MATH31011 Mathematical Logic

This is the former 314/MA3011

 SEMESTER: First
CONTACT: Professor Peter Symonds (M/P8) CREDIT RATING: 10
Aims: To introduce students to Predicate Logic culminating in Gödel’s Completeness Theorem.
Intended Learning Outcomes: On successful completion of the course students will:
  • Be able to work with a formal language.
  • Understand how to use interpretations and models.
  • Be able to give simple proofs from the axioms.
  • Understand the importance of consistency and completeness.
Pre-requisites: 112, 152 (ex-UMIST), MT1101 (ex-VUM)

This Course unit is NOT available to students who have taken MT2151 in previous years
Dependent Courses: None
Course Description: The course concentrates on one of the most important results of 20th century logic, Gödel's Completeness Theorem for Predicate Logic. This theorem links two fundamental concepts of Mathematics, truth and provability, and provides deep insights into ways of mathematical thinking. Prospective students should enjoy abstract ideas and have the ability to understand mathematical proofs of the type which occur in Pure Mathematics.
Teaching Mode: 2 Lectures per week
1 Tutorial per week
Private Study: 5 hours per week
Recommended Texts: E Mendelson, Introduction to Mathematical Logic, (4th edition), 1997 or earlier edition, Chapman Hall.
Assessment Methods: Coursework: 20%
Coursework Mode: Test in Week 7
Examination: 80%
Examination is of 2 hours duration at the end of the First Semester.
No of lectures: Syllabus
7 Propositional logic: truth tables, formal language, interpretations, modus ponens, axioms, deduction theorem, consistency, completeness, Löwenheim-Skolem theorem, completeness theorem.
6 Predicate logic: formal language, interpretations, rules of inference, axioms, deduction theorem.
7 Predicate logic (continued): consistency, completeness, Löwenheim-Skolem theorem, Gödel's completeness theorem.
2 Compactness theorem with applications.

 Last revised August, 2006