Logic and Set Theory

Description

Examines the logical foundations of concepts used throughout mathematics, such as order and equivalence relations, number and continuity. The use of infinity in mathematical arguments is investigated and implicit assumptions about infinite sets are exposed. Notions of infinity are formulated precisely and it is shown how infinite sets may be counted and compared in size. It is seen that, even in something as basic as set theory, 'truth' is not absolute.

Availability

Callaghan Campus

  • Semester 2 - 2015

Learning Outcomes

1. Learn about the logical foundations of such mathematical concepts as number, continuity and set

2. Gain an appreciation of the usefulness and limitations of the development of theories from axioms

3. Understand the concept of infinity and its role in mathematics.

Content

  1. The need for a rigorous treatment of the infinite in mathematics
  2. The Zermelo-Fraenkel Axioms
  3. Order
  4. Ordinal and cardinal numbers
  5. Transfinite induction
  6. The Axiom of Choice
  7. The Continuum Hypothesis.

Assumed Knowledge

MATH2320 or MATH2330

Assessment Items

Written Assignment: Assignments (x3)

Project: Project on a chosen topic.

Formal Examination: Examination

Contact Hours

Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term