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.
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| |
| 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.
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| |
| 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 |
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| 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) |