Group Theory and Linear Algebra (MAST20022)

Undergraduate level 2Points: 12.5On Campus (Parkville)

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Overview

Availability
Semester 2
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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: 9 April 2025

Eligibility and requirements

Prerequisites

One of

Code Name Teaching period Credit Points
MAST10008 Accelerated Mathematics 1
Semester 1 (On Campus - Parkville)
 12.5
MAST10007 Linear Algebra
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
Summer Term (Dual-Delivery - Parkville)
 12.5
MAST10022 Linear Algebra: Advanced
Semester 1 (On Campus - 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 (On Campus - Parkville)
 12.5
MAST20026 Real Analysis
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
 12.5
MAST20033 Real Analysis: Advanced
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: 9 April 2025

Assessment

DescriptionTimingPercentage

Three written assignments due at regular intervals amounting to a total of up to 50 pages

  • 50 pages
Throughout the semester20%

A written examination

  • 3 hours
During the examination period80%

Additional details

This Dual-Delivery subject has On Campus assessment components.

Last updated: 9 April 2025

Dates & times

  • Semester 2
    CoordinatorPaul Zinn-Justin
    Mode of deliveryOn Campus (Parkville)
    Contact hours3 x one hour lectures per week, 1 x one hour practice class per week
    Total time commitment170 hours
    Teaching period24 July 2023 to 22 October 2023
    Last self-enrol date 4 August 2023
    Census date31 August 2023
    Last date to withdraw without fail22 September 2023
    Assessment period ends17 November 2023

    Semester 2 contact information

    p.zinn@unimelb.edu.au

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.

Additional delivery details

This Dual-Delivery subject has On Campus assessment components.

Last updated: 9 April 2025

Further information

Last updated: 9 April 2025