MT3501 Linear Mathematics 2

2024 to 2025 Semester 1

Curricular information may be subject to change

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 9

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

12.00 noon Mon (even weeks), Tue and Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr T D H Coleman

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Yoav Len

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

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-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2501

Assessment pattern

2-hour Written Examination = 90%, Coursework = 10%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks) and 1 tutorial (x 10 weeks).

Scheduled learning hours

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

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)