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MT3501   Linear Mathematics 2

Academic year(s): 2024-2025

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 9

Semester: 1

Planned timetable: 12.00 noon Mon (even weeks), Tue and Thu

This module continues the study of vector spaces and linear transformations begun in MT2501. It aims to show the importance of linearity in many areas of mathematics ranging from linear algebra through to geometric applications to linear operators and special functions. The main topics covered include: diagonalisation and the minimum polynomial; Jordan normal form; inner product spaces; orthonormal sets and the Gram-Schmidt process.

Relationship to other modules

Pre-requisite(s): Before taking this module you must pass MT2501

Learning and teaching methods and delivery

Weekly contact: 2.5 lectures (x 10 weeks) and 1 tutorial (x 10 weeks).

Scheduled learning hours: 35

Guided independent study hours: 115

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 90%, Coursework = 10%

As defined by QAA
Written examinations : 90%
Practical examinations : 0%
Coursework: 10%

Re-assessment: Oral examination = 100%

Personnel

Module coordinator: Dr T D H Coleman
Module teaching staff: Dr Yoav Len
Module coordinator email tdhc@st-andrews.ac.uk

Intended learning outcomes

  • Develop a deeper understanding of vector spaces and linear transformations begun in MT2501
  • Appreciate the mathematical underpinnings of linear mathematics and their application to solving problems in pure mathematics, applied mathematics, theoretical physics, and statistics
  • Understand and be able to apply various computational methods, such as those to find: the matrix of transformation; eigenvalues and eigenvectors; determinants; diagonal, upper triangular, Jordan normal matrices; dual transformation, basis, and spaces; quotient spaces, and quotient linear transformations.
  • Show a geometric understanding of linear mathematics, and the way this motivated the development of linear mathematics (for example, why matrix multiplication is defined the way it is, the meaning of the determinant, and so on)