• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
Specialist
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• Dr Vigleik Angeltveit
• Mode of delivery In Person
• Co-taught Course
• Offered in Second Semester 2021
Algebraic Topology (MATH6204)

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

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.

## 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.

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.

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
2021 \$4110
International fee paying students
Year Fee
2021 \$5880
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

The list of offerings for future years is indicative only.
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
6251 26 Jul 2021 02 Aug 2021 31 Aug 2021 29 Oct 2021 In Person N/A