## Home Page for Math 4L03: Introduction to Mathematical Logic Winter 2010-2011

Textbook: Propositional and predicate calculus: A model of argument, Derek Goldrei, Springer.
Course objective: To learn the fundamental ideas of mathematical logic.  Our goal is to prove and understand the philosophically significant completeness theorem, and the practically significant compactness theorem.

Instructor: Dr. D. Haskell, HH316, ext.27244

Course meeting time: M 12:30-13:20, T 13:30-14:20, R 12:30-13:20 in BSB 115
Office hours: T 9:30-11:30, R 9:30-10:30

TA

Course requirements, in brief (consult the course information sheet  for more detailed information).
Attendance and class participation: 20%
Homework: 20%
Midterm: 20%
Final: 40%

Announcements

Homework assignments (Page references are to the Goldrei textbook.)

Homework 1: p.30 2.10,
p47 2.29, 2.31,
p62 2.46

Homework 2: p.83 2.83, 2.85, 2.86
p.99 3.14, 3.15
p.106 3.21

Homework 3: p.161 4.21, 4.22, 4.23, 4.24
p.184 4.52

Homework 4: p.184 4.55
p.206 4.95
p.207 4.98, 4.99
p.213 4.108
p.215 4.111

Homework 5: p.242 5.20, 5.22
p.245 5.27
p.264 5.39

Course Calendar

The course calendar is subject to change as we move through the semester. Changes in homework due dates and midterm dates will be announced in the announcements section of this webpage.

 Dates Monday Tuesday Thursday Required Reading and  Recommended Problems Week 1 Jan 3 - 7 Propositional calculus: construction and interpretation of propositional formulas Propositional calculus: construction and interpretation of propositional formulas instructor absent - class meet to discuss the reading assignment Goldrei: (1.1, 1.2), 2.1, 2.2, 2.3 and embedded exercises Week 2 Jan 10 - 14 Propositional calculus: logical equivalence and consequence Propositional calculus: logical equivalence and consequence Propositional calculus: logical equivalence and consequence Homework 1 due Goldrei: 2.4, 2.6 and embedded exercises Week 3 Jan 17 - 21 Propositional calculus: formal deductions Propositional calculus: formal deductions Propositional calculus: formal deductions Goldrei: 3.1, 3.2 and embedded exercises Week 4 Jan 24 - 28 Propositional calculus: soundness and completeness Propositional calculus: soundness and completeness Propositional calculus: soundness and completeness Homework 2 due Goldrei: 3.3 and embedded exercises Week 5 Jan 31 - Feb 4 Predicate calculus: first-order languages Predicate calculus: first-order languages Predicate calculus: first-order languages Goldrei: 4.1, 4.2 to p. 148 and embedded exercises Week 6 Feb 7 - 11 Predicate calculus: first-order languages Predicate calculus: logical equivalence Predicate calculus: logical equivalence Homework 3 due Goldrei: 4.2 to end, 4.3 to p. 173 and embedded exercises Week 7 Feb 14 - 18 Predicate calculus: logical equivalence Predicate calculus: axiom systems Predicate calculus: axiom systems Goldrei: 4.3 to end, 4.4 We will discuss especially exercises 4.76 and 4.77 Feb 21 - 25 READING WEEK READING WEEK READING WEEK Week 8 Feb 28 - Mar 4 Predicate calculus: substructures and isomorphisms Predicate calculus: substructures and isomorphisms Predicate calculus: formal deduction system Goldrei: 4.5 and embedded exercises Week 9 Mar 7 - 11 Predicate calculus: formal deduction system Predicate calculus: soundness theorem Predicate calculus: soundness theorem Homework 4 due Goldrei: 5.1, 5.2 and embedded exercises Week 10 Mar 14 - 18 Predicate calculus: soundness theorem Predicate calculus: completeness theorem Midterm Goldrei: 5.3 and embedded exercises Week 11 Mar 21 - 25 Predicate calculus: completeness theorem Predicate calculus: completeness theorem Applications of compactness: axiomatizability Homework 5 due Goldrei: 5.4, 5.5 and embedded exercises Week 12 Mar 28 - Apr 1 Applications of compactness: Lowenheim-Skolem Applications of compactness: Lowenheim-Skolem Applications of compactness: Lowenheim-Skolem Week 13 Apr 4 - 8 review Homework 6 due