• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Mode of delivery In Person
• Co-taught Course
• Offered in First Semester 2025
• STEM Course
Foundations of Mathematics (MATH8343)

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

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Explain the fundamental concepts from the foundations of mathematics and its role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of logical and set theoretical techniques.
3. Analyze and explain concepts from the foundations of mathematics.
4. Prove theorems in the foundations of mathematics.
5. Critically evaluate naive approaches to codifying the foundation of mathematics.

## Indicative Assessment

1. Assignments (approximately 1 per week/per topic) (80) [LO 1,2,3,4,5]
2. Final Exam (20) [LO 1,2,4]
3. Precise weights of % assessment will be determined in consultation with the class in the first week of semester. (null) [LO null]

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

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 1 hours of tutorials/workshops/labs per week.
• Approximately 82 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.

## Inherent Requirements

No specific inherent requirements have been identified for this course

## 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.

## Prescribed Texts

There are no prescribed texts.

## Assumed Knowledge

A solid background in mathematics is expected. Typically requires MATH2322 or MATH3104 with a grade of over 60% (ir their equivalents) or MATH6118

## Fees

Tuition fees are for the academic year indicated at the top of the page.

Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees

Student Contribution Band:
1
Unit value:
6 units

If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Where there is a unit range displayed for this course, not all unit options below may be available.

Units EFTSL
6.00 0.12500
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

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.

### First Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
3363 17 Feb 2025 24 Feb 2025 31 Mar 2025 23 May 2025 In Person N/A