• Offered by Mathematical Sciences Institute
  • ANU College ANU Joint Colleges of Science
  • Classification Advanced
    Specialist
  • Course subject Mathematics
  • Areas of interest Mathematics
  • Academic career Postgraduate
  • Course convener
    • Dr Vigleik Angeltveit
  • Mode of delivery In Person
  • Co-taught Course MATH4204
  • Offered in Second Semester 2018
    See Future Offerings

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.

Learning Outcomes

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.

Indicative Assessment

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)

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

Three lectures per week and regular workshops.

Requisite and Incompatibility

Incompatible with MATH4204

You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.

Fees

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:
Band 2
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.

Units EFTSL
6.00 0.12500
Domestic fee paying students
Year Fee
2018 $3660
International fee paying students
Year Fee
2018 $5160
Note: Please note that fee information is for current year only.

Offerings and Dates

The list of offerings for future years is indicative only

Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery
7653 23 Jul 2018 30 Jul 2018 31 Aug 2018 26 Oct 2018 In Person

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