recitation. This week in review. Homework hints. LaTeX tutorial. |
Week 1 | Notes: Logic-I. Propositional logic. Circuits. Getting formal. |
1M Sep 27 | Complaining about the room. Boolean domain 𝔹. Basic operators. Truth tables. Circuits. |
1T Sep 28 | Boolean domain 𝔹. Basic operators. Truth tables. Circuits. WFFs. Truth assignments |
1T Sep 28 | Homework 1 due at 5 pm |
1W Sep 29 | More Boolean operators. De Morgan’s laws. Equivalence. WFFs and their semantics. |
1R Sep 30 | WFFs, ta's. BNF and grammars. Satisfiability, tautologies, equivalence. Addition Short-circuited evaluation |
1F Oct 01 | WFFs, now with BNF. Satisfiability, tautologies, equivalence. Addition circuit. |
1U Oct 03 | Sunday@4 Recitation |
Week 2 | Notes: Logic-II. Completeness, soundness, compactness. Quantifiers. Set theory. |
2M Oct 04 | Finish addition circuit. A formal system of logic. Completeness, soundness, compactness. |
2T Oct 05 | A formal system for Boolean logic. Completeness, soundness, compactness. Tiling the plane |
2T Oct 05 | Homework 2 due at 5 pm |
2W Oct 06 | Review of formal proofs. Completeness, soundness, compactness. Adding quantifiers, enlarging the syntax. |
2R Oct 07 | Adding quantifiers, enlarging the syntax. Elements of set theory. |
2F Oct 08 | Unnoticed things you encounter often. Review of first-order logic. Truth. Vocabulary of set theory. |
2U Oct 10 | Sunday@4 Recitation: Representing a tic-tac-toe position with Booleans. Practice with binary conversions. |
Week 3 | Notes: Sets. Operations on sets. Russell’s paradox. Important sets. |
3M Oct 11 | Set operations and identities, including De Morgan’s law. Russell’s paradox. Cross products. Binary strings. |
3T Oct 12 | Set operations and identities, including De Morgan’s law. Russell’s paradox. Cross products. Binary strings. ASCII |
3T Oct 12 | Homework 3 due at 5 pm |
3W Oct 13 | De Morgan’s. Binary strings. Bytes and words. Representing integers with 2’s complement, reals with IEEE floats. |
3R Oct 14 | Representing integers with two’s complement, reals with IEEE 754. Sets with an operation: groups. |
3F Oct 15 | No lecture: watch at least 56:00-end of Lecture 3R. Online office hours in lieu of lecture. |
3U Oct 17 | Sunday@4 Recitation |
Week 4 | Sets, continued. Languages, regular languages. Notes: relations and functions |
4M Oct 18 | Cross product (n-fold). Strings, concatenation, languages. Relations. Equivalence relations |
4T Oct 19 | Cross product (n-fold). Strings, concatenation, languages. Regular languages. Relations. Equivalence relations |
4T Oct 19 | Homework 4 due at 5 pm |
4W Oct 20 | Strings, concatenation, languages. The star operator. Regular languages. The Chomsky hierarchy |
4R Oct 21 | Review relations, equivalence relations. Functions. 1-to-1 and onto. ZF(C). Poem. Number your days |
4F Oct 22 | Review relations, equivalence relations. Functions. 1-to-1 and onto. |
4U Oct 24 | Sunday@4 Recitation |
Week 5 | Functions, cont. Equinumerous sets. Induction Notes: relations and functions |
5M Oct 25 | Composition. Func(A,B), Perm(A). Most functions can’t be computed. Symmetric group Sn |
5T Oct 26 | Composition. Inverses. Func(A,B). Most functions can’t be computed. Symmetric group Sn. Equicardinal sets. |
5W Oct 27 | Permutations. Iterating a function. Blockciphers. Giant cycles, rhos. Representing a point in Sn. Equicardinal sets |
5W Oct 27 | Homework 5 due at 5 pm |
5W Oct 27 | Midterm released at 5 pm |
5R Oct 28 | Equinumerous sets: ℕ, ℤ, ℚ. Diagonalization: the reals are uncountable. SB Theorem. Peano axioms. Induction |
5F Oct 29 | Equinumerous sets. Diagonalization: the reals are uncountable. Peano axioms |
5F Oct 29 | Midterm due at 5 pm |
5U Oct 31 | Sunday@4 Recitation |
Week 6 | Going over MT. Number theory. Induction. Notes: numbers and induction |
6M Nov 01 | Went over midterm questions. Concretized what is “practical”. |
6T Nov 02 | Went over midterm questions. Concretized what is “practical”. Number theory. Induction. The sum Sn=1+2+...+n. |
6W Nov 03 | Types of induction. Various examples: sum#1, sum#2. The Fund Thm of Arith. |
6W Nov 03 | Homework 6 due at 5 pm |
6R Nov 04 | More induction: sum of first n odds; n2 + n is even; Fund Thm of Arith; triominoe tiling; dispensing envelopes. |
6F Nov 05 | More induction: Fund Thm of Arith; dispensing envelopes; n2 + n is even. |
6U Nov 07 | Sunday@4 Recitation |
Week 7 | Number theory. Induction. Notes: numbers (part 2) |
7M Nov 08 | Triomino tiling. Well-ordering. Division Theorem. Different views of mod. Euler&rsquop;s algorithm for the gcd. |
7T Nov 09 | Well-ordering. Division Theorem. Different views of mod. Euler’s algorithm. The group ℤn*. DH key exchange. |
7W Nov 10 | Lagrange's Thm. Fermat's Little Thm. The group ℤn*. DH key exchange. |
7W Nov 10 | Homework 7 due at 5 pm |
7R Nov 11 | Holiday (Veterans Day) — no class |
7F Nov 12 | Move day. Here is the annotated list of films screened. Make sure you understand the third problem. |
7U Nov 14 | Sunday@4 Recitation |
Week 8 | Recursion, recurrence relations, and asymptotics. Notes: recursion Notes: asymptotics. |
8M Nov 15 | Mystery metal object. Num of tic-tac-toe games. Towers of Hanoi puzzle. |
8T Nov 16 | Num of tic-tac-toe games. Towers of Hanoi. Recurrence relations. Karatsuba multiplication. Big-O. |
8W Nov 17 | Karatsuba’s algorithm. Solving recurrences. Big-O notation. |
8W Nov 17 | Homework 8 due at 5 pm |
8R Nov 18 | Big-O, Ω, and Θ. Recursion trees. Binary search. Mergesort. Calculating partition numbers. |
8F Nov 19 | Big-O, Ω, and Θ. Recursion trees. Binary search. Mergesort. |
8U Nov 21 | Sunday@4 Recitation |
Week 9 | Counting and a touch of probability. Notes: counting. Notes: probability. |
9M Nov 22 | P(n,k) and C(n,k). Sum rule, product rule, inclusion/exclusion. Practice counting. |
9T Nov 23 | Sum rule, product rule, inclusion/exclusion. Practice counting. Probability calculations. |
9W Nov 24 | More practice counting. More fighting with the microphone that hates me. Probability basics. |
9W Nov 24 | Homework 9 due at 5 pm |
9R Nov 25 | Holiday (Thanksgiving) (You don’t really want to kill/eat any abused animals, do you?) |
9F Nov 26 | Holiday (Thanksgiving) |
9U Nov 28 | Sunday@4 Recitation is moved to Monday@5 this week |
Week 10 | Probability. PHP. Graphs. Notes: probability. Notes: pigeonhole principle. Notes: graph theory.. |
10M Nov 29 | Probability spaces, events, RVs, expectation. Examples. |
10M Nov 29 | Monday@5 Recitation |
10T Nov 30 | (1) Probability spaces, events, RVs, expectation. Birthday surprise. Let’s Make a Deal. (2) Pigeonhole principle. |
10W Dec 01 | Review of probability basics. Birthday surprise. Monty Hall problem. Pigeonhole principle and examples. |
10R Dec 02 | Homework 10 due at 11 am |
10R Dec 02 | Another PHP example. Graph theory basics. Concluding remarks. |
10F Dec 03 | Graph theory basics (isomorphism, Eulerian & Hamiltonian graphs, colorability). Concluding remarks. |
10S Dec 04 | 1pm Zoom-based review session. Try to do the final exam first. |
Week 11 | Finals week |
Mon Dec 06 | 1pm Final for Section B (TR). Wellman 106 and Wellman 226 |
Fri Dec 10 | 8am Final for Section A (MWF). Wellman 1 (A-H), Wellman 25 (I-L), and Wellman 6 (M-Z) |