Logic and Set Theory

Course code MATH3010Units 10Level 3000Faculty of Science and Information TechnologySchool of Mathematical and Physical Sciences

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.

Not available in 2014

Previously offered in 2013, 2008, 2006, 2004
ObjectivesStudents will
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.
Content1. 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.
Replacing Course(s)n/a
Transitionn/a
Industrial Experience0
Assumed KnowledgeMATH2320 or MATH2330
Modes of DeliveryInternal Mode
Teaching MethodsLecture
Assessment Items
Essays / Written Assignments
Examination: Formal
Projects
Contact HoursLecture: for 3 hour(s) per Week for Full Term