• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Course convener
• Dr Vigleik Angeltveit
• Mode of delivery In Person
• Co-taught Course
• Offered in Second Semester 2020
Algebraic Topology Honours (MATH4204)

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 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:

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.

5. Ability to conduct some (limited) independent research under expert supervision.

## Indicative Assessment

Assessment will be based on:

• Assignment 1 (20%: LO 1-5)
• Assignment 2 (20%; LO 1-5)
• Assignment 3 (20%; LO 1-5)
• Presentation (10%; LO 1-5)
• Take home exam (30%; 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.

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

To enrol in this course you must have successfully completed MATH2322 or MATH3104 and completion of one of MATH3345, MATH3320 or MATH3342. Incompatible with MATH6204.

## 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:
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

## Course fees

Domestic fee paying students
Year Fee
2020 \$4050
International fee paying students
Year Fee
2020 \$5760
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
8583 27 Jul 2020 03 Aug 2020 31 Aug 2020 30 Oct 2020 In Person View