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Algebra (MAST30005)
Undergraduate level 3Points: 12.5On Campus (Parkville)
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 1
Email: nganter@unimelb.edu.au
Overview
Availability | Semester 1 |
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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:
- prove results about rings, modules and fields;
- apply the Euclidean algorithm in a general context, including polynomials;
- calculate the Jordan Normal form of a matrix;
- describe the Galois correspondence for the splitting field of a polynomial.
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: 27 April 2024
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: 27 April 2024
Assessment
Additional details
Two or three written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).
Last updated: 27 April 2024
Dates & times
- Semester 1
Principal coordinator Nora Ganter 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 27 February 2017 to 28 May 2017 Last self-enrol date 10 March 2017 Census date 31 March 2017 Last date to withdraw without fail 5 May 2017 Assessment period ends 23 June 2017 Semester 1 contact information
Email: nganter@unimelb.edu.au
Time commitment details
Estimated total time commitment of 170 hours
Last updated: 27 April 2024
Further information
- Texts
Prescribed texts
Recommended texts and other resources
Michael Artin, Algebra, 2nd Edition, Pearson, 2010.
- Subject notes
This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.
- Related Handbook entries
This subject contributes to the following:
Type Name Informal specialisation Pure Mathematics Informal specialisation Pure Mathematics Informal specialisation Science-credited subjects - new generation B-SCI and B-ENG. Informal specialisation Selective subjects for B-BMED Informal specialisation Pure Mathematics Major Pure Mathematics - Breadth options
This subject is available as breadth in the following courses:
- 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: 27 April 2024