Reading assignments are from Barrington, Discrete Mathematics: A Foundation for Computer Science, fifth draft. A course packet, consisting of chapters 1-4 in one volume and chapters 5, 9, 14, and 15 in the other, is available at cost at Collective Copies in downtown Amherst.
Lecture Class meetings are MWF 11:15-12:05 in LGRT (the tower) room 101. There are two discussion sections, both meeting 10:10-11:00 on Fridays. Section 1 meets in ELAB 323 and Section 2 meets in the Computer Science Building room 142. The TA's and I will probably alternate leading each discussion section. There are two evening midterm exams as indicated -- the regular lecture classes those days are cancelled though I may use the first one as a makeup for snow cancellations if necessary.
PART I: Logic and Number Theory Wed 19 Jan L01 Sets and Strings (1.1, 1.2) Fri 21 Jan D01 NO DISCUSSION (snow) Fri 21 Jan L02 Propositions and Boolean Operations (1.4) Mon 24 Jan L03 Set Operations and Truth Tables (1.5, 1.6) Wed 26 Jan L04 Rules for Propositional Proofs (1.7) Fri 28 Jan D02 A Murder Mystery (1.9) Fri 28 Jan L05 Propositional Proof Strategies (1.8) Mon 31 Jan L06 Predicates and Relations (1.10, 2.1) Wed 02 Feb L07 Quantifiers and Languages (2.3, 2.5) Fri 04 Feb D03 Translating Quantifiers (2.4) Fri 04 Feb L08 Proofs With Quantifiers (2.6) Mon 07 Feb L09 Relations and Functions (2.8, 2.9) Wed 09 Feb L10 Partial Orders (2.10) Fri 11 Feb D04 Practicing Proofs (2.7) Fri 11 Feb L11 Equivalence Relations (2.11) Mon 14 Feb L12 Divisibility and Primes (3.1) Wed 16 Feb L13 Modular Arithmetic (3.3) Fri 18 Feb D05 Infinitely Many Primes (3.4) Fri 18 Feb L14 The Chinese Remainder Theorem (3.5) Mon 21 Feb --- NO CLASS (Presidents' Day) Tue 22 Feb L15 The Fundamental Theorem of Arithmetic (3.6) Wed 23 Feb X01 FIRST MIDTERM (7-9 pm, location TBA) on Lectures 1-15 (no lecture) PART II: Induction, Trees, and Searching Fri 25 Feb D06 Recursive Algorithms (4.2) Fri 25 Feb L16 Recursive Definition (4.1) Mon 28 Feb L17 Proof by Induction for Naturals (4.3) Wed 02 Mar L18 Variations on Induction for Naturals (4.4) Fri 04 Mar D07 Fibonacci Numbers (4.5) Fri 04 Mar L19 Proving the Basic Facts of Arithmetic (4.6) Mon 07 Mar L20 Strings and String Operations (4.7) Wed 09 Mar L21 Induction for Problem Solving (4.11) Fri 11 Mar D08 Boolean Expressions (9.2) Fri 11 Mar L22 Graphs, Paths, and Trees (4.9, 9.1) SPRING BREAK Mon 21 Mar L23 Recursion on Trees (9.3) Tue 22 Mar --- Last Day to Drop With W Wed 23 Mar L24 General, Breadth-First and Depth-First Search (9.4, 9.5) Fri 25 Mar D09 Middle-First Search and Matrices (9.7) Fri 25 Mar L25 DFS and BFS on Graphs (9.6) Mon 28 Mar L26 Uniform-Cost and A-Star Search (9.8, 9.9) Wed 30 Mar L27 Games and Adversary Search (9.10) Fri 01 Apr D10 Hexapawn (9.11) Mon 04 Apr --- SECOND MIDTERM (7-9 pm, location TBA) on Lectures 16-27 (no lecture) PART III: Regular Expressions, Finite-State Machines, and Computability Fri 01 Apr L28 Regular Expressions and Their Languages (5.1, 5.2) Wed 06 Apr L29 Proving Regular Language Identities (5.4) Fri 08 Apr D11 Designing Regular Expressions (5.3) Fri 08 Apr L30 Proving Properties of the Regular Languages (5.5) Mon 11 Apr L31 What DFA's Can and Can't Do (14.1, 14.2) Wed 13 Apr L32 The Myhill-Nerode Theorem (14.3) Fri 15 Apr D12 Minimizing Finite Automata (14.3) Fri 15 Apr L33 NFA's and the Subset Construction (14.5, 14.6) Mon 18 Apr --- NO CLASS (Patriots' Day) Wed 20 Apr L34 Killing λ-Moves: λ-NFA's to NFA's (14.7) Fri 22 Apr D13 Practicing NFA Constructions (14.9) Fri 22 Apr L35 Constructing NFA's from Regular Expressions (14.8) Mon 25 Apr L36 State Elimination: NFA's Into Regular Expressions (14.10) Wed 27 Apr L37 Two-Way Automata and Turing Machines (15.1, 15.6) Fri 29 Apr D14 Course Evaluations Fri 29 Apr L38 Turing Machine Semantics (15.8) Mon 02 May L39 The Halting Problem and Unsolvability (15.10) Final Exam (cumulative) during exam period as arranged by the UniversityLast modified 24 January 2011