Algebraic topology studies properties of topological spaces and maps between them by associating algebraic invariants (fundamental groups, homology groups, cohomology groups) to each space. This course gives a solid introduction to fundamental ideas and results that are employed nowadays in most areas of mathematics, theoretical physics and computer science. This course aims to understand some fundamental ideas in algebraic topology; to apply discrete, algebraic methods to solve topological problems; to develop some intuition for how algebraic topology relates to concrete topological problems.
Topics to be covered include:
Fundamental group and covering spaces; Brouwer fixed point theorem and Fundamental theorem of algebra; Homology theory and cohomology theory; Jordan-Brouwer separation theorem, Lefschetz fixed theorem; some additional topics (Orientation, Poincare duality, if time permits)
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of algebraic topology and their role in modern mathematics and applied contexts.
- Demonstrate accurate and efficient use of algebraic topology techniques.
- Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from algebraic topology.
- Apply problem-solving using algebraic topology techniques applied to diverse situations in physics, engineering and other mathematical contexts.
- Conduct some (limited) independent research under expert supervision.
Indicative Assessment
- Weekly assignments (40) [LO 1,2,3,4,5]
- Mid semester exam (20) [LO 1,2,3,4]
- End of semester exam (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 may consist of 3 x 12 hours (36 hours total) of lectures and 1 x 12 hours of workshops (12 hours total) per semester.
• 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
Prescribed Texts
Algebraic Topology, by Allen Hatcher
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 |
|---|---|
| 2023 | $4320 |
- International fee paying students
| Year | Fee |
|---|---|
| 2023 | $6180 |
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.
Second Semester
| Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|
| 7534 | 24 Jul 2023 | 31 Jul 2023 | 31 Aug 2023 | 27 Oct 2023 | In Person | N/A |
