Analysis 1 is a foundational course in Mathematics, leading on to other areas of analysis, such as topology and measure theory, complex analysis, functional analysis, and harmonic analysis. It also provides important tools for application areas such as theoretical computer science, physics, 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.
Note: This is an Honours Pathway Course: It emphasises mathematical rigour and proof and develops the application of the theory to topics such as differential equations.
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.
Indicative Assessment
- Regular written assignments (20-30%) (30) [LO 1,2,3,4]
- Mid semester exam (30-40%) (30) [LO 1,2,3,4]
- Final exam (40-50%) (40) [LO 1,2,3,4]
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).
- Approximately 84 hours of self-directed study which will include preparation for lectures, workshops, assignments and exams.
Inherent Requirements
No specific inherent requirements have been identified in this course.
Requisite and Incompatibility
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.
Majors
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 |
Course fees
- Domestic fee paying students
| Year | Fee |
|---|---|
| 2025 | $4680 |
- International fee paying students
| Year | Fee |
|---|---|
| 2025 | $6720 |
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 |
|---|---|---|---|---|---|---|
| 3551 | 17 Feb 2025 | 24 Feb 2025 | 31 Mar 2025 | 23 May 2025 | In Person | View |