MATH336-16S2 (C) Semester Two 2016

Foundations of Mathematics

15 points, 0.1250 EFTS
11 Jul 2016 - 13 Nov 2016

Description

An introduction to the philosophy of mathematics, classical and intuitionistic logic, set theory, and Gödel's theorems.

What is mathematics? What is the connection between truth and provability? What are the limitations of mathematics? Is every mathematical truth provable, at least in principle? "Foundations of mathematics" is the name given to the examination of such questions using mathematical methods wherever applicable. The technical mathematical background required for this course is fairly minimal (for example, it does not require a background course on analysis), so the course should be accessible to some philosophers and computer scientists; nevertheless, a measure of mathematical/intellectual maturity is an advised prerequisite.

Part 1: Classical propositional and predicate logic; valuations, proof trees, and derivations; soundness and completeness; the compactness theorem and its applications

Part 2: Axiomatic Zermelo-Fraenkel set theory; ordinals; the axiom of choice and the continuum hypothesis; independence of axioms.

Part 3: Gödel's incompleteness theorems.

Learning Outcomes

By the end of the course, the students will have an appreciation of some of the major breakthroughs in mathematical logic in the first 70 years of the twentieth century, and they will be able to carry out technical work in formal logic and set theory.

In particular they should:

  • understand the fundamentals of proof and model theory, for classical propositional and predicate logic, up to the Gödel-Henkin completeness theorem, the compactness theorem, and the upward Löwenheim-Skolem theorem
  • understand, and use, the axioms of Zermelo-Fraenkel set theory, in particular in the development of the theory of ordinals
  • understand the proof and the significance of Gödel's incompleteness theorems

Pre-requisites

30 points in MATH or EMTH at 200 level, as approved by the Head of School.

Restrictions

MATH 208, MATH 308

Timetable 2016

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Tuesday 10:00 - 11:00 Erskine 441 11 Jul - 21 Aug
5 Sep - 16 Oct
Lecture B
Activity Day Time Location Weeks
01 Monday 10:00 - 11:00 Erskine 441 11 Jul - 21 Aug
5 Sep - 16 Oct
Lecture C
Activity Day Time Location Weeks
01 Wednesday 16:00 - 17:00 Erskine 441 11 Jul - 21 Aug
5 Sep - 16 Oct

Course Coordinator / Lecturer

Maarten McKubre-Jordens

Lecturer

Thomas Forster

Assessment

Assessment Due Date Percentage 
Take-Home Test 1 30%
Take-Home Test 2 30%
Take-Home Test 3 40%

Fees

Domestic fee $720.00

International fee $3,450.00

For further information see Mathematics and Statistics.

All MATH336 Occurrences

  • MATH336-16S2 (C) Semester Two 2016