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Groups, Categories & Homological Algebra (MAST90068)
Graduate courseworkPoints: 12.5On Campus (Parkville)
For information about the University’s phased return to campus and in-person activity in Winter and Semester 2, please refer to the on-campus subjects page.
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 2
Please refer to the LMS for up-to-date subject information, including assessment and participation requirements, for subjects being offered in 2020.
Overview
Availability | Semester 2 |
---|---|
Fees | Look up fees |
As well as being beautiful in its own right, algebra is used in many areas of mathematics, computer science and physics. This subject provides a grounding in several fundamental areas of modern advanced algebra including Lie groups, combinatorial group theory, category theory and homological algebra.
The material complements that covered in the subject Commutative and Mutlilinear Algebra without assuming it as prerequisite.
Intended learning outcomes
On completion of this subject, students should have an understanding of:
- The geometry of Lie groups, and important examples coming from linear groups;
- Lie algebras, the exponential map, and the relation with Lie groups;
- Basic category theory: categories, functors, natural transformations, adjoints. (Co)products, universal objects, (co)limits, especially pushouts and pullbacks;
- Homological algebra: (pro/in)jective objects, resolutions, chain complexes, homotopy, the snake lemma. Applications: Ext, Tor, group homology;
- Free groups, presentations, free products (with amalgamation);
- Noncommutative algebra: semisimple rings, modules, Wedderburn theorem.
Be able to:
- prove results about Lie groups and algebras;
- give presentations of groups and algebras;
- construct and compute derived functors.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments
Last updated: 3 November 2022
Eligibility and requirements
Prerequisites
The following, or equivalent.
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST30005 | Algebra | Semester 1 (On Campus - Parkville) |
12.5 |
Corequisites
None
Non-allowed subjects
None
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 3 November 2022
Assessment
Due to the impact of COVID-19, assessment may differ from that published in the Handbook. Students are reminded to check the subject assessment requirements published in the subject outline on the LMS
Description | Timing | Percentage |
---|---|---|
Up to 40 pages of assignments (three assignments worth 10% each, due early, mid and late in semester)
| Throughout the teaching period | 30% |
A written examination
| During the examination period | 70% |
Last updated: 3 November 2022
Dates & times
- Semester 2
Coordinator Christian Haesemeyer Mode of delivery On Campus (Parkville) Contact hours 36 total, comprising 3 one-hour lectures per week Total time commitment 170 hours Teaching period 3 August 2020 to 1 November 2020 Last self-enrol date 14 August 2020 Census date 21 September 2020 Last date to withdraw without fail 16 October 2020 Assessment period ends 27 November 2020 Semester 2 contact information
Time commitment details
170 hours
Last updated: 3 November 2022
Further information
- Texts
Prescribed texts
None
Recommended texts and other resources
Representations of compact Lie groups,by Theodor Bröcker, Tammo tom Dieck, Springer Graduate Texts in Mathematics, 1985.
Representations and Cohomology, I and II, by David J. Benson, Cambridge University Press, 1998.
An introduction to homological algebra, by Charles Weibel, Cambridge University Press, 1995. - Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (Mathematics and Statistics) Course Doctor of Philosophy - Engineering Course Ph.D.- Engineering Course Master of Philosophy - Engineering Informal specialisation Mathematics and Statistics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Last updated: 3 November 2022