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Group Theory and Linear Algebra (MAST20022)
Undergraduate level 2Points: 12.5Dual-Delivery (Parkville)
From 2023 most subjects will be taught on campus only with flexible options limited to a select number of postgraduate programs and individual subjects.
To learn more, visit COVID-19 course and subject delivery.
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 2
Overview
Availability | Semester 2 - Dual-Delivery |
---|---|
Fees | Look up fees |
This subject introduces the theory of groups, which is at the core of modern algebra, and which has applications in many parts of mathematics, chemistry, computer science and theoretical physics. It also develops the theory of linear algebra, building on material in earlier subjects and providing both a basis for later mathematics studies and an introduction to topics that have important applications in science and technology.
Topics include: modular arithmetic and RSA cryptography; abstract groups, homomorphisms, normal subgroups, quotient groups, group actions, symmetry groups, permutation groups and matrix groups; theory of general vector spaces, inner products, linear transformations, spectral theorem for normal matrices, Jordan normal form.
Intended learning outcomes
On completion of this subject, students should:
Understand the concepts of:
- abstract groups, homomorphisms and quotient groups;
- abstract vector spaces, inner product spaces and linear transformations;
Be able to:
- do calculations in modular arithmetic and apply these to RSA cryptography;
- find eigenvalues, eigenvectors, minimal polynomials and normal forms for linear transformations;
- analyse groups of permutations, symmetries, and matrices;
- prove simple results in group theory and linear algebra.
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: 22 March 2024
Eligibility and requirements
Prerequisites
One of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10008 | Accelerated Mathematics 1 | Semester 1 (Dual-Delivery - Parkville) |
12.5 |
MAST10007 | Linear Algebra |
Summer Term (Dual-Delivery - Parkville)
Semester 2 (Dual-Delivery - Parkville)
Semester 1 (Dual-Delivery - Parkville)
|
12.5 |
MAST10022 | Linear Algebra: Advanced | Semester 1 (Dual-Delivery - Parkville) |
12.5 |
MAST10013 UMEP Maths for High Achieving Students
MAST10018 Linear Algebra Extension Studies
AND
One of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10009 | Accelerated Mathematics 2 | Semester 2 (Dual-Delivery - Parkville) |
12.5 |
MAST20026 | Real Analysis |
Semester 2 (Dual-Delivery - Parkville)
Semester 1 (Dual-Delivery - Parkville)
|
12.5 |
MAST20033 | Real Analysis: Advanced | Semester 1 (Dual-Delivery - 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: 22 March 2024
Assessment
Description | Timing | Percentage |
---|---|---|
Three written assignments due at regular intervals amounting to a total of up to 50 pages
| Throughout the semester | 20% |
A written examination
| During the examination period | 80% |
Additional details
This Dual-Delivery subject has On Campus assessment components.
Last updated: 22 March 2024
Dates & times
- Semester 2
Coordinator Paul Zinn-Justin Mode of delivery Dual-Delivery (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 25 July 2022 to 23 October 2022 Last self-enrol date 5 August 2022 Census date 31 August 2022 Last date to withdraw without fail 23 September 2022 Assessment period ends 18 November 2022 Semester 2 contact information
Time commitment details
Estimated total time commitment of 170 hours
Additional delivery details
This Dual-Delivery subject has On Campus assessment components.
Last updated: 22 March 2024
Further information
- Texts
Prescribed texts
Lecture Notes for Group Theory and Linear Algebra, Department of Mathematics and Statistics.
- 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 Science Discipline subjects - new generation B-SCI Informal specialisation Pure Mathematics Major Pure Mathematics Breadth Track Accelerated 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.
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
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 22 March 2024