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
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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.
Referenced entries (3)
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- MATH3343 · 2027 · saved source not linked
- MATH4343 · 2027 · saved source not linked
- MATH6203 · 2027 · saved source not linked
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.
Published offerings
Future offerings are indicative. Only recognised 2027 sessions with a published class number are offered in the enrolment demo.
| Year | Session | Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|---|---|
| 2027 | First Semester | 4636 | 22 Feb 2027 | 01 Mar 2027 | 31 Mar 2027 | 28 May 2027 | In Person | N/A |
| 2028 | First Semester | 6117 | 21 Feb 2028 | 28 Feb 2028 | 31 Mar 2028 | 26 May 2028 | In Person | N/A |
Complete offering text
ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage. The list of offerings for future years is indicative only. Class summaries, if available, can be accessed by clicking on the View link for the relevant class number. 2027 2028 First Semester Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary 4636 22 Feb 2027 01 Mar 2027 31 Mar 2027 28 May 2027 In Person N/A First Semester Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary 6117 21 Feb 2028 28 Feb 2028 31 Mar 2028 26 May 2028 In Person N/A
Source evidence (1 saved copy)
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assets/Courses/Computational Foundations/8000/Foundations of Mathematics/Foundations of Mathematics - ANU.html
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