All reading and discussion assignments are from Barrington, A Mathematical Foundation for Computer Science, fourth draft.
Date of second midterm corrected 27 March 2006.
PART I: Logic and Number Theory
Wed 01 Feb L01 Sets and Strings (1.1,1.2) (no discussion)
Fri 03 Feb L02 Propositions and Sets (1.4,1.5)
Mon 06 Feb L03 Propositional Proofs (1.6,1.7)
M/W 06 Feb D01 What is a Proof? (1.3)
Wed 08 Feb L04 Propositional Proof Strategies (1.8)
Fri 10 Feb L05 Predicates and Relations (1.10, 2.1)
Mon 13 Feb L06 Quantifiers (2.3)
M/W 13 Feb D02 Translating Quantifiers (2.4)
Wed 15 Feb L07 Proofs With Quantifiers (2.6)
Fri 17 Feb L08 Properties of Relations and Functions (2.8,2.9)
Mon 20 Feb --- Holiday (Presidents' Day)
Tue 21 Feb L09 (Monday schedule) Partial Orders (2.10)
T/W 21 Feb D03 (Tuesday is Monday) Practicing Proofs (2.7)
Wed 22 Feb L10 Equivalence Relations (2.11)
Thu 23 Feb X01 EVENING EXAM on Lectures 1-10
PART II: Number Theory and Induction
Fri 24 Feb L11 Divisibility and Primes (3.1)
Mon 27 Feb L12 Modular Arithmetic (3.3)
M/W 27 Feb D04 Infinitely Many Primes (3.4)
Wed 01 Mar L13 The Chinese Remainder Theorem (3.5)
Fri 03 Mar L14 The Fundamental Theorem of Arithmetic (3.6)
Mon 06 Mar L15 Recursive Definition (4.1)
M/W 06 Mar D05 Recursive Algorithms (4.2)
Wed 08 Mar L16 Proof By Induction for Naturals (4.3)
Fri 10 Mar L17 Variations on Induction for Naturals (4.4)
Mon 13 Mar L18 Proving the Basic Facts of Arithmetic (4.6) (DAVE AWAY)
M/W 13 Mar --- No discussion this week
Wed 15 Mar L19 Strings and String Operations (4.7) (DAVE AWAY)
Fri 17 Mar --- No lecture (DAVE AWAY)
SPRING BREAK
Mon 27 Mar L20 Graphs and Paths (4.9)
M/W 27 Mar D06 Naturals and Strings (4.8)
Wed 29 Mar L21 Induction for Problem Solving (4.11)
Thu 30 Mar X02 EVENING EXAM on Lectures 11-21
PART III: Regular Expressions, Combinatorics and Graph Theory
Fri 31 Mar L22 Regular Expressions and Languages (5.1,5.2)
Mon 03 Apr L23 Proving Regular Language Identities (5.4)
M/W 03 Apr D07 Designing Regular Expressions (5.3)
Wed 05 Apr L24 Proving Properties of the Regular Languages (5.5)
Fri 07 Apr L25 Counting: Sum, Product, and Inclusion/Exclusion Rules (6.1,6.2)
Mon 10 Apr L26 The First and Second Counting Problems (6.3,6.4)
M/W 10 Apr D08 The Problem of Sorting (6.5)
Wed 12 Apr L27 The Third Counting Problem (6.6)
Fri 14 Apr L28 The Fourth Counting Problem (6.7)
Mon 17 Apr --- Holiday (Patriot's Day)
M/W 17 Apr --- No discussion this week
Wed 19 Apr L29 (Monday Schedule) Basic Probability (7.6)
Fri 21 Apr L30 Expected Value (7.7)
Mon 24 Apr L31 Graphs and Adjacency Matrices (8.1,8.2)
M/W 24 Apr D09 Paths and Matrices (not in book)
Wed 26 Apr L32 Counting Paths With Matrices (8.3)
Thu 27 Apr X03 EVENING EXAM on Lectures 22-32
PART IV: Finite-State Machines and Computability
Fri 28 Apr L33 What DFA's Can and Can't Do (9.1,9.2)
Mon 01 May L34 The Myhill-Nerode Theorem (9.3)
M/W 01 May D10 Minimizing DFA's (9.3)
Wed 03 May L35 NFA's and the Subset Construction (9.5,9.6)
Fri 05 May L36 Killing Lambda-Moves: Lambda-NFA's to NFA's (9.7)
Mon 08 May L37 NFA's to Regular Expressions to Lambda-NFA's (9.8,9.10)
M/W 08 May D11 Practicing Multiple Constructions (9.9)
Wed 10 May L38 Two-Way DFA's and Turing Machines (10.1,10.6)
Fri 12 May L39 Turing Machine Semantics (10.8)
Mon 15 May L40 The Halting Problem (10.10)
M/W 15 May D12 Course Evaluations
Wed 17 May L41 Review and Coming Attractions
Final Exam as scheduled by the University
Last modified 10 April 2006