Applied Mathematics Computation In Context Level A Form 1 Answers

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. You will have a great choice of courses, individual attention in small classes, and a challenging syllabus which emphasises reasoning, rigour and application.

Mathematics at Aberdeen is ranked 3rd in Scotland by The Guardian's Best UK Universities, 2021.

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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, engineers, physicists, etc.

You will learn from teachers and researchers internationally recognised as leaders in pure mathematics, especially algebra, analysis, geometry and topology and on their application to complex systems, particularly in biology.

Mathematics and computational science are used in almost every field of science, engineering, industry, and technology and a degree in Applied Mathematics is the gateway to a wide variety of challenging careers.

However, it is not just about crunching numbers – it is about solving problems and looking for opportunities. Employers are keen to recruit mathematicians because they can think logically and analyse new developments in business, commerce or technology, opening up opportunities especially in the financial sector, computing and information technology, geophysics and data analysis.

You will thrive in our friendly and vibrant international community, on our beautiful medieval campus with great facilities for learning, sports and leisure, and the many opportunities to develop the extra skills and interests – and the broader horizons – that will give you the competitive advantage in whichever career path you choose.

This Applied Mathematics MA programme covers the core courses as studied in the pure Mathematics MA 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.

What You'll Study

Year 1

Year 1

Compulsory Courses

Calculus 1 (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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Programming for Sciences and Engineering (CS1028)

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.

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Understanding Data (ST1506)

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.

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Optional Courses

Select a further 60 credit points from courses of choice.

Year 2

Year 2

Compulsory Courses

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 )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 rigourous mathematical proofs, valid reasoning, and the avoidance of fallacious arguments.

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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 II (MA2509)

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.

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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.

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

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Probability (MA2010)

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.

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Optional Courses

Select a further 45 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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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 differential equation systematically from a purely mathematical viewpoint. Such abstraction is fundamental to the understanding of this concept.

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Optional Courses

Select a further 15 credit points from courses of choice, plus select 45 credit points from courses below.

MX4086 - Optimisation Theory

MX45049 - Geometry

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 & 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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Financial Mathematics (MX4087)

Knots (MX4540)

15 Credit Points

A knot is a closed curve in three dimensions. How can we tell if two knots are the same? How can we tell if they are different? This course answers these questions by developing many different "invariants" of knots. It is a pure mathematics course, drawing on simple techniques from a variety of places, but with an emphasis on examples, computations and visual reasoning.

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Year 4

Year 4

Compulsory Courses

Project A (PX4011)

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.

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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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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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Optional Courses

Select a further 30 credit points from MX Level 4 courses, plus 15 credit points from courses of choice.

MX4086 - Optimisation Theory

Financial Mathematics (MX4087)

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
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 has been taught here since 1495.
Smaller class sizes (approx. 25 in Honours Years) and friendly, approachable staff.
Challenging syllabus emphasizing rigour, taught by leading researchers.
Notable former staff include Colin Maclaurin and James Clerk Maxwell.
Flexible curriculum, including the opportunity to study Mathematics alongside other subjects.
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

Qualifications

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

General Entry Requirements

2021 Entry

2022 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 have achieved BB, and who meet one of the widening participation criteria are encouraged to apply and will be considered. 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.

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*

Adjusted: BB*

*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.

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 information
Fee category	Cost
RUK	£9,250
Students Admitted in 2021/22	£9,250
EU / International students	£18,000
Students Admitted in 2021/22	£18,000
Home Students	£1,820
Students Admitted in 2021/22	£1,820

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 InfoHub Tuition Fees page.

Our Funding Database

View all funding options in our Funding Database.

Undergraduate EU Scholarship

The Aberdeen Global Undergraduate Scholarship is open to European Union (EU) students.

This is an £8,000 tuition fee discount available to eligible self-funded Undergraduate students who would have previously been eligible for Home (Scottish/EU) fee status.

View Undergraduate EU Scholarship

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. Staff changes will occur from time to time; please see our InfoHub pages for further information.

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