ECS 20 — Winter 2022 — Lecture List
Date Topic
Week 1
1M Jan 03 Discussion 1: LaTeX tutorial. John’s example.tex and the resulting example.pdf
1T Jan 04 L01: Introduction (slides). Course basics. Counting paths. Five riffle shuffles isn’t enough. Problem-solving hints.
1R Jan 06 L02: Logic 1. Well-known sets. Booleans 𝔹. Basic operators. Truth tables. Representing numbers. Boolean-modeling thesis.
Week 2
2M Jan 10 Discussion 2: Introduction to sets. Rational and irrational numbers. Interactive notes from Zane.
2T Jan 11 L03: Logic 2. Review. IMPLIES, IFF, XOR, NAND, NOR. NAND and NOR are functionally complete. Formal treatment.
2W Jan 12 PS1 is due at 5pm.
2R Jan 13 L04: Logic 3 (slides). Adder circuit. Tautologies. Formal proof systems. Completeness and soundness. The English/logic gap.
3F Jan 14 Quiz #1 is due by 7pm
Week 3
3M Jan 17 Holiday. No discussion sections. Office hours as usual.
3T Jan 18 L05: Proofs (slides, scribbles). Proofs chosen to illustrate recurring themes. Assigned reading: A Mathematician’s Lament
3W Jan 19 PS2 is due at 5pm.
3R Jan 20 L06: Sets 1. Describing sets. Defining operations on sets. Equivalences. Paradoxes of naive set theory.
Week 4
4M Jan 24 Discussion 4. Quantifiers. Subsets. Element-of vs. subset-of. Interactive notes from Zane.
4T Jan 25 L07: Sets 2. Powerset. Cross products. Axiomatic set theory – ZFC. Strings, languages, and operators on them.
4W Jan 26 PS3 is due at 5pm.
4R Jan 27 L08: Sets 3. Regular languages. Sets represent integers and reals. Sets with operations. Relations.
4F Jan 28 Quiz #2 is due by 7pm
Week 5
5M Jan 31 Discussion 5: Introduction to relations and functions.
5T Feb 01 L09: Relations and Functions 1. Reviewing definitions. Equivalence relations induce partitions. Integers mod n. Functions.
5W Feb 02 PS4 is due at 5pm.
5R Feb 03 L10: Relations and Functions 2. Injective, surjective, and bijective functions. Inverses. Creating a permutation. Infinities.
Week 6
6M Feb 07 Discussion 6. Going over practice midterm from 2013.
6T Feb 08 L11: Relations and Functions 3. Equinumerous and uncountable sets. CSB Thm. Continuum Hypothesis. Efficiency. Asymptotics.
6W Feb 09 PS5 is due at 5pm.
6R Feb 10 L12: Induction and Recursion 1. Peano axioms. Mathematical induction. Examples, including envelopes, triominoes.
6F Feb 11 Go to Gradescope and take the midterm! It is due at 7pm sharp. Midterm instructions.
Week 7
7M Feb 14 Discussion 7: going over the midterm.
7T Feb 15 L13: Induction and Recursion 2. Strong induction: Fund Th of Arith. Induction on a defn. Counting tic-tac-toe games. Towers of Hanoi.
7W Feb 16 No homework due today!
7R Feb 17 L14: Induction and Recursion 3 Using Fund Th of Arith. Karatsuba mult. Recurrence relations. Binary search. Mergesort.
Week 8
8M Feb 21 Discussion 8.
8T Feb 22 L15: Integers and the Pigeonhole Principle. Statement and examples of the PHP. Division theorem. GCD algorithm. Inverses in ℤn*.
8W Feb 23 PS6 is due at 5pm.
8R Feb 24 L16: Counting 1. Principles, including sum rule, product rule, inclusion/exclusion. P(n,k), C(n,k). Examples.
8F Feb 25 Quiz #3 is due by 7pm. Given on Gradescope (not Canvas)
Week 9
9M Feb 28 Discussion 9.
9T Mar 01 L17: Counting 2. Review. More examples of counting, such as poker hands. Elements of probability.
9W Mar 02 PS7 is due at 5pm.
9R Mar 03 L18: Probability. Prob space (sample space, prob measure). RVs and expectation. Conditional probability. Many examples.
Week 10
10M Mar 07 Discussion 10.
10M Mar 07 Quiz #4 is due at 7pm.
10T Mar 08 L19: Graphs. Definitions. Isomorphisms. Sum of degrees. Representing graphs. Eulerian and Hamiltonian Graphs. Coloring.
10W Mar 09 PS8 is due at 5pm.
10R Mar 10 L20: On Being a Computer Scientist Human Being in the Time of Collapse. Where we are at and what we should do.
Week 11
11U Mar 12 Review session 1. Online, going over 2000 Practice Final.
11M Mar 13 Review session 2. Wellman 216, 2021 Practice Final.
11T Mar 15 6-8 pm Final in Wellman 2 (Surnames A-L) and in Wellman 26 (surnames M-Z).