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MT2501 Linear Mathematics

Academic year

2025 to 2026 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

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 8

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 (weeks 1, 3, 5, 8, 10), Wed and Fri [Semester 1]; 11.00 am Mon (weeks 2, 4, 6, 8, 11), Tue and Thu [Semester 2]

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

Module coordinator

Prof J D Mitchell

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

Module Staff

S1: Prof James Mitchell; Dr Finn Smith S2: Dr Alex Russell

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 extends the knowledge and skills that students have gained concerning matrices and systems of linear equations. It introduces the basic theory of vector spaces, linear independence, linear transformations and diagonalization. These concepts are used throughout the mathematical sciences and physics. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT1002,IF MT1002 HAS NOT BEEN PASSED THEN A AT ADVANCED HIGHER MATHEMATICS, OR A AT A-LEVEL FURTHER MATHEMATICS, OR A AT BOTH A-LEVEL MATHEMATICS AND A-LEVEL PHYSICS.

Assessment pattern

2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5-hours lectures (x 10 weeks), 1 tutorial (x 5 weeks), 1 examples class (x 5 weeks)

Scheduled learning hours

35

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

  • Demonstrate an understanding of basic mathematical concepts in each of the module core topics (systems of linear equations, matrix theory, vector spaces, linear transformations, eigen-theory, and diagonalisation)
  • Demonstrate an understanding of basic skills and techniques in dealing with concrete examples in each of the above core topics
  • Demonstrate an ability to provide theoretical explanations for general facts about each of the core topics
  • Apply all of the above competencies to solve a wide range of familiar and unfamiliar problems in the core topics

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics please consult the School Handbook, at /mathematics-statistics/students/ug/module-choices-2000/

MT2501 Linear Mathematics

Academic year

2025 to 2026 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

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 8

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 (weeks 1, 3, 5, 8, 10), Wed and Fri [Semester 1]; 11.00 am Mon (weeks 2, 4, 6, 8, 11), Tue and Thu [Semester 2]

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

Module coordinator

Dr A J B Russell

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

Module Staff

S1: Prof James Mitchell; Dr Finn Smith S2: Dr Alex Russell

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 extends the knowledge and skills that students have gained concerning matrices and systems of linear equations. It introduces the basic theory of vector spaces, linear independence, linear transformations and diagonalization. These concepts are used throughout the mathematical sciences and physics. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT1002,IF MT1002 HAS NOT BEEN PASSED THEN A AT ADVANCED HIGHER MATHEMATICS, OR A AT A-LEVEL FURTHER MATHEMATICS, OR A AT BOTH A-LEVEL MATHEMATICS AND A-LEVEL PHYSICS.

Assessment pattern

2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5-hours lectures (x 10 weeks), 1 tutorial (x 5 weeks), 1 examples class (x 5 weeks)

Scheduled learning hours

35

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

  • Demonstrate an understanding of basic mathematical concepts in each of the module core topics (systems of linear equations, matrix theory, vector spaces, linear transformations, eigen-theory, and diagonalisation)
  • Demonstrate an understanding of basic skills and techniques in dealing with concrete examples in each of the above core topics
  • Demonstrate an ability to provide theoretical explanations for general facts about each of the core topics
  • Apply all of the above competencies to solve a wide range of familiar and unfamiliar problems in the core topics

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics please consult the School Handbook, at /mathematics-statistics/students/ug/module-choices-2000/

MT2501 Linear Mathematics

Academic year

2026 to 2027 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

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 8

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 (weeks 1, 3, 5, 8, 10), Wed and Fri [Semester 1]; 11.00 am Mon (weeks 2, 4, 6, 8, 11), Tue and Thu [Semester 2]

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

Module Staff

S1: TBD S2: TBD

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 extends the knowledge and skills that students have gained concerning matrices and systems of linear equations. It introduces the basic theory of vector spaces, linear independence, linear transformations and diagonalization. These concepts are used throughout the mathematical sciences and physics. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT1002,IF MT1002 HAS NOT BEEN PASSED THEN A AT ADVANCED HIGHER MATHEMATICS, OR A AT A-LEVEL FURTHER MATHEMATICS, OR A AT BOTH A-LEVEL MATHEMATICS AND A-LEVEL PHYSICS.

Assessment pattern

2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5-hours lectures (x 10 weeks), 1 tutorial (x 5 weeks), 1 examples class (x 5 weeks)

Scheduled learning hours

35

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

  • Demonstrate an understanding of basic mathematical concepts in each of the module core topics (systems of linear equations, matrix theory, vector spaces, linear transformations, eigen-theory, and diagonalisation)
  • Demonstrate an understanding of basic skills and techniques in dealing with concrete examples in each of the above core topics
  • Demonstrate an ability to provide theoretical explanations for general facts about each of the core topics
  • Apply all of the above competencies to solve a wide range of familiar and unfamiliar problems in the core topics

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics see our Module choices at 1000 and 2000 level page.

Syllabus

  • Matrices and determinants: basic revision of matrices & relevant fields (especially complex numbers); revision of e.r.o.’s; system of linear equations; determinants and their basic properties; matrix inverses; solutions of systems of linear equations.
  • Vector spaces: Definition of vector spaces; examples of vector spaces (with emphasis on geometrical intuition); basic properties of vector spaces; subspaces.
  • Linear independence and bases: spanning sets; linear independence, bases, dimension.
  • Linear transformations: definition of linear transformation and examples (including trace), the matrix of a linear transformation; rank and nullity (including proof of Rank-Nullity Theorem); the rank of a matrix and reduced echelon form; rank and the matrix of a linear transformation.
  • Eigenvalues, eigenvectors and diagonalization: eigenvalues and eigenvectors; change of basis; powers of matrices, symmetric matrices and quadratic forms.

MT2501 Linear Mathematics

Academic year

2026 to 2027 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

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 8

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 (weeks 1, 3, 5, 8, 10), Wed and Fri [Semester 1]; 11.00 am Mon (weeks 2, 4, 6, 8, 11), Tue and Thu [Semester 2]

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

Module coordinator

Dr A J B Russell

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

Module Staff

S1: TBD S2: TBD

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 extends the knowledge and skills that students have gained concerning matrices and systems of linear equations. It introduces the basic theory of vector spaces, linear independence, linear transformations and diagonalization. These concepts are used throughout the mathematical sciences and physics. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT1002,IF MT1002 HAS NOT BEEN PASSED THEN A AT ADVANCED HIGHER MATHEMATICS, OR A AT A-LEVEL FURTHER MATHEMATICS, OR A AT BOTH A-LEVEL MATHEMATICS AND A-LEVEL PHYSICS.

Assessment pattern

2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5-hours lectures (x 10 weeks), 1 tutorial (x 5 weeks), 1 examples class (x 5 weeks)

Scheduled learning hours

35

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

  • Demonstrate an understanding of basic mathematical concepts in each of the module core topics (systems of linear equations, matrix theory, vector spaces, linear transformations, eigen-theory, and diagonalisation)
  • Demonstrate an understanding of basic skills and techniques in dealing with concrete examples in each of the above core topics
  • Demonstrate an ability to provide theoretical explanations for general facts about each of the core topics
  • Apply all of the above competencies to solve a wide range of familiar and unfamiliar problems in the core topics

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics see our Module choices at 1000 and 2000 level page.

Syllabus

  • Matrices and determinants: basic revision of matrices & relevant fields (especially complex numbers); revision of e.r.o.’s; system of linear equations; determinants and their basic properties; matrix inverses; solutions of systems of linear equations.
  • Vector spaces: Definition of vector spaces; examples of vector spaces (with emphasis on geometrical intuition); basic properties of vector spaces; subspaces.
  • Linear independence and bases: spanning sets; linear independence, bases, dimension.
  • Linear transformations: definition of linear transformation and examples (including trace), the matrix of a linear transformation; rank and nullity (including proof of Rank-Nullity Theorem); the rank of a matrix and reduced echelon form; rank and the matrix of a linear transformation.
  • Eigenvalues, eigenvectors and diagonalization: eigenvalues and eigenvectors; change of basis; powers of matrices, symmetric matrices and quadratic forms.