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. Problemsolving hints. 
1R Jan 06  L02: Logic 1. Wellknown sets. Booleans 𝔹. Basic operators. Truth tables. Representing numbers. Booleanmodeling 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. Elementof vs. subsetof. 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 tictactoe 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 ℤ_{n}*. 
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  68 pm Final in Wellman 2 (Surnames AL) and in Wellman 26 (surnames MZ). 