- Code MATH6204
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
All activities that form part of this course will be delivered remotely in Sem 2 2020.
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
- Fundamental theorem of algebra
- Homology theory and cohomology theory
- Jordan-Brouwer separation theorem
- Lefschetz fixed theorem
- Additional topics (Orientation, Poincare duality, if time permits)
Note: Graduate students attend joint classes with undergraduates but will be assessed separately.
Upon successful completion, students will have the knowledge and skills to:
On satisfying the requirements of this course, students will have the knowledge and skills to:
1. Explain the fundamental concepts of algebraic topology and their role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of algebraic topology techniques.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from algebraic topology.
4. Apply problem-solving using algebraic topology techniques applied to diverse situations in physics, engineering and other mathematical contexts.
Assessment will be based on:
- Assignment 1 (10%: LO 1-4)
- Assignment 2 (10%; LO 1-4)
- Assignment 3 (10%; LO 1-4)
- Presentation (10%; LO 1-4)
- Final exam (60%; LO 1-4)
In response to COVID-19: Please note that Semester 2 Class Summary information (available under the classes tab) is as up to date as possible. Changes to Class Summaries not captured by this publication will be available to enrolled students via Wattle.
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WorkloadThree lectures per week and regular workshops.
Requisite and Incompatibility
You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.
Tuition fees are for the academic year indicated at the top of the page.
If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
- Student Contribution Band:
- Unit value:
- 6 units
If you are an undergraduate student and 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). You can find your student contribution amount for each course at Fees. Where there is a unit range displayed for this course, not all unit options below may be available.
Offerings, Dates and Class Summary Links
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Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.