58勛圖

MT1003 Pure and Applied 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

1pm (Mon, Tue, Thur, Fri)

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

Module Staff

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 aims to provide students with experience of both pure and applied mathematics, and the role that mathematical computing plays in both subjects. Exposure to new topics in this module will enable students to further develop their skills and experience in mathematics and give them insight into areas available for study in later years.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT1002

Assessment pattern

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

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

4 lectures (x 10 weeks), 1 computing laboratory (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

140

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 key concepts in pure mathematics (nature of proof, functions and relations, formal constructions of number systems, elementary number theory) and be able to solve problems in these areas
  • Demonstrate an understanding of key concepts in applied mathematics (continuous time mathematical models; discrete time mathematical models; some elementary numerical methods)
  • Understand introductory concepts for mathematical computing in Python (types, loops, lists and arrays, functions, writing programs) and apply these to problems in both pure and applied mathematics
  • Present mathematical ideas clearly and coherently, displaying logical and structured arguments when presenting solutions to problems

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

  • Proof and mathematical argument
  • Sets and functions
  • Relations and equivalence relations
  • Properties of rings and fields
  • Rational numbers, irrational numbers, real numbers
  • Fundamental theorem of algebra
  • Elementary number theory
  • Numerical methods for root finding
  • Polynomial interpolation and applications to numerical differentiation and numerical integration
  • Solution of first and second order linear difference equations
  • Applications of difference equations to population dynamics
  • First order non-linear difference equations, chaos, and the logistic map
  • Simple continuous mathematical models applied to mechanical problems with Newton’s laws of motion
  • Introduction to mathematical computing using Python (including programs and data types, order of operations, representation of floating points, lists and arrays, loops, decision making, functions, NumPy, debugging)