This course introduces the key concepts of modern abstract analysis. The philosophy of this course is that modern analysis plays a fundamental role in mathematics itself and in applications to areas such as physics, computer science, economics and engineering.
Topics to be covered include elementary set theory, metric spaces, sequences, uniform convergence, continuity, the contraction mapping principle, integral equations and differential equations, topological spaces. The special topic for MATH6110 students has, for example, previously included an introduction to one or more of the following topics: axiomatic set theory; the construction of the natural numbers, integers, rationals and reals; the p-adic numbers; harmonic analysis; numerical analysis; the prime number theorem.
Note: This course is partially co-taught with the undergraduate course MATH2320 but will be assessed separately. Masters students will have a separate additional class each week on an additional special topic, and additional assessment item(s).
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of real analysis and their role in modern mathematics and applied contexts.
- Demonstrate accurate and efficient use of real analysis techniques.
- Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from real analysis.
- Apply problem-solving using real analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts.
- Use deep knowledge and understanding of advanced real analysis to formulate responses to complex concrete and abstract problems.
Indicative Assessment
- Assignments (15-22.5%) (20) [LO 1,2,3,4]
- Mid semester exam (22.5%-30%) (25) [LO 1,2,3,4]
- Final exam (30-37.5%) (30) [LO 1,2,3,4]
- Written report or assignments on special topic.Regardless of performance on other assessment items, a minimum score of 35% on this report is required to pass the course. (This is known as a 'course hurdle'.) (25) [LO 1,2,3,4,5]
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.
Workload
The expected workload will consist of approximately 130 hours throughout the semester including:
- Face-to face component which will consist of three 1-hour lectures each week for 12 weeks (36 hours) and ten 1-hour workshops (one each week in ten of twelve weeks) throughout the semester (10 hours).
- 12 x 1 hour extension lectures per semester (12 hours).
- Approximately 72 hours of self-directed study which will include preparation for lectures, workshops, assignments and exams.
Inherent Requirements
No specific inherent requirements have been identified for this course.
Requisite and Incompatibility
You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.
Prescribed Texts
No prescribed texts.
Preliminary Reading
- W. Rudin, Principles of Mathematical Analysis, McGraw-Hill.
- J. Giles, Introduction to the Analysis of Metric Spaces, Australian Mathematical Society lecture series no. 3.
- G. Simmons, Introduction to Topology and Modern Analysis, McGraw-Hill.
- H. Royden, Real Analysis, Prentice-Hall, various editions.
- T.W. Korner, A Companion to Analysis, American Mathematical Society.
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 |
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.
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 |
|---|---|---|---|---|---|---|
| 2548 | 23 Feb 2026 | 02 Mar 2026 | 31 Mar 2026 | 29 May 2026 | In Person | N/A |