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MT1002 Mathematics

Academic year

2025 to 2026 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

20

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 7

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

9.00 am

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

Module coordinator

Prof T Neukirch

Prof T Neukirch
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 Thomas Neukirch; Dr Stefania Lisai; Prof Kenneth Falconer; Dr Finn Smith S2: Prof Lars Olsen; Dr Aidan Naughton; Dr Andrew Wright; Dr Stephen Cantrell

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 is designed to introduce students to the ideas, methods and techniques which they will need for applying mathematics in the physical sciences or for taking the study of mathematics further. It aims to extend and enhance their skills in algebraic manipulation and in differential and integral calculus, to develop their geometric insight and their understanding of limiting processes, and to introduce them to complex numbers and matrices.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT1001. IF MT1001 HAS NOT BEEN PASSED, YOU MUST HAVE AT LEAST GRADE B IN ADVANCED HIGHER MATHEMATICS OR GRADE B IN A-LEVEL MATHEMATICS OR AN EQUIVALENT MATHEMATICS QUALIFICATION.

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

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

Scheduled learning hours

60

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

Guided independent study hours

145

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 concepts in each of the module core topics (complex numbers, matrices, limits, differential equations, integration, hyperbolic functions, vectors, series, proof)
  • Demonstrate an understanding of basic skills and techniques in dealing with concrete examples in each of the core topics
  • Apply these skills and techniques to solve a wide range of familiar and unfamiliar problems in the core topics
  • Demonstrate an understanding of how to communicate mathematical ideas clearly and coherently

MT1002 Mathematics

Academic year

2025 to 2026 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

20

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 7

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

9.00 am

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

Module coordinator

Prof L O R Olsen

Prof L O R Olsen
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 Thomas Neukirch; Dr Stefania Lisai; Prof Kenneth Falconer; Dr Finn Smith S2: Prof Lars Olsen; Dr Aidan Naughton; Dr Andrew Wright; Dr Stephen Cantrell

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 is designed to introduce students to the ideas, methods and techniques which they will need for applying mathematics in the physical sciences or for taking the study of mathematics further. It aims to extend and enhance their skills in algebraic manipulation and in differential and integral calculus, to develop their geometric insight and their understanding of limiting processes, and to introduce them to complex numbers and matrices.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT1001. IF MT1001 HAS NOT BEEN PASSED, YOU MUST HAVE AT LEAST GRADE B IN ADVANCED HIGHER MATHEMATICS OR GRADE B IN A-LEVEL MATHEMATICS OR AN EQUIVALENT MATHEMATICS QUALIFICATION.

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

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

Scheduled learning hours

66

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

Guided independent study hours

134

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 concepts in each of the module core topics (complex numbers, matrices, limits, differential equations, integration, hyperbolic functions, vectors, series, proof)
  • Demonstrate an understanding of basic skills and techniques in dealing with concrete examples in each of the core topics
  • Apply these skills and techniques to solve a wide range of familiar and unfamiliar problems in the core topics
  • Demonstrate an understanding of how to communicate mathematical ideas clearly and coherently

MT1002 Mathematics

Academic year

2026 to 2027 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

20

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 7

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

9.00 am

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 is designed to introduce students to the ideas, methods and techniques which they will need for applying mathematics in the physical sciences or for taking the study of mathematics further. It aims to extend and enhance their skills in algebraic manipulation and in differential and integral calculus, to develop their geometric insight and their understanding of limiting processes, and to introduce them to complex numbers and matrices.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT1001. IF MT1001 HAS NOT BEEN PASSED, YOU MUST HAVE AT LEAST GRADE B IN ADVANCED HIGHER MATHEMATICS OR GRADE B IN A-LEVEL MATHEMATICS OR AN EQUIVALENT MATHEMATICS QUALIFICATION.

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

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

Scheduled learning hours

60

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

Guided independent study hours

145

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 concepts in each of the module core topics (complex numbers, matrices, limits, differential equations, integration, hyperbolic functions, vectors, series, proof)
  • Demonstrate an understanding of basic skills and techniques in dealing with concrete examples in each of the core topics
  • Apply these skills and techniques to solve a wide range of familiar and unfamiliar problems in the core topics
  • Demonstrate an understanding of how to communicate mathematical ideas clearly and coherently

Additional information from school

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

Syllabus

  • Complex Numbers: their arithmetic, equations involving complex numbers, Argand diagram, modulus-argument form, de Moivre’s theorem, powers and roots, geometric applications
  • Proof: logical argument and need for precision in mathematics, selected proof techniques (by deduction, by contradiction, contrapositive, by exhaustion, by induction)
  • Limits of functions, L’Hôpital’s rule, limit of a sequence
  • Hyperbolic functions and their inverses, derivatives and integrals
  • Integration: definition, by substitution, with partial fractions, by parts, involving trigonometric and hyperbolic functions and their inverses
  • Series: telescoping series, harmonic series, nth term test, ratio test, power series and radius of convergence, Maclaurin series
  • Matrices, determinants and linear equations: basic matrix operations, algebraic properties, special matrices, geometric applications, matrix inverses, matrix determinants
  • Vectors: vector operations including scalar and vector product, triple products, geometric applications including equations of lines and planes.

MT1002 Mathematics

Academic year

2026 to 2027 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

20

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 7

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

9.00 am

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

Module coordinator

Prof L O R Olsen

Prof L O R Olsen
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 is designed to introduce students to the ideas, methods and techniques which they will need for applying mathematics in the physical sciences or for taking the study of mathematics further. It aims to extend and enhance their skills in algebraic manipulation and in differential and integral calculus, to develop their geometric insight and their understanding of limiting processes, and to introduce them to complex numbers and matrices.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT1001. IF MT1001 HAS NOT BEEN PASSED, YOU MUST HAVE AT LEAST GRADE B IN ADVANCED HIGHER MATHEMATICS OR GRADE B IN A-LEVEL MATHEMATICS OR AN EQUIVALENT MATHEMATICS QUALIFICATION.

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

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

Scheduled learning hours

66

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

Guided independent study hours

134

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 concepts in each of the module core topics (complex numbers, matrices, limits, differential equations, integration, hyperbolic functions, vectors, series, proof)
  • Demonstrate an understanding of basic skills and techniques in dealing with concrete examples in each of the core topics
  • Apply these skills and techniques to solve a wide range of familiar and unfamiliar problems in the core topics
  • Demonstrate an understanding of how to communicate mathematical ideas clearly and coherently

Additional information from school

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

Syllabus

  • Complex Numbers: their arithmetic, equations involving complex numbers, Argand diagram, modulus-argument form, de Moivre’s theorem, powers and roots, geometric applications
  • Proof: logical argument and need for precision in mathematics, selected proof techniques (by deduction, by contradiction, contrapositive, by exhaustion, by induction)
  • Limits of functions, L’Hôpital’s rule, limit of a sequence
  • Hyperbolic functions and their inverses, derivatives and integrals
  • Integration: definition, by substitution, with partial fractions, by parts, involving trigonometric and hyperbolic functions and their inverses
  • Series: telescoping series, harmonic series, nth term test, ratio test, power series and radius of convergence, Maclaurin series
  • Matrices, determinants and linear equations: basic matrix operations, algebraic properties, special matrices, geometric applications, matrix inverses, matrix determinants
  • Vectors: vector operations including scalar and vector product, triple products, geometric applications including equations of lines and planes.