Commutative and Multilinear Algebra (MAST90025)
Graduate courseworkPoints: 12.5Not available in 2020
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
Please refer to the LMS for up-to-date subject information, including assessment and participation requirements, for subjects being offered in 2020.
Overview
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The subject covers aspects of multilinear and commutative algebra as well as two substantial applications. Within multilinear algebra this includes bilinear forms and `multilinear products’ of vector spaces, such as tensor products. Commutative algebra concerns itself with properties of commutative rings, such as polynomial rings and their quotients and to modules over such rings. Both topics have wide application, both to other parts of mathematics and to physics. Much of this theory was developed for applications in geometry and in number theory, and the theorems can be used to cast substantial light on problems from geometry and number theory.
Intended learning outcomes
After completing this subject, students should gain:
- a deeper understanding of the theory of rings, modules and multilinear algebra;
- an understanding of the basic concepts of Commutative Algebra such as localisation, Noetherian, associated primes and integral extensions;
- an understanding of the basic concepts of Multilinear Algebra such as bilinear forms and tensor, symmetric and exterior powers of algebras;
- an understanding of how these basic concepts apply in areas of mathematics other than algebra;
- the ability to pursue further studies in this and related areas.
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: 12 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: 12 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 60 pages of written assignments (three assignments worth 25% each, due early, mid and late in semester)
| During the teaching period | 75% |
A written examination
| During the examination period | 25% |
Last updated: 12 November 2022
Dates & times
Not available in 2020
Time commitment details
170 hours
Last updated: 12 November 2022
Further information
- Texts
- Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Science (Mathematics and Statistics) Course Ph.D.- Engineering Course Doctor of Philosophy - 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.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
Last updated: 12 November 2022