CMPSCI 250: Fall 2007

Syllabus and Course Schedule

Prof. David Mix Barrington

All reading and discussion assignments are from Barrington, A Mathematical Foundation for Computer Science, fourth draft.

PART I:  Logic and the Language of Mathematics

Wed 05 Sep ---  NO DISCUSSION before first lecture!
Wed 05 Sep L01  Sets and Strings (1.1,1.2) (no discussion)
Fri 07 Sep L02  Propositions and Sets (1.4,1.5) 
Mon 10 Sep L03  Propositional Proofs (1.6,1.7)
Wed 12 Sep D01  What is a Proof? (1.3)
Wed 12 Sep L04  Propositional Proof Strategies (1.8)
Fri 14 Sep L05  Predicates and Relations (1.10, 2.1)
Mon 17 Sep L06  Quantifiers (2.3)
Wed 19 Sep D02  Translating Quantifiers (2.4)
Wed 19 Sep L07  Proofs With Quantifiers (2.6)
Fri 21 Sep L08  Properties of Relations and Functions (2.8,2.9)
Mon 24 Sep L09  Partial Orders (2.10)
Wed 26 Sep D03  Practicing Proofs (2.7)
Wed 26 Sep L10  Equivalence Relations (2.11)
Thu 27 Sep X01  EVENING EXAM (7-9 pm) on Lectures 1-10

PART II: Number Theory and Induction

Fri 28 Sep L11  Divisibility and Primes (3.1)
Mon 01 Oct L12  Modular Arithmetic (3.3) 
Wed 03 Oct D04  Infinitely Many Primes (3.4)
Wed 03 Oct L13  The Chinese Remainder Theorem (3.5) 
Fri 05 Oct L14  The Fundamental Theorem of Arithmetic (3.6)
Mon 08 Oct ---  HOLIDAY (Columbus Day):  NO LECTURE
Tue 09 Oct ---  (Mon sched) NO LECTURE (Dave Away) (SUBJECT TO CHANGE)
Wed 10 Oct L15  Recursive Definition (4.1) (Dave Away)
Fri 12 Oct L16  Proof By Induction for Naturals (4.3) (Dave Away) 
Mon 15 Oct L17  Variations on Induction for Naturals (4.4)
Wed 17 Oct L18  Proving the Basic Facts of Arithmetic (4.6) 
Wed 17 Oct D05  Fibonacci Numbers (4.5)
Fri 19 Oct L19  Strings and String Operations (4.7, not on test)
Mon 22 Oct L20  Graphs and Paths (4.9)
Wed 24 Oct D06  Naturals and Strings (4.8)
Wed 24 Oct L21  Induction for Problem Solving (4.11)
Thu 25 Oct X02  EVENING EXAM (7-9 pm) on Lectures 11-21

PART III:  Regular Expressions, Trees, and Searching

Fri 26 Oct L22  Adjacency Matrices (8.2)
Mon 29 Oct L23  Paths and Matrix Powering (8.3)
Wed 31 Oct D07  Markov Processes (8.4)
Wed 31 Oct L24  NO LECTURE -- Optional Makeup Exam
Fri 02 Nov L25  (more on 8.3, review of makeup)
Mon 05 Nov L26  Trees and Their Uses, Recursion (T.1,T.2)
Wed 07 Nov D08  To Be Announced (not in book)
Wed 07 Nov L27  General Search Trees (T.3)
Fri 09 Nov L28  General Breadth-First and Depth-First Search (T.4)
Mon 12 Nov ---  HOLIDAY (Veteran's Day): NO LECTURE
Wed 14 Nov ---  NO DISCUSSION this week (since no Wednesday)
Wed 14 Nov L29  (Monday Schedule) BFS and DFS on Graphs (T.5)
Fri 16 Nov L30  Uniform-Cost and A-Star Search (T.6,T.7)
Mon 19 Nov L31  Game Trees and Adversary Search (T.8)
Tue 20 Nov X03  EVENING EXAM (7-9 pm) on Lectures 22-31
Fri 23 Nov ---  HOLIDAY (Thanksgiving):  NO LECTURE

PART IV: Counting and Probability

Mon 26 Nov L32  Sum, Product, and Inclusion/Exclusion Rules (6.1,6.2)
Wed 28 Nov D09  The Problem of Sorting (6.5)
Wed 28 Nov L33  First and Second Counting Problems (6.3,6.4)
Fri 30 Nov L34  The Third Counting Problem (6.6)
Mon 03 Dec L35  The Fourth Counting Problem (6.7)
Wed 05 Dec D10  Listing Permutations and Combinations (6.8)
Wed 05 Dec L36  Finite Probability Distributions (P.1)
Fri 07 Dec L37  Expected Value (P.2)
Mon 10 Dec L38  Variance and Standard Deviation (P.3)
Wed 12 Dec D11  Course Evaluations
Wed 12 Dec L39  The Binomial Distribution (P.4)
Fri 14 Dec L40  Review and Coming Attractions

Final Exam Tuesday 18 December, 1:30-3:30 p.m., ELAB 303

Last modified 5 November 2007