ECS 20 — Winter 2022 — Lecture List |
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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 |
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). |