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Linear Algebra: Advanced (MAST10022)

Undergraduate level 1Points: 12.5On Campus (Parkville)

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Overview

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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: 19 September 2024