ECS 20 — Fall 2013 — Lecture-by-Lecture Summaries
| 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.
| L2 T 10/01
|| Sean Davis lectures on logic. Truth tables.
Logical equivalence. De Morgan’s law. Circuits. Conditionals, biconditionals.
| 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
|| First-order logic: syntax, examples, English-translation. 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; cake-cutting.
| 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)
| 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!
| D6 M 11/11
|| “Virtual discussion section” because of holiday.
Review of one-to-one and onto functions. Hints on homework.
| L14 T 11/12
|| Definition of big-O 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. Big-O 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. Bondy-Chvatal Thm. longest and shortest paths. 2- and 3-colorability.
| 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.
| 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