Facundo Manuel Canale
Applied Mathematics, MA
Introduction
Applied Mathematics at Aberdeen gives you all the benefits of a top-quality mathematical education in a thriving centre of mathematical teaching and research, with focus on how we apply mathematics to better understand our world today.
Study Information
At a Glance
- Learning Mode
- On Campus Learning
- Degree Qualification
- MA
- Duration
- 48 months
- Study Mode
- Full Time
- Start Month
- September
- UCAS Code
- G122
- Pathway Programme Available
- Undergraduate Foundation Programme
Mathematics is not just about crunching numbers – it’s about logical thinking, solving problems, decision making and understanding why things work – the main skills that recruiters look for in potential employees. Mathematicians are in high demand across a range of sectors, including IT, finance, engineering and teaching.
Pure maths is about solving problems and developing theories within mathematics but applied maths is more about using mathematical theory to solve problems in other areas, including science, engineering, and physics. A lot of the theory that gets developed by pure mathematicians later becomes useful for applied mathematicians (and engineers, physicists etc.).
This Applied Mathematics BSc programme covers the core courses as studied in the pure Mathematics BSc degree. Additional core courses offered specifically in the Applied Maths degree include, Engineering Mathematics and Advanced Calculus. There are also a range of optional courses that can be chosen from both maths and physics areas.
BSc or MA?
Both the BSc and MA Mathematics and BSc and MA Applied Mathematics degrees consist of the same core mathematics courses. The difference between the MA and BSc programmes is the choice of optional courses alongside your core mathematics courses.
What You'll Study
- Year 1
-
Compulsory Courses
- Getting Started at the University of Aberdeen (PD1002)
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This course, which is prescribed for level 1 undergraduate students (and articulating students who are in their first year at the University), is studied entirely online, takes approximately 5-6 hours to complete and can be taken in one sitting, or spread across a number of weeks.
Topics include orientation overview, equality and diversity, health, safety and cyber security and how to make the most of your time at university in relation to careers and employability.
Successful completion of this course will be recorded on your Enhanced Transcript as ‘Achieved’.
- Programming 1 (CS1032)
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15 Credit Points
This course will be delivered in two halves. The first half will provide a self-contained introduction to computer programming. It will be accessible to all undergraduates. Students will be exposed to the basic principles of computer programming, e.g. fundamental programming techniques, concepts, algorithms and data structures. The course contains lectures where the principles are systematically developed. As the course does not presuppose knowledge of these principles, we start from basic intuitions. The second half will be particularly of use to those studying Science and Engineering subjects, broadly interpreted, as well as Computing and IT specialists. It will include a gentle introduction to professional issues and security concepts.
- Calculus 1 (MA1005)
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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.
- Algebra (MA1006)
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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.
- Understanding Data (ST1506)
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15 Credit Points
This is a statistics course open to all first and second year students. It is a useful course for students whose degree subject involves some amount of statistical analysis. The course teaches students how to summarise data effectively and how to correctly interpret it. Among the topics covered are sampling strategies, probability theory, confidence intervals and hypothesis tests. There are also weekly computer practicals using the statistics software RStudio. The mathematical context is emphasised but students are not expected to have a high level of maths.
- Calculus II (MA1508)
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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.
- Set Theory (MA1511)
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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.
Optional Courses
Select a further 30 credit points from courses of choice.
- Year 2
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Compulsory Courses
- Analysis i (MA2009)
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15 Credit Points
Analysis provides the rigorous, 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) and continuity 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 rigorous mathematical proofs, valid reasoning, and the avoidance of fallacious arguments.
- Linear Algebra i (MA2008)
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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.
- Probability (MA2010)
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15 Credit Points
Probability theory is concerned with the analysis of random phenomena by providing an abstract mathematical framework to study them within the language of set theory. This is done by the concepts of "probability spaces" and "random variables". The theory began in the 16th century in attempts to analyze games of chance; In 1812 Pierre Simon Laplace wrote: "It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge."
The course is recommended to anyone interested in the foundations and applications of mathematics.
- Analysis II (MA2509)
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15 Credit Points
Analysis provides the rigorous, foundational underpinnings of calculus. This course builds on the foundations in Analysis I, and explores the notions of differential calculus, Riemann integrability, sequences of functions, and power series.
The techniques of careful rigorous 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.
- Linear Algebra II (MA2508)
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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.
Optional Courses
Select a further 45 credit points from courses of choice.
- Year 3
-
Compulsory Courses
- Group Theory (MX3020)
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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. Sylow p-subgroups are introduced and the three Sylow theorems are proved. Throughout symmetric groups are consulted as a source of examples.
- 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.
- Analysis Iv (MX3535)
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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.
- Differential Equations (MX3536)
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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 differential equation systematically from a purely mathematical viewpoint. Such abstraction is fundamental to the understanding of this concept.
Optional Courses
Select one of the following options:
- Optimisation Theory (MX4086)*
- Financial Mathematics (MX4087)*
Select a further 15 credit points from courses of choice, plus select 30 credit points from courses below.
- Metric and Topological Spaces (MX3036)
- Rings and Fields (MX3531)
- Knots (MX4540)* OR Geometry (MX4549)*
* Courses are offered in alternate years. MX4086 and MX4549 will be offered in 2022-2023.
- Metric and Topological Spaces (MX3036)
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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.
- Rings & Fields (MX3531)
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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.
- Optimisation Theory (MX4086)
-
15 Credit Points
Linear optimisation is a method to achieve the best outcome 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.
- Geometry (MX4549)
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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.
- Year 4
-
Compulsory Courses
- Project A (PX4011)
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30 Credit Points
PX4011 provides the opportunity to carry out an independent, open-ended, piece of research work. This can be in an area of physics (astronomy, nuclear physics, superconductors, dynamical systems etc.) or in related subjects where physicists tools can be applied (generation of proteins, biomechanics, infectious diseases etc.). The project can be dissertation based, practical or computational. You will develop: presentation skills; experience of reading and thinking about a specialist topic in depth; critical analysis skills of your own and other people’s scientific work and project management skills. This will help prepare for your future career beyond university.
- Nonlinear Dynamics & Chaos Theory i (MX4085)
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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.
- Modelling Theory (MX4553)
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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.
- Nonlinear Dynamics & Chaos Theory II (MX4555)
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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.
Optional Courses
Select one of the following options:
- Optimisation Theory (MX4086)*
- Financial Mathematics (MX4087)*
* Courses are offered in alternate years. MX4086 will be offered in 2022-2023.
Select a further 15 credit points from MX Level 4 courses, plus 15 credit points from courses of choice.
A graduating curriculum for the Honours programme must include 90 credit points from Level 4 MX courses.
We will endeavour to make all course options available. However, these may be subject to change - see our Student Terms and Conditions page.
How You'll Study
Learning Methods
- Group Projects
- Individual Projects
- Lectures
- Research
- Seminars
- 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.
Why Study Applied Mathematics?
- 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.
- We offer a degree in Pure Mathematics and a degree in Applied Mathematics to suit your taste and interests. You will only need to make the choice in your 3rd year.
- Our challenging syllabus reflects our specialist expertise and emphasises reasoning, rigour and the argumentative side of mathematics as well the high levels of communication skills in demand by employers.
- Our graduates are highly employable, with many going on to pursue careers in business and banking, as well as the science and tech sector, particularly as actuaries, data scientists, economists or market analysts.
- We offer excellent student experience delivered by enthusiastic staff combined with small class sizes, approximately 25 or less in the Honours years.
- Notable former mathematicians associated with the University of Aberdeen include Colin Maclaurin and James Clerk Maxwell, who is widely regarded as one of the greatest scientists who have ever lived due to his revolutionary work on electricity, magnetism, and optics.
- 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.
- The department run a number of key events and seminars throughout the year, giving you the chance to network with students and academics.
- Interactions with applied maths are fostered through our involvement in the Institute for Pure and Applied Mathematics, comprised of the Department of Mathematics together with the Institute for Complex Systems and Mathematical Biology.
What Our Students Say
Helen Taylor
Entry Requirements
Qualifications
The information below is provided as a guide only and does not guarantee entry to the University of Aberdeen.
General Entry Requirements
- 2024 Entry
-
SQA Highers
Standard: AABB*
Applicants who have achieved AABB (or better), are encouraged to apply and will be considered. Good performance in additional Highers/ Advanced Highers may be required.
Minimum: BBB*
Applicants who have achieved BBB (or are on course to achieve this by the end of S5) are encouraged to apply and will be considered. Good performance in additional Highers/Advanced Highers will normally be required.
Adjusted: BB*
Applicants who achieve BB over S4 and S5 and who meet one of the widening access criteria are guaranteed a conditional offer. Good performance in additional Highers/Advanced Highers will be required.
*Including good performance in Mathematics by the end of your senior phase of education.
More information on our definition of Standard, Minimum and Adjusted entry qualifications.
A LEVELS
Standard: BBB*
Minimum: BBC*
Adjusted: CCC*
*Including good performance in Mathematics by the end of your senior phase of education.
More information on our definition of Standard, Minimum and Adjusted entry qualifications.
International Baccalaureate
32 points, including 5, 5, 5 at HL*.
*Including good performance in Mathematics by the end of your senior phase of education.
Irish Leaving Certificate
5H with 3 at H2 AND 2 at H3*
*Including good performance in Mathematics by the end of your senior phase of education.
- 2025 Entry
-
SQA Highers
Standard: BBBB*
Applicants who have achieved BBBB (or better), are encouraged to apply and will be considered. Good performance in additional Highers/ Advanced Highers may be required.
Minimum: BBC
Applicants who have achieved BBC at Higher and meet one of the widening participation criteria above are encouraged to apply and are guaranteed an unconditional offer for MA, BSc and BEng degrees.
Adjusted: BB
Applicants who have achieved BB at Higher, and who meet one of the widening participation criteria above are encouraged to apply and are guaranteed an adjusted conditional offer for MA, BSc and BEng degrees.
We would expect to issue a conditional offer asking for one additional C grade at Higher.
Foundation Apprenticeship: One FA is equivalent to a Higher at A. It cannot replace any required subjects.
*Including good performance in Mathematics by the end of your senior phase of education.
More information on our definition of Standard, Minimum and Adjusted entry qualifications.
A LEVELS
Standard: BBC*
Minimum: BCC*
Adjusted: CCC*
*Including good performance in Mathematics by the end of your senior phase of education.
More information on our definition of Standard, Minimum and Adjusted entry qualifications.
International Baccalaureate
32 points, including 5, 5, 5 at HL*.
*Including good performance in Mathematics by the end of your senior phase of education.
Irish Leaving Certificate
5H with 3 at H2 AND 2 at H3*
*Including good performance in Mathematics by the end of your senior phase of education.
The information displayed in this section shows a shortened summary of our entry requirements. For more information, or for full entry requirements for Arts and Social Sciences degrees, see our detailed entry requirements section.
English Language Requirements
To study for an Undergraduate degree at the University of Aberdeen it is essential that you can speak, understand, read, and write English fluently. The minimum requirements for this degree are as follows:
IELTS Academic:
OVERALL - 6.0 with: Listening - 5.5; Reading - 5.5; Speaking - 5.5; Writing - 6.0
TOEFL iBT:
OVERALL - 78 with: Listening - 17; Reading - 18; Speaking - 20; Writing - 21
PTE Academic:
OVERALL - 59 with: Listening - 59; Reading - 59; Speaking - 59; Writing - 59
Cambridge English B2 First, C1 Advanced or C2 Proficiency:
OVERALL - 169 with: Listening - 162; Reading - 162; Speaking - 162; Writing - 169
Read more about specific English Language requirements here.
International Applicants who do not meet the Entry Requirements
The University of Aberdeen International Study Centre offers preparation programmes for international students who do not meet the direct entry requirements for undergraduate study. Discover your foundation pathway here.
Fees and Funding
You will be classified as one of the fee categories below.
| Fee category | Cost |
|---|---|
| RUK | £9,250 |
| Tuition Fees for 2025/26 Academic Year | |
| EU / International students | £20,800 |
| Tuition Fees for 2025/26 Academic Year | |
| Home Students | £1,820 |
| Tuition Fees for 2025/26 Academic Year |
Scholarships and Funding
Students from England, Wales and Northern Ireland, who pay tuition fees may be eligible for specific scholarships allowing them to receive additional funding. These are designed to provide assistance to help students support themselves during their time at Aberdeen.
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 Tuition Fees page.
Our Funding Database
View all funding options in our Funding Database.
Careers
Applied mathematicians go on to careers in computer science, engineering, and business. You may decide to specialise and study to postgraduate level or you may decide to work and specialise at the same time.
Our Experts
Information About Staff Changes
You will be taught by a range of experts including professors, lecturers, teaching fellows and postgraduate tutors. However, these may be subject to change - see our Student Terms and Conditions page.
Discover Uni
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Get in Touch
Contact Details
- Address
-
Student Recruitment & Admissions
University of Aberdeen
University Office
Regent Walk
Aberdeen
AB24 3FX