Linear Algebra: Advanced (MAST10022)

Undergraduate level 1Points: 12.5On Campus (Parkville)

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Overview

Availability
Semester 1
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This subject covers the same material as MAST10007 Linear Algebra, but to a greater depth including a greater emphasis on mathematical rigour and proof.

This subject gives a solid grounding in key areas of modern mathematics needed in science and technology. It develops the concept of a vector space, including linear transformations, matrices and the methods of linear algebra. There will be an emphasis on the axiomatic treatment of vector spaces, linear transformations, and inner product spaces.

Students will develop the ability to use the methods of linear algebra and gain an appreciation of mathematical proof including the ability to prove results about vector spaces.

Topics covered include: systems of linear equations; matrices and determinants; vectors in real n-space, cross product, lines and planes; general vector spaces; linear independence; bases and dimension; linear transformations; eigenvalues and eigenvectors; inner product spaces; symmetric and orthogonal matrices; diagonalisation of linear transformations and matrices.

Intended learning outcomes

Students completing this subject should:

 

  • be able to use matrix techniques to represent and solve a system of simultaneous linear equations
  • understand the use of vectors as a tool for describing lines and planes in solid geometry
  • understand the axiomatic definition of an abstract vector spaces of arbitrary dimension
  • understand linear transformations, their matrix representations and applications
  • be familiar with the use of a computer package for symbolic and numeric calculation
  • be able to construct a simple mathematical proof

Generic skills

  • 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
  • computer skills: the ability to use mathematical computing packages

Last updated: 14 February 2025

Eligibility and requirements

Prerequisites

Required subjects

A study score of at least 36 in VCE Specialist Mathematics 3/4, or equivalent

OR

Code Name Teaching period Credit Points
MAST10021 Calculus 2: Advanced No longer available

OR

Option 1

Code Name Teaching period Credit Points
MAST10005 Calculus 1 No longer available

with a mark of at least 80%

OR

Option 2

Code Name Teaching period Credit Points
MAST10006 Calculus 2 No longer available

with a mark of at least 75%

OR

Option 3

MAST10019: Calculus Extension studies

with a mark of at least 75%

Corequisites

None

Non-allowed subjects

Code Name Teaching period Credit Points
MAST10007 Linear Algebra No longer available
MAST10008 Accelerated Mathematics 1 No longer available
No longer available

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: 14 February 2025

Assessment

DescriptionTimingPercentage

Four to Six written assignments due at regular intervals during the semester (approximately 15 hours in total, 12%).

  • 15 pages
Throughout the semester12%

An on-line mid-semester test

  • 45 minutes
Mid semester8%

One 45-minute computer laboratory test held at the end of semester (10%).

  • 45 minutes (each)
End of semester10%

3-hour written examination in the examination period (70%).

  • 3 hours
During the examination period70%

Last updated: 14 February 2025

Dates & times

  • Semester 1
    CoordinatorLawrence Reeves
    Mode of deliveryOn Campus (Parkville)
    Contact hours3 x one hour lectures per week, 1 x one hour practice class per week, 1 x one hour computer laboratory class per week
    Total time commitment170 hours
    Teaching period26 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 ends21 June 2024

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: 14 February 2025

Further information

Last updated: 14 February 2025