ECS 20 — Fall 2021 — LecturebyLecture Schedule 


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: LogicI. 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 Shortcircuited evaluation 
1F Oct 01  WFFs, now with BNF. Satisfiability, tautologies, equivalence. Addition circuit. 
1U Oct 03  Sunday@4 Recitation 
Week 2  Notes: LogicII. 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 firstorder logic. Truth. Vocabulary of set theory. 
2U Oct 10  Sunday@4 Recitation: Representing a tictactoe 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 56:00end 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 (nfold). Strings, concatenation, languages. Relations. Equivalence relations 
4T Oct 19  Cross product (nfold). 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. 1to1 and onto. ZF(C). Poem. Number your days 
4F Oct 22  Review relations, equivalence relations. Functions. 1to1 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 S_{n} 
5T Oct 26  Composition. Inverses. Func(A,B). Most functions can’t be computed. Symmetric group S_{n}. Equicardinal sets. 
5W Oct 27  Permutations. Iterating a function. Blockciphers. Giant cycles, rhos. Representing a point in S_{n}. 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 S_{n}=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; n^{2} + n is even; Fund Thm of Arith; triominoe tiling; dispensing envelopes. 
6F Nov 05  More induction: Fund Thm of Arith; dispensing envelopes; n^{2} + n is even. 
6U Nov 07  Sunday@4 Recitation 
Week 7  Number theory. Induction. Notes: numbers (part 2) 
7M Nov 08  Triomino tiling. Wellordering. Division Theorem. Different views of mod. Euler&rsquop;s algorithm for the gcd. 
7T Nov 09  Wellordering. Division Theorem. Different views of mod. Euler’s algorithm. The group ℤ_{n}^{*}. DH key exchange. 
7W Nov 10  Lagrange's Thm. Fermat's Little Thm. The group ℤ_{n}^{*}. 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 tictactoe games. Towers of Hanoi puzzle. 
8T Nov 16  Num of tictactoe games. Towers of Hanoi. Recurrence relations. Karatsuba multiplication. BigO. 
8W Nov 17  Karatsuba’s algorithm. Solving recurrences. BigO notation. 
8W Nov 17  Homework 8 due at 5 pm 
8R Nov 18  BigO, Ω, and Θ. Recursion trees. Binary search. Mergesort. Calculating partition numbers. 
8F Nov 19  BigO, 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 Zoombased 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 (AH), Wellman 25 (IL), and Wellman 6 (MZ) 