COMPSCI 250: Winter 2021


Syllabus and Course Schedule

Instructor: Ghazaleh Parvini

Reading assignments are from David Mix Barrington: A Mathematical Foundation for Computer Science (revised preliminary edition, 2020), available as an e-book from Kendall Hunt.

PART I: Logic and Number Theory

Week1:

Mon 7 Dec L01 Sets and Strings,Propositions (1.1, 1.2,1.4)

Tue 8 Dec L02 Boolean Operations,Set Operations (1.4, 1.5)

Wed 9 Dec L03 Truth Tables, Rules for Propositional Proofs (1.5, 1.6, 1.7)

Thu 10 Dec L04 Propositional Proof Strategies, Predicates (1.8,1.10)

Fri 11 Dec L05 Relations, Quantifiers (2.1,2.3) (END OF ADD/DROP)

Week2:

Mon 14 Dec L06 Proofs With Quantifiers, Functions (2.3, 2.5,2.6)

Mon 15 Dec L07 Relations and Functions (2.8, 2.9)

Tue 16 Dec L08 Equivalence Relations and Partial Orders (2.10,2.11)

Wed 17 Dec L09 Divisibility and Primes and Modular Arithmetic (3.1, 3.3)

Thu 18 Dec L10 The Chinese Remainder Theorem and The Fundamental Theorem of Arithmetic (3.5, 3.6)

PART II: Induction, Trees, and Searching

Week3:

Mon 21 Dec L11 Recursive Definition and Induction (4.1, 4.3)

Tue 22 Dec L12 Proof by Induction for Naturals,Variations on Induction for Naturals (4.3,4.4)

Wed 23 Dec L13 Induction for Problem Solving, (4.11)

Fri 24 Dec L14 Strings and String Operations (4.7)

Week4:

Mon 28 Dec 15 General, Breadth-First, and Depth-First Search (9.4, 9.5)

Tue 29 Dec L16 Graphs, Paths, and Trees, Recursion on Trees (4.9, 9.1,9.3)

Wed 30 Dec L17 BFS and DFS on Graphs (9.6)

Thu 31 Dec L18 Uniform-Cost and A* Search (9.8, 9.9)

PART III: Regular Expressions, Finite-State Machines, and Computability

Week5:

Mon 4 Jan L19 Regular Expressions and Their Languages (5.1, 5.2)

Wed 05 Jan L20 Proving Regular Language Identities and Properties (5.4,5.5)

Mon 06 Jan L21 What DFA's Can and Can't Do (14.1, 14.2)

Wed 07 Jan L22 The Myhill-Nerode Theorem (14.3)

Fri 08 Jan L23 NFA's and the Subset Construction (14.5, 14.6)

Week6:

Mon 11 Jan L24 Killing λ-moves: λ-NFA's to NFA's, Constructing NFA's from Regular Expressions (14.7,14.8)

Tue 12 Jan L25 State Elimination: NFA's to Regular Expressions (14.10)

Wed 13 Jan L26 Two-Way Automata and Turing Machines (15.1, 15.6)

Thu 14 Jan L27 Turing Machine Semantics and Universal Turing Machine (15.8,15.10)

Final Exam: Friday Jan 15