Algebra (MAST30005)
Undergraduate level 3Points: 12.5On Campus (Parkville)
Overview
| Availability | Semester 1 |
|---|---|
| Fees | Look up fees |
Algebra has a long history of important applications throughout mathematics, science and engineering, and is also studied for its intrinsic beauty. In this subject we study the algebraic laws satisfied by familiar objects such as integers, polynomials and matrices. This abstraction simplifies and unifies our understanding of these structures and enables us to apply our results to interesting new cases. Students will gain further experience with abstract algebraic concepts and methods. General structural results are proved and algorithms developed to determine the invariants they describe.
Intended learning outcomes
On completion of this subject, students should
Have an understanding of:
- rings, factorization in rings, principal ideal domains, Euclidean domains;
- modules, free modules, structure theorem for finitely generated modules over a principal ideal domain;
- fields, field extensions, finite fields, Galois extensions; splitting fields and the Galois correspondence.
Be able to:
- apply the Euclidean algorithm in a general context, including polynomials;
- prove results about rings, modules and fields;
- describe the Galois correspondence for the splitting field of a polynomial.
- calculate the Jordan Normal form of a matrix;
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: 9 April 2025
Eligibility and requirements
Prerequisites
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20022 | Group Theory and Linear Algebra | Semester 2 (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: 9 April 2025
Assessment
| Description | Timing | Percentage |
|---|---|---|
Two or three written assignments due at regular intervals amounting to a total of up to 50 pages
| During the teaching period | 20% |
A written examination
| During the examination period | 80% |
Last updated: 9 April 2025
Dates & times
- Semester 1
Coordinator Arun Ram Mode of delivery On Campus (Parkville) Contact hours 3 x one hour lectures per week, 1 x one hour practice class per week Total time commitment 170 hours Teaching period 26 February 2024 to 26 May 2024 Last self-enrol date 8 March 2024 Census date 3 April 2024 Last date to withdraw without fail 3 May 2024 Assessment period ends 21 June 2024 Semester 1 contact information
Time commitment details
Estimated total time commitment of 170 hours
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 9 April 2025
Further information
- Texts
- Subject notes
- Related Handbook entries
This subject contributes to the following:
Type Name Major Pure Mathematics Informal specialisation Pure Mathematics Informal specialisation Pure Mathematics specialisation Informal specialisation Science Discipline subjects - new generation B-SCI Informal specialisation Pure Mathematics - Breadth options
This subject is available as breadth in the following courses:
- Bachelor of Arts
- Bachelor of Commerce
- Bachelor of Design
- Bachelor of Environments
- Bachelor of Fine Arts (Acting)
- Bachelor of Fine Arts (Animation)
- Bachelor of Fine Arts (Dance)
- Bachelor of Fine Arts (Film and Television)
- Bachelor of Fine Arts (Music Theatre)
- Bachelor of Fine Arts (Production)
- Bachelor of Fine Arts (Screenwriting)
- Bachelor of Fine Arts (Theatre)
- Bachelor of Fine Arts (Visual Art)
- Bachelor of Music
- 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: 9 April 2025