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Mathematical Sciences Institute · ANU College of Systems and Society
This course is a critical approach to the foundations of mathematics. In other mathematics classes, the philosophical concepts at the most basic foundations are usually treated naively. The question of what exactly a number is, or what a set or a proof or an algorithm are, is completely ignored. Some evidence that these matters are not insubstantial is that in the early twentieth century, naive attempts to address them by the great logicians of the time led to famous paradoxes and a period known as the Crisis in Foundations of Mathematics. This course will address these matters directly and rigorously. It spends a few weeks on each of the following topics: - First order logic - Axiomatisation of set theory - Model theory - Computability - Godel's Incompleteness Theorem - Other topics in logic and set theory To enrol in this course you need to be undertaking the MATH-HSPC Honours specialisation.
Assignments (approximately 1 per week/per topic)
Learning outcomes 1, 2, 3, 4, 5
Final Exam
Learning outcomes 1, 2, 4
Precise % weighting of assessment will be determined in consultation with the class in the first week of semester. (null) [LO null]
The expected workload will consist of approximately 130 hours throughout the semester including: - Face-to-face component which may consist of 1 x 1 lectures and 1 x 2 hours of tutorials/workshops/labs per week. - Approximately 94 hours of self-directed study which will include preparation for lectures, tutorials and other assessment tasks. The exact workload distribution will vary from year to year.
There are no prescribed texts.