MATH8343
Foundations of Mathematics
- Credit
- 6 units
- Catalogue year
- 2027
- Recorded offerings
- First Semester
Course information
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 logicAxiomatisation of set theoryModel theoryComputabilityGodel's Incompleteness TheoremOther topics in logic and set theory
Requisite and Incompatibility
To enrol in this course you need to be active in the Master of Mathematical Sciences (Advanced) or Master of Science in Mathematical Sciences. Incompatible with MATH3343, MATH4343 and MATH6203.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
Explain the fundamental concepts from the foundations of mathematics and its role in modern mathematics and applied contexts.
Demonstrate accurate and efficient use of logical and set theoretical techniques.
Critically analyze and explain concepts from the foundations of mathematics.
Prove theorems in the foundations of mathematics.
Critically evaluate naive approaches to codifying the foundation of mathematics.
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