ECS 20 — Fall 2013 — LecturebyLecture Summaries 


Lecture  Topic 
L1 R 9/26  Brief introduction. Example probs: a simple sum; sqrt(2) is irrational; moves for Towers of Hanoi; 5 shuffles won’t randomize a deck. Scribe notes. 
L2 T 10/01  Sean Davis lectures on logic. Truth tables. Logical equivalence. De Morgan’s law. Circuits. Conditionals, biconditionals. Inference. Handout. 
L3 R 10/03  Designing an addition circuit. Disjunctive normal form (DNF). Formal defs for WFFs. Truth asignments. Satisfiablity and tautology. 
D2 M 10/07  Mock quiz (order of precedence, truth tables, De Morgan’s laws, sentential logic formulas. PS2 notes. 
L4 T 10/08  Quiz 1. Axioms and formal proofs. Completeness, soundness, and compactness. A result on tiling. 
L5 R 10/10  Firstorder logic: syntax, examples, Englishtranslation. Completeness and soundness. Treatment of number theory and set theory. 
D3 M 10/14  CNF. Quantifiers. Truth tables. Writing and negating quantified formulas. NAND is logically complete 
L6 T 10/15  Axioms of arithemetic. The principle of induction, and examples: a summation; buying envelopes; trominos; cakecutting. Sets. 
L7 R 10/17  Writing sets. Russell’s paradox. Member, subset. Union, intersection, difference, xor. Groups. R, N, Z; BITS, BYTES, WORDS32, FLOAT64. 
D4 M 10/21  Q2 + PS4 notes. Induction examples. Strong induction. Envelope substitution. 
L8 T 10/22  Quiz 2. Cartesian product, unordered product. Power set. Representing sets on a computer: dictionaries (with a list) and UNION/FIND. 
L9 R 10/24  Alphabets, strings, languages. Concatenation, Kleene closure (star). Regular expressions &
languages. Relations, equivalence relations, functions.

L10 T 10/29  Blocks (equivalence classes), and modding out by an equivalence relation. Relation to partitions. Injective and surjective functions. 
L11 R 10/31  Midterm. The photo was of Andrew Wiles, the force behind the proof of Fermat’s Last ‘Theorem’. 
D5 R 11/04  Prof. Rogaway went over the midterm, explain the solution to each problem. 
L12 T 11/05  Review of function vocabulary and notation. Common functions for CS. Comparing the size of infinite sets. Cardinal numbers. 
L13 R 11/07  Comparing A, B. There are uncountably many languages. Some langauges can’t be decided by computers. Review: log, exp, n! BigO notation. 
D6 M 11/11  “Virtual discussion section” because of holiday. Review of onetoone and onto functions. Hints on homework. 
L14 T 11/12  Definition of bigO and Theta notation. Proper and informal use. Eg: searching a list, binary search, bignum multiplication. 
L15 R 11/14  An odd way to multiply: Karatsuba multiplication. Solving the recurrence relation underlying it. Pigeonhole principle and applications. 
D7 M 11/18  Solving recurrence relations with repeatd substitutions and recursion trees. BigO and Theta: ranking by order of growth. 
L16 T 11/19  Quiz 3. Strong form of the Pigeonhole Principle. Graph theory: formal definitions and vocabulary. Isomorphism. Representation of graphs. 
L17 R 11/22  Quiz discussion: importance of precise English. Review of graph terminology. Bipartite graphs, DFS. Paths, cycles, connectivity. Euler’s theorem. 
D8 M 11/25  Discussion of HW. Finish graph theory: Connectivity. Hamiltonian cycles. BondyChvatal Thm. longest and shortest paths. 2 and 3colorability. 
L18 T 11/26  Counting. Lots of examples, mostly using n!, P(n,r) and C(n,r). Principle of inclusion/exclusion. 
Lxx R 11/29  Holiday. You can come, but you’ll be pretty lonely in that big room. 
D9 M 12/02  Counting examples: factorials, permutations, combinations, blackjack. 
L19 T 12/3  Probablity. Probability of different poker hands. Formal definition of a probablity spaces. Events, sum rule, independence. Examples. 
L20 R 12/5  Finishing probablity: random variables and expected values. The funky subway. Monty Hall. Practice exam. Closing comments. 
Lxx R 12/12  Final 10:30 am  12:30 pm in our usual room 