All reading and discussion assignments are from Barrington, A Mathematical Foundation for Computer Science, third draft.
PART I: Logic and Number Theory
Wed 26 Jan L01 Sets and Strings (1.1,1.2) (no discussion)
Fri 28 Jan L02 Propositions and Sets (1.4,1.5)
Mon 31 Jan L03 Propositional Proofs (1.6,1.7)
M/W 02 Feb D01 A Murder Mystery (1.9)
Wed 02 Feb L04 Propositional Proof Strategies (1.8)
Fri 04 Feb L05 Predicates and Relations (1.10, 2.1)
Mon 07 Feb L06 Quantifiers (2.3)
M/W 09 Feb D02 Translating Quantifiers (2.4)
Wed 09 Feb L07 Proofs With Quantifiers (2.6)
Fri 11 Feb L08 Properties of Relations and Functions (2.8,2.9)
Mon 14 Feb L09 Partial Orders and Equivalence Relations (2.10,2.11)
M/W 16 Feb D03 Practicing Proofs (2.7)
Wed 16 Feb L10 Divisibility and Primes (3.1)
Fri 18 Feb L11 Modular Arithmetic (3.3)
Mon 21 Feb --- Holiday (Presidents' Day)
Wed 23 Feb L12 Infinitely Many Primes (3.4) (no discussion, Monday sched)
Thu 24 Feb X01 EVENING EXAM on Lectures 1-12
PART II: Induction and Regular Expressions
Fri 25 Feb L13 The Chinese Remainder Theorem (3.5)
Mon 28 Feb L14 The Fundamental Theorem of Arithmetic (3.6)
M/W 02 Mar D04 Recursive Algorithms (4.2)
Wed 02 Mar L15 Recursive Definition (4.1)
Fri 04 Mar L16 Proof By Induction for Naturals (4.3)
Mon 07 Mar L17 Variations on Induction for Naturals (4.4)
M/W 09 Mar D05 Fibonacci Numbers (4.5)
Wed 09 Mar L18 Proving the Basic Facts of Arithmetic (4.6)
Fri 11 Mar L19 Strings and String Operations (4.7)
SPRING BREAK
Mon 21 Mar L20 Graphs and Paths (4.9)
M/W 23 Mar D06 Naturals and Strings (4.8)
Wed 23 Mar L21 Induction for Problem Solving (4.11)
Fri 25 Mar L22 Regular Expressions and Languages (5.1,5.2)
Mon 28 Mar L23 Proving Regular Language Identities (5.4)
M/W 28 Mar D07 Designing Regular Expressions (5.3)
Wed 30 Mar L24 Proving Properties of the Regular Languages (5.5)
Thu 31 Mar X02 EVENING EXAM on Lectures 13-24
PART III: Combinatorics and Graph Theory
Fri 01 Apr L25 Counting: Sum, Product, and Inclusion/Exclusion Rules (6.1,6.2)
Mon 04 Apr L26 The First and Second Counting Problems (6.3,6.4)
M/W 06 Apr D08 The Problem of Sorting (6.5)
Wed 06 Apr L27 The Third Counting Problem (6.6)
Fri 08 Apr L28 The Fourth Counting Problem (6.7)
Mon 11 Apr L29 Counting Balanced Parentheses (6.9,6.10)
M/W 13 Apr D09 Listing Permutations and Combinations (6.8)
Wed 13 Apr L30 Basic Probability (7.6)
Fri 15 Apr L31 Expected Value (7.7)
Mon 18 Apr --- Holiday (Patriots' Day)
Wed 20 Apr L32 Graphs and Adjacency Matrices (8.1,8.2) (no discussion)
Thu 21 Apr L33 Counting Paths With Matrices (8.3) (Monday sched)
Thu 21 Apr X03 EVENING EXAM on Lectures 22-33
PART IV: Finite-State Machines and Computability
Fri 22 Apr L34 What DFA's Can and Can't Do (9.1,9.2)
Mon 25 Apr L35 The Myhill-Nerode Theorem (9.3)
M/W 27 Apr D10 Minimizing DFA's (9.3)
Wed 27 Apr L36 NFA's and the Subset Construction (9.5,9.6)
Fri 29 Apr L37 Killing Lambda-Moves: Lambda-NFA's to NFA's (9.7)
Mon 02 May L38 Regular Expressions to Lambda-NFA's (9.8)
M/W 04 May D11 Practicing Multiple Constructions (9.9)
Wed 04 May L39 State Elimination: NFA's to Regular Expressions (9.10)
Fri 06 May L40 Two-Way DFA's and Turing Machines (10.1,10.6)
Mon 09 May L41 Turing Machine Semantics and the Halting Problem (10.8,10.10)
M/W 11 May D12 Course Evaluations
Wed 11 May L42 Review and Coming Attractions
Final Exam as scheduled by the University
Last modified 24 January 2005