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 Hasbrouck 134. 101. There are two discussion sections, both on Fridays in the Computer Science Building room 142: Section D01 meeting 12:20-1:10 and Section D02 meeting 2:30-3:20. The TA's and I will move around among discussion sections. There are two evening midterm exams as indicated -- a discussion class near each one is cancelled.
PART I: Logic and Number Theory
Mon 23 Jan L01 Sets and Strings (1.1, 1.2)
Wed 25 Jan L02 Propositions and Boolean Operations (1.4)
Fri 27 Jan L03 Set Operations and Truth Tables (1.5, 1.6)
Fri 27 Jan D01 What Is a Proof? (1.3)
Mon 30 Jan L04 Rules for Propositional Proofs (1.7)
Wed 01 Feb L05 Propositional Proof Strategies (1.8)
Fri 03 Feb L06 Predicates and Relations (1.10, 2.1)
Fri 03 Feb D02 A Murder Mystery (1.9)
Mon 06 Feb L07 Quantifiers and Languages (2.3, 2.5)
Wed 08 Feb L08 Proofs With Quantifiers (2.6)
Fri 10 Feb L09 Relations and Functions (2.8, 2.9)
Fri 10 Feb D03 Practicing Proofs (2.7)
Mon 13 Feb L10 Partial Orders (2.10)
Wed 15 Feb L11 Equivalence Relations (2.11)
Fri 17 Feb L12 Divisibility and Primes (3.1)
Fri 17 Feb D04 Playing With Numbers (3.2)
Mon 20 Feb --- NO CLASS (President's Day Holiday)
Wed 22 Feb L13 Modular Arithmetic (3.3)
Fri 24 Feb L14 The Chinese Remainder Theorem (3.5)
Fri 24 Feb L14 NO DISCUSSION
Mon 27 Feb L15 The Fundamental Theorem of Arithmetic (3.6)
Tue 28 Feb X01 FIRST MIDTERM (7-9 pm, Morrill 2 room 131) on Lectures 1-15
PART II: Induction, Trees, and Searching
Wed 29 Feb L16 Recursive Definition (4.1)
Fri 02 Mar L17 Proof by Induction for Naturals (4.3)
Fri 02 Mar D05 Recursive Algorithms (4.2)
Mon 05 Mar L18 Variations on Induction for Naturals (4.4)
Wed 07 Mar L19 Proving the Basic Facts of Arithmetic (4.6)
Fri 09 Mar L20 Strings and String Operations (4.7)
Fri 09 Mar D06 Fibonacci Numbers (4.5)
Mon 12 Mar L21 Induction for Problem Solving (4.11)
Tue 13 Mar --- Last Day to Drop With W
Wed 14 Mar L22 Graphs, Paths, and Trees (4.9, 9.1)
Fri 16 Mar L23 Recursion on Trees (9.3)
Fri 16 Mar D07 Boolean Expressions (9.2)
SPRING BREAK
Mon 26 Mar L24 General, Breadth-First and Depth-First Search (9.4, 9.5)
Wed 28 Mar L25 BFS and DFS on Graphs (9.6)
Fri 30 Mar L26 Uniform-Cost and A-Star Search (9.8, 9.9)
Fri 30 Mar --- NO DISCUSSION
Mon 02 Apr L27 Games and Adversary Search (9.10)
Tue 03 Apr X02 SECOND MIDTERM (7-9 pm, location Morrill 2 room 131) on Lectures 16-27
PART III: Regular Expressions, Finite-State Machines, and Computability
Wed 04 Apr L28 Regular Expressions and Their Languages (5.1, 5.2)
Fri 06 Apr L29 Proving Regular Language Identities (5.4)
Fri 06 Apr D08 Designing Regular Expressions (5.3)
Mon 09 Apr L30 Proving Properties of the Regular Languages (5.5)
Wed 11 Apr L31 What DFA's Can and Can't Do (14.1, 14.2)
Fri 13 Apr L32 The Myhill-Nerode Theorem (14.3)
Fri 13 Apr D09 Minimizing Finite Automata (14.3)
Mon 16 Apr --- NO CLASS (Patriots' Day Holiday)
Tue 17 Apr L33 NFA's and the Subset Construction (14.5, 14.6)
Wed 18 Apr L34 Killing λ-Moves: λ-NFA's to NFA's (14.7)
Fri 20 Apr L35 Constructing NFA's from Regular Expressions (14.8)
Fri 20 Apr D10 Practicing NFA Constructions (14.9)
Mon 23 Apr L36 State Elimination: NFA's Into Regular Expressions (14.10)
Wed 25 Apr L37 Two-Way Automata and Turing Machines (15.1, 15.6)
Fri 27 Apr L38 Turing Machine Semantics (15.8)
Fri 27 Apr D11 Course Evaluations
Mon 30 Apr L39 The Halting Problem and Unsolvability (15.10)
Final Exam (cumulative) Tuesday 8 May, 8-10 a.m.
Last modified 28 February 2012