Time: Wednesday 11:3012:50, Friday 1:102:30
Recitation: Tuesday 11:3012:50
Place: Campbell Hall, room A4
Semester: Fall 2004
Michael's office hours: Hill 409, by
appointment.
Sam's office hours: Hill 418, by
appointment.
Date  Sections  Topics  Problems 
9/1  1.6, 1.7  sets, subsets  1.6: 4, 6, 8, 10, 12, 14, 16, 18, 22, 24.c 1.7: 2, 4, 10, 20, 22 (justify your answer), 24, 38, 40, 48 (see definition in 47), 50 (see definition after 48, assume the university will buy all the equipment and departments will borrow what they need temporarily) 
9/3  1.8  functions mapping set to set, domain, codomain, range, onetoone, onto, inverse, composition  
9/8  1.1  propositions, and, or, not, xor, truth tables, implication, contrapositive, converse, inverse  
9/10  1.2  translating logic expressions, equivalences, tautology, contradiction, contingency, DeMorgan, distributive, associative  1.1: 10, 12, 16, 22, 24(d,e), 28(c,f), 30 1.8: 2(b,c) (justify your answer), 6, 12, 14(a,b,if not, give counterexample), 16, 18, 22 (give values for all elements of S), 24 (name the range), 28, 30, 34 (optional), 66.b 
9/15  10.1, 10.2  complementation, Boolean expressions (recursive definition), literal, minterm, DNF, CNF  
9/17  10.3  combinatorial circuit, and gate, or gate, inverter, half adder, full adder  1.1: 34(b, c; see pg. 14 for bitwise definition), 44, 48
(consistent means "their conjunction is not a
contradiction"), 52 (optional), 54 (optional) 1.2: 4(a), 6, 10 (detailed proofs, see pg. 25 for example), 12, 30 (optional), 40 10.1: 2, 4(b,d), 6(b,d, optional), 26 (optional), 32 (detailed proof, optional), 34 (detailed proof, optional) 
9/22  1.3  predicate, propositional function, universal quantification, existential quantification, predicate calculus, connection to conjunction and disjunction  
9/24  1.4, 1.5 (start)  nested quantifiers, negating nested quantifiers, proof, axioms, rules of inference, fallacy, lemma, corollary, conjecture, valid arguments, modus ponens  1.3: 2(a,b), 10, 12, 22 1.7: 6(a,d,e,g, use quantifiers), 12(a,d, use quantifiers) 10.2: 4(c,d, sum of products means DNF), 6, 8 (answer should be in CNF), 12(c,d), 18 (downarrow is "nor"), 20(a,c, justify your answer) 10.3: 2 (give formula), 4 (give formula), 6(c,d), 10, 12 (build the circuit, using the full and half subtractors as components), 16, 18 
9/29  1.5 (rest)  universal/existential instantiation/generalization, direct proof, indirect proof, proof by contradiction, proof by cases, nonconstructive existence proof, strategystealing argument  
10/1  MIDTERM  
10/6  3.1, 3.2 (remotely)  1.3: 26, 30, 34, 38, 40, 42 (supply the inference rules),
46 (give counterexample), 50 (see notation in problem
48), 56, 58 1.4: 8, 10, 12(j,k,l), 16(d,e), 22, 30, 38 (say "true" if no counterexample exists), 42, 48 

10/8  3.3  induction, basis, inductive hypothesis  1.5: 12 (name the inference rule of fallacy for each), 14 (evaluate the validity of the reasoning, not the validity of the statements), 16, 18, 20, 28, 36, 38, 42, 48, 50, 52, 54, 56, 60 (supply the inference rule), 64 (optional), 74 
10/13  3.4  strong induction  
10/15  3.4 (more)  induction, recursion  3.1: 2, 4, 6 (hint: from class), 8 (hint: from class),
12 (compare quadratic mean, a, and b), 20, 22, 26, 28, 32
(optional) 3.2: 6(d,e,h), 10(a,e), 20, 30, 38 (optional), 42 (optional) 3.3: 4, 6 (cute one!), 8, 12, 14 
10/20  3.5  recursion, iteration, repeated squaring  
10/22  7.1, 7.3  relations, reflexive, symmetric, antisymmetric, transitive, directed graph, matrices (Eric Allender covering)  
10/27  7.4  closure, path, connectivity relation  
10/29  7.5, 7.6  3.3: 16, 18, 24, 28, 30, 36, 42 (ask if you need the
definition of matrix multiplication), 44, 48, 50, 52, 54,
58 (Hn = 1/1 + 1/2 + ... + 1/n) 3.4: 6, 8, 12 (fn is the nth Fibonacci number), 14 (hint: use a proof by induction and carefully apply the definition of fn), 18, 22, 26 (optional), 28, 30, 36 (use the definition from the solution to problem 35), 42, 44, 46, 48 (see the definition immediately above), 50, 54 

11/3  MIDTERM  
11/5  11.1  natural language, vocabulary, sentence, empty string, language, phrasestructure grammar, directly derivable, derivable, derivation  7.1: 4, 8, 20 (see definition before problem 16), 22, 24
(see definition above the problem), 30, 34(a,d, see
definition before problem 32), 36, 48 (optional), 56 7.3: 8, 14(c,d,e), 20, 24 (list the ordered pairs), 32 7.4: 2, 10, 14 (optional), 18, 22, 24 7.5: 2, 6 (Hint: Think about the range of f.), 10, 24, 28 
11/10  11.1, 11.3  parse tree, finite state automaton  
11/12  11.2  finite state transducer  (Due a week from Tuesday) 7.5: 30, 34 (recall [x,y] includes the endpoints and (x,y) doesn't), 40, 42 7.6: 4, 6, 8 (bar means "divisibility"), 10, 16, 22, 26, 28, 30 (can draw a diagram), 38, 48 (optional), 56 11.1: 2, 6 (give a proof by induction) 
11/17  11.3, 11.4  regular sets, regular languages, NFAs, DFAs  
11/19  11.4  Kleene's theorem, pumping  11.1: 8 (show everything generated has this form and
everything of this form can be generated), 12, 16, 18, 24 11.3: 2, 8 (use definition of set equality), 12 (give a regular expression for your answer), 22, 24, 26 
11/24  NO CLASS  
11/26  NO CLASS  
12/1  11.5, 2.2  halting problem, Big O  
12/3  2.2, A.1  bigO, bigOmega, bigTheta, logs, exponentials  2.2: 2, 6, 8, 12, 14(d,e,f), 18, 22, 26, 36 11.1: 20 11.3: 2, 8.b, 10, 18 
12/8  wrap up  
12/10  juggling, siteswap notation  
12/20  FINAL 