Introduction

Mathematics is vital to the physical and engineering sciences, and very significant in the economic, social and biological sciences. It is the essential tool with which scientists formulate theories and analyse their consequences.

This programme is studied on campus.

Our well-thought-of programme consists of two main threads which progress throughout the four years of study; Analysis and Algebra. In addition, in the first two years we teach several courses on foundations. In the final two years we broaden our offer to other areas of Mathematics such as Topology and Geometry.

Mathematics is a powerful universal language used to describe situations in abstract terms. At the heart of manipulation with abstract mathematical objects are precision, logical thinking and reasoning skills. Studying and doing mathematics requires a high level of communication skills. Employers highly value these skills and the subsequent versatility of our graduates.

Both the MA and BSc Mathematics degrees study the same core courses. The difference comes in the choices that students can make through their optional courses.

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Key Programme Information

At a Glance

Learning Mode
On Campus Learning
Degree Qualification
MA
Duration
48 months
Study Mode
Full Time
Start Month
September
UCAS Code
G102

What You'll Study

Year 1

Year 1

Compulsory Courses

Calculus i (MA1005) - 15 Credit Points

Calculus is the mathematical study of change, and is used in many areas of mathematics, science, and the commercial world. This course covers differentiation, limits, finding maximum and minimum values, and continuity. There may well be some overlap with school mathematics, but the course is brisk and will go a long way quickly.

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Algebra (MA1006) - 15 Credit Points

This course introduces the concepts of complex numbers, matrices and other basic notions of linear algebra over the real and complex numbers. This provides the necessary mathematical background for further study in mathematics, physics, computing science, chemistry and engineering.

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Calculus II (MA1508) - 15 Credit Points

The aim of the course is to provide an introduction to Integral Calculus and the theory of sequences and series, to discuss their applications to the theory of functions, and to give an introduction to the theory of functions of several variables.

This provides the necessary mathematical background for further study in mathematics, physics, computing science, chemistry and engineering.

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Set Theory (MA1511) - 15 Credit Points

Set theory was introduced by Cantor in 1872, who was attempting to understand the concept of "infinity" which defied the mathematical world since the Greeks. Set Theory is fundamental to modern mathematics - any mathematical theory must be formulated within the framework of set theory, or else it is deemed invalid. It is the alphabet of mathematics.

In this course we will study naive set theory. Fundamental object such as the natural numbers and the real numbers will be constructed. Structures such as partial orders and functions will be studied. And of course, we will explore infinite sets.

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Professional Skills Part 1 (PD1001)

This course, which is prescribed for level 1 students and optional for level 2 students, is studied entirely online and covers topics relating to careers and employability, equality and diversity and health, safety and wellbeing. During the course you will learn about the Aberdeen Graduate Attributes, how they are relevant to you and the opportunities available to develop your skills and attributes alongside your University studies. You will also gain an understanding of equality and diversity and health, safety and wellbeing issues. Successful completion of this course will be recorded on your Enhanced Transcript as ‘Achieved’ (non-completion will be recorded as ‘Not Achieved’). The course takes approximately 3 hours to complete and can be taken in one sitting, or spread across a number of weeks and it will be available to you throughout the academic year.This course, which is prescribed for level 1 students and optional for level 2 students and above, is studied entirely online and covers topics relating to careers and employability, equality and diversity and health, safety and wellbeing. During the course you will learn about the Aberdeen Graduate Attributes, how they are relevant to you and the opportunities available to develop your skills and attributes alongside your University studies. You will also gain an understanding of equality and diversity and health, safety and wellbeing issues. Successful completion of this course will be recorded on your Enhanced Transcript as ‘Achieved’ (non-completion will be recorded as ‘Not Achieved’). The course takes approximately 3 hours to complete and can be taken in one sitting, or spread across a number of weeks and it will be available to you throughout the academic year

View detailed information about this course

Optional Courses

  • Select a further 60 credit points from courses of choice
Year 2

Year 2

Compulsory Courses

Linear Algebra i (MA2008) - 15 Credit Points

Linear algebra is the study of vector spaces and linear maps between them and it is a central subject within mathematics.

It provides foundations for almost all branches of mathematics and sciences in general. The techniques are used in engineering, physics, computer science, economics and others. For example, special relativity and quantum mechanics are formulated within the framework of linear algebra.

The two courses Linear Algebra I and II aim at providing a solid foundation of the subject.

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Analysis i (MA2009) - 15 Credit Points

Analysis provides the rigourous, foundational underpinnings of calculus. It is centred around the notion of limits: convergence within the real numbers. Related ideas, such as infinite sums (a.k.a. series), continuity, and differentiation, are also visited in this course. Care is needed to properly use the delicate formal concept of limits. At the same time, limits are often intuitive, and we aim to reconcile this intuition with correct mathematical reasoning. The emphasis throughout this course is on rigourous mathematical proofs, valid reasoning, and the avoidance of fallacious arguments.

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Linear Algebra II (MA2508) - 15 Credit Points

Linear algebra is the study of vector spaces and linear maps between them and it is a central subject within mathematics.

It provides foundations for almost all branches of mathematics and sciences in general. The techniques are used in engineering, physics, computer science, economics and others. For example, special relativity and quantum mechanics are formulated within the framework of linear algebra.

The two courses Linear Algebra I and II aim at providing a solid foundation of the subject.

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Analysis II (MA2509) - 15 Credit Points

Analysis provides the rigourous, foundational underpinnings of calculus. This course builds on the foundations in Analysis I, and explores the notions of Riemann integrability, Cauchy sequences, sequences of functions, and power series. The techniques of careful rigourous argument seen in Analysis I will be further developed. Such techniques will be applied to solve problems that would otherwise be inaccessible. As in Analysis I, the emphasis of this course is on valid mathematical proofs and correct reasoning.

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Optional Courses

  • Select a further 60 credit points from courses of choice
Year 3

Year 3

Compulsory Courses

Group Theory (MX3020) - 15 Credit Points

Group theory concerns the study of symmetry. The course begins with the group axioms, which provide an abstract setting for the study of symmetry. We proceed to study subgroups, normal subgroups, and group actions in various guises. Group homomorphisms are introduced and the related isomorphism theorems are proved. Composition series are introduced and the Jordan-Holder theorem is proved. Sylow p-subgroups are introduced and the three Sylow theorems are proved. Throughout symmetric groups are consulted as a source of examples.

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Metric and Topological Spaces (MX3036) - 15 Credit Points

The aim of the course is to introduce the basic concepts of metric spaces and their associated topology, and to apply the ideas to Euclidean space and other examples.

An excellent introduction to "serious mathematics" based on the usual geometry of the n dimensional spaces.

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Rings and Fields (MX3531) - 15 Credit Points

Many examples of rings will be familiar before entering this course. Examples include the integers modulo n, the complex numbers and n-by-n matrices with real entries. The course develops from the fundamental definition of ring to study particular classes of rings and how they relate to each other. We also encounter generalisations of familiar concepts, such as what is means for a polynomial to be prime.

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Analysis Iii (MX3035) - 15 Credit Points

Analysis provides the rigourous, foundational underpinnings of calculus. The focus of this course is multivariable analysis, building on the single-variable theory from MA2009 Analysis I and MA2509 Analysis II. Concepts and results around multivariable differentiation are comprehensively established, laying the ground for multivariable integration in MX3535 Analysis IV. As in Analysis I and II, abstract reasoning and proof-authoring are key skills emphasised in this course.

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Analysis Iv (MX3535) - 15 Credit Points

Analysis provides the rigourous, foundational underpinnings of calculus. This course builds on MX3035 Analysis III, continuing the development of multivariable calculus, with a focus on multivariable integration. Hilbert spaces (infinite dimensional Euclidean spaces) are also introduced. Students will see the benefit of having acquired the formal reasoning skills developed in Analysis I, II, and III, as it enables them to work with increasingly abstract concepts and deep results. Techniques of rigourous argumentation continue to be a prominent part of the course.

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Differential Equations (MX3536) - 15 Credit Points

Differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. In this course we will study the concept of a differentialk equation systematically from a purely mathematical viewpoint. Such abstraction is fundamental to the understanding of this concept.

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Optional Courses

  • Optimisation Theory (MX4086) OR Geometry (MX4549)
  • Select a further 15 credit points from courses of choice
Optimisation Theory (MX4086) - 15 Credit Points

Linear optimisation is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. It is widely used in business and economics, and is also utilised for some engineering problems. Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proved useful in modeling diverse types routing, scheduling, assignment, and design.

View detailed information about this course

Geometry (MX4549) - 15 Credit Points

One of the aims of the course is to understand the mathematical concept of curvature. We will do this by first studying the geometry of polygonal surfaces, and then by looking at smooth surfaces in Euclidean space.

Polygonal surfaces provide a set of very easy examples with which we can explore the new ideas and quantities. They also allow us to develop the intuition needed in the later part of the course.

View detailed information about this course

Year 4

Year 4

Compulsory Courses

Galois Theory (MX4082) - 15 Credit Points

Galois theory is based around a simple but ingenious idea: that we can study field extensions by instead studying the structure of certain groups associated to them. This idea can be employed to solve some problems which confounded mathematicians for centuries, including the impossibility of trisecting an angle with ruler and compass alone, and the insolubility of the general quintic equation.

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Project (MX4023) - 15 Credit Points

The 4th year project is a good opportunity to do some research in an area of mathematics which is not covered in any other course. A choice of project topics will be made available to students before the start of the semester. Students will be expected to have regular meetings with their project supervisor. A written report should be submitted at the end of the course, with a presentation taking place shortly afterwards. Students should be able to demonstrate in the project that they have a good understanding of the topic they covered, often through working out examples.

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Complex Analysis (MX4557) - 15 Credit Points

This course asks what happens when concepts such as convergence of sequences and series, continuity and differentiability, are applied in the complex plane? The results are much more beautiful, and often, surprisingly, simpler, than over the real numbers. This course also covers contour integration of complex functions, which has important applications in Physics and Engineering.

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Optional Courses

Select four of the following courses:

  • Measure Theory (MX4083)
  • Nonlinear Dynamics I (MX4085)
  • Optimisation Theory (MX4086)
  • Algebraic Topology (MX4546)
  • Modelling Theory (MX4553)
  • Nonlinear Dynamics II (MX4555)
  • Geometry (MX4549)

Select a further 15 credit points from courses of choice

Measure Theory (MX4083) - 15 Credit Points

Measure theory provides a systematic framework to the intuitive concepts of the length of a curve, the area of a surface or the volume of a solid body. It is foundational to modern analysis and other branches of mathematics and physics.

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Nonlinear Dynamics & Chaos Theory i (MX4085) - 15 Credit Points

This course covers the fundamental mathematical concepts required for the description of dynamical systems, i.e., systems that change in time. It discusses nonlinear systems, for which typically no analytical solutions can be found; these systems are pivotal for the description of natural systems in physics, engineering, biology etc. Emphasis will be on the study of phase spaces.

Next to the theory of relativity and quantum mechanics, chaos and dynamical systems theory is been considered as one of three major advances in the natural sciences. This course offers the mathematics behind this paradigm changing theory.

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Algebraic Topology (MX4546) - 15 Credit Points

Algebraic topology is a tool for solving topological or geometric problems with the use of algebra. Typically, a difficult geometric or topological problem is translated into a problem in commutative algebra or group theory. Solutions to the algebraic problem then provide us with a partial solution to the original topological one.

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Modelling Theory (MX4553) - 15 Credit Points

This course was designed to show you what you can do with everything you learnt in your degree. We will use mathematical techniques to describe a fast variety of “real-world” systems: spreading of infectious diseases, onset of war, opinion formation, social systems, reliability of a space craft, patterns on the fur of animals (morphogenesis), formation of galaxies, traffic jams and others. This course will boost your employability and it will be exciting to see how everything you learnt comes together.

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Nonlinear Dynamics & Chaos Theory II (MX4555) - 15 Credit Points

This second part of the course covers more advanced mathematical concepts required for the description of dynamical systems. It continues the study of nonlinear systems, for which typically no analytical solutions can be found; these systems are pivotal for the description of natural systems.

Emphasis will be on the study of higher dimensional and chaotic systems. This second part of the course introduces stability criteria for more complex systems and outlines several key results that govern the behaviour of nonlinear dynamical system, such as requirements for chaotic behaviour and recurrence properties.

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Geometry (MX4549) - 15 Credit Points

One of the aims of the course is to understand the mathematical concept of curvature. We will do this by first studying the geometry of polygonal surfaces, and then by looking at smooth surfaces in Euclidean space.

Polygonal surfaces provide a set of very easy examples with which we can explore the new ideas and quantities. They also allow us to develop the intuition needed in the later part of the course.

View detailed information about this course

Optimisation Theory (MX4086) - 15 Credit Points

Linear optimisation is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. It is widely used in business and economics, and is also utilised for some engineering problems. Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proved useful in modeling diverse types routing, scheduling, assignment, and design.

View detailed information about this course

Number Theory (MX4545) - 15 Credit Points

This course concerns the integers, and more generally the ring of algebraic integers in an algebraic number field. The course begins with statements concerning the rational integers, for example we discuss the Legendre symbol and quadratic reciprocity. We also prove a result concerning the distribution of prime numbers. In the latter part of the course we study the ring of algebraic integers in an algebraic number field. One crucial result is the unique factorisation of a nonzero ideal as a product of primes, generalising classical prime factorisation in the integers.

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Course Availability

We will endeavour to make all course options available; however, these may be subject to timetabling and other constraints. Please see our InfoHub pages for further information.

How You'll Study

Learning Methods

  • Group Projects
  • Individual Projects
  • Lectures
  • Research
  • Tutorials

Assessment Methods

Students are assessed by any combination of three assessment methods:

  • coursework such as essays and reports completed throughout the course;
  • practical assessments of the skills and competencies learnt on the course; and
  • written examinations at the end of each course.

The exact mix of these methods differs between subject areas, year of study and individual courses.

Honours projects are typically assessed on the basis of a written dissertation.

Further Information

View detailed learning and assessment information for this programme

How the programme is taught

The typical time spent in scheduled learning activities (lectures, tutorials, seminars, practicals), independent self-study or placement is shown for each year of the programme based on the most popular course choices selected by students.

How the programme is assessed

The typical percentage of assessment methods broken down by written examination, coursework or practical exams is shown for each year of the programme based on the most popular course choices selected by students.

Year 1

Learning Method
scheduled: 31%
independent: 69%
placement: 0%
Assessment
written: 69%
coursework: 30%
practical: 1%

Year 2

Learning Method
scheduled: 26%
independent: 74%
placement: 0%
Assessment
written: 74%
coursework: 26%
practical: 0%

Year 3

Learning Method
scheduled: 23%
independent: 77%
placement: 0%
Assessment
written: 70%
coursework: 30%
practical: 0%

Year 4

Learning Method
scheduled: 18%
independent: 82%
placement: 0%
Assessment
written: 67%
coursework: 32%
practical: 1%

Why Study Mathematics?

  • Mathematics has been taught here since 1495.
  • Smaller class sizes (approx. 25 in Honours Years) and friendly, approachable staff.
  • We offer a degree in Pure Mathematics and degree in Applied Mathematics to suit your taste and interests. You will only need to make the choice in your 3rd year.
  • We offer a range of choices with your degree programme, across both the sciences (BSc) and the Arts (MA). You can focus your attention entirely on Mathematics or you can spread your interests to combine it with other subjects.
  • Challenging syllabus emphasizing rigour, taught by leading researchers.
  • Notable former staff include Colin Maclaurin and James Clerk Maxwell.
  • The department run a number of key events and seminars throughout the year, giving you the chance to network with students and academics.
  • Excellent employment prospects and options of further study. Mathematics graduates tend to have the widest arrange of careers and further study options open to them, compared to any other degree. 

Entry Requirements

You will find all the information you require about entry requirements on our dedicated 'Entry Requirements' page. You can also find out about the different types of degrees, offers, advanced entry, and changing your subject.

Qualifications

The information below is provided as a guide only and does not guarantee entry to the University of Aberdeen.

SQA Highers - AABB*

A Levels - BBB*
IB - 32 points, 5 at HL*
ILC - 5H with 3 at H2 AND 2 at H3 OR AAABB, obtained in a single sitting. (B must be at B2 or above)*

*SQA Higher or GCE A Level or equivalent qualification in Mathematics is required.

Advanced Entry - Advanced Highers ABB or A Levels ABB or IB 34 points (6 at HL), including A in Mathematics.

Further detailed entry requirements for Arts and Social Sciences degrees.

English Language Requirements

To study for a degree at the University of Aberdeen it is essential that you can speak, understand, read, and write English fluently. Read more about specific English Language requirements here.

Fees and Funding

You will be classified as one of the fee categories below.

Fee Waiver

For international students (all non-EU students) entering in 2017/18, the 2017/18 tuition fee rate will apply to all years of study; however, most international students will be eligible for a fee waiver in their final year via the International Undergraduate Scholarship.

Most RUK students (England, Wales and Northern Ireland) on a four year honours degree will be eligible for a full-fees waiver in their final year. Scholarships and other sources of funding are also available.

Fee information
Fee category Cost
Home / EU £1,820
All Students
RUK £9,250
Students Admitted in 2018/19 Academic Year
International Students £14,600
Students Admitted in 2018/19 Academic Year

Additional Fees

  • In exceptional circumstances there may be additional fees associated with specialist courses, for example field trips. Any additional fees for a course can be found in our Catalogue of Courses.
  • For more information about tuition fees for this programme, including payment plans and our refund policy, please visit our InfoHub Tuition Fees page.

Our Funding Database

View all funding options in our Funding Database.

Careers

A degree in Mathematics is the gateway to a wide variety of challenging careers. Employers are keen to recruit mathematicians for their ability to think logically and analyse new developments whether in technology, business or commerce. Mathematics lends itself to a career in the financial sector, actuarial sector, computing and information technology, geophysics and data analysis. Not to forget careers in education.

Employers that have employed our graduates include: Lloyds Banking Group, HSBC, NHS Grampian, Office of National Statistics, CGG, Community Energy Scotland and Schlumberger.

Career Opportunities

  • Account Manager
  • Financial Manager
  • Graduate Project Manager

Our Experts

Head of Department
Dr Assaf Libman

Information About Staff Changes

You will be taught by a range of experts including professors, lecturers, teaching fellows and postgraduate tutors. Staff changes will occur from time to time; please see our InfoHub pages for further information.

Facilities

Image for Sir Duncan Rice Library
Sir Duncan Rice Library

Sir Duncan Rice Library

The University’s award winning Sir Duncan Rice Library is listed in the “Top 20 spellbinding University libraries in the World”. It contains over a million volumes, more than 300,000 e-books and 21,000 journals.

Find out more

Unistats

Unistats draws together comparable information in areas students have identified as important in making decisions about what and where to study. You can compare these and other data for different degree programmes in which you are interested.

Get in Touch

Contact Details

Address
Student Recruitment & Admissions Service
University of Aberdeen
University Office
Regent Walk
Aberdeen
AB24 3FX