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Undergraduate Programme Specification

MSci Mathematics and Statistics & Op Research

Academic Year 2021/22

A programme specification is required for any programme on which a student may be registered. All programmes of the University are subject to the University's Quality Assurance processes. All degrees are awarded by Queen's University Belfast.

Programme Title MSci Mathematics and Statistics & Op Research Final Award
(exit route if applicable for Postgraduate Taught Programmes)
Master in Science
Programme Code MTH-MSCI UCAS Code GGC3 HECoS Code 100403 - Mathematics - 67
100406 - Statistics - 33
ATAS Clearance Required No
Mode of Study Full Time
Type of Programme Undergraduate Master Length of Programme 4 Academic Year(s) Total Credits for Programme 480
Exit Awards available

Institute Information

Teaching Institution

Queen's University Belfast

School/Department

Mathematics & Physics

Quality Code
https://www.qaa.ac.uk/quality-code

Higher Education Credit Framework for England
https://www.qaa.ac.uk/quality-code/higher-education-credit-framework-for-england

Level 7

Subject Benchmark Statements
https://www.qaa.ac.uk/quality-code/subject-benchmark-statements

The Frameworks for Higher Education Qualifications of UK Degree-Awarding Bodies
https://www.qaa.ac.uk/docs/qaa/quality-code/qualifications-frameworks.pdf

Mathematics, Statistics and Operational Research (2019)

Accreditations (PSRB)

Institute of Mathematics and its Applications

Date of most recent Accreditation Visit 04-07-13

Regulation Information

Does the Programme have any approved exemptions from the University General Regulations
(Please see General Regulations)

No

Programme Specific Regulations

Students will not be permitted to register for Stage 2 unless they have passed all their core Level 1 modules.

Transfers to Other Pathways
At the end of Stage 2, Students may transfer to other Pathways (BSc, or if they have achieved a weighted average of at least 55%, before rounding MSci), provided they have passed all the compulsory modules on the Pathway to which they are transferring up to that time of transfer.

Progression
At the end of Stages 2 and 3, students require an overall weighted average of at least 55% before rounding to progress to the next stage.
At the end of stages 2 and 3, students with an overall weighted average of less than 55% before rounding will be required to transfer to the BSc degree.

To progress from stage 3 to stage 4 students must maintain a weighted average of at least 55% before rounding
Students who fail to maintain this average will be required to transfer to the BSc pathway. They may be awarded a BSc degree if they meet the criteria for this award.

M.Sci. Mathematics, Statistics and Operational Research
For progression from Level 3 to Level 4, in addition to the standard University regulations for progress and the threshold average of 55%, a pass mark must be obtained in (a) SOR1020 and SOR1021, and (b) at least four out of SOR2002, SOR2003, either SOR2004 or SOR3004, SOR3001, SOR3008 and SOR3012. Students who satisfy the overall University progress criteria and the threshold average, but not the stated pass criterion, may progress onto Level 4 of the M.Sci. Mathematics degree.
For students who do not meet the threshold progression average of 55%, the following applies. If they satisfy the overall University criteria for the award of a B.Sc. degree and the pass criterion stated above, they may be awarded a B.Sc. degree in Mathematics, Statistics and Operational Research. If they satisfy the overall University criteria for the award of a B.Sc. degree, but not the pass criterion, they may be awarded a B.Sc. degree in Mathematics.

Students with protected characteristics

N/A

Are students subject to Fitness to Practise Regulations

(Please see General Regulations)

No

Educational Aims Of Programme

- Demonstrate good understanding of the main body of knowledge for mathematics, including some advanced topics, and demonstrate good skill in manipulation of this knowledge, including in its application to problem solving

- Apply core mathematics concepts in loosely defined contexts, through the judicious use of analytical and computational methods, tools and techniques and high-level skills in the development and evaluation of logical mathematical arguments

- Analyse complex problems through their formulation in terms of mathematics, including the ability to define the essence of problems, to formulate problems mathematically, and to interpret the solutions

- Communicate mathematical arguments accurately to a range of audiences in both written and oral form

- Develop an advanced project in mathematics competently

- Demonstrate the ability to function professionally as a statistician

Learning Outcomes

Learning Outcomes: Cognitive Skills

On the completion of this course successful students will be able to:

Apply mathematical knowledge logically and accurately in the solution of examples and complex problems

Teaching/Learning Methods and Strategies

By its nature, mathematics has to be presented logically. The lectures and model examples to problems provide exemplars of this logical structure. They also identify the tools needed to address certain problems. Tutorial problems and assignments offer the students opportunities to develop their logical reasoning skills, to develop skills in organising their reasoning and application of mathematics, and to develop skills in the selection of techniques.

Methods of Assessment

The assessment of these skills is implicit in most methods of assessment, including exams, coursework, practical and project work. The overall degree of success in any assessment depends to a large extent on students’ mastery of logical and accurate methods of solution, well-organised structure of answers, and the identification of the appropriate solution method.

Conduct an advanced mathematical investigation involving statistics and/or operational research under supervision

Teaching/Learning Methods and Strategies

The project modules will offer the students the opportunity to identify what it takes to carry out an extended, advanced investigation in pure or applied mathematics. These skills are also developed through extended assignments in a wide range of modules across the entire spectrum

Methods of Assessment

These skills are assessed mainly through project reports and oral presentations on project work of increasing complexity, culminating in the final project

Analyse complex problems and situations in mathematical terms, and identify the appropriate mathematical tools and techniques for their solution

Teaching/Learning Methods and Strategies

By its nature, mathematics has to be presented logically. The lectures and model examples to problems provide exemplars of this logical structure. They also identify the tools needed to address certain problems. Tutorial problems and assignments offer the students opportunities to develop their logical reasoning skills, to develop skills in organising their reasoning and application of mathematics, and to develop skills in the selection of techniques.

Methods of Assessment

The assessment of these skills is implicit in most methods of assessment, including exams, coursework, practical and project work. The overall degree of success in any assessment depends to a large extent on students’ mastery of logical and accurate methods of solution, well-organised structure of answers, and the identification of the appropriate solution method.

Organise their work in a structured manner

Teaching/Learning Methods and Strategies

By its nature, mathematics has to be presented logically. The lectures and model examples to problems provide exemplars of this logical structure. They also identify the tools needed to address certain problems. Tutorial problems and assignments offer the students opportunities to develop their logical reasoning skills, to develop skills in organising their reasoning and application of mathematics, and to develop skills in the selection of techniques.

Methods of Assessment

The assessment of these skills is implicit in most methods of assessment, including exams, coursework, practical and project work. The overall degree of success in any assessment depends to a large extent on students’ mastery of logical and accurate methods of solution, well-organised structure of answers, and the identification of the appropriate solution method.

Learning Outcomes: Knowledge & Understanding

On the completion of this course successful students will be able to:

Demonstrate specialist knowledge and associated skills in a particular area of pure or applied mathematics at a level suitable as a starting point for research

Teaching/Learning Methods and Strategies

The extended projects at Level 4 provide an opportunity for in-depth study of a particular topic under one-to-one supervision

Methods of Assessment

The specialist knowledge and skills are assessed through the project dissertation and an oral presentation.

Demonstrate some understanding of the connection between different areas of mathematics and/or between mathematics / statistics and other sciences and application areas

Teaching/Learning Methods and Strategies

Lectures provide the core method for the presentation of the knowledge required for students to be successful. Each lecture-based module has associated tutorials, and, where appropriate, practical classes to assist the student with the development of understanding of the core contents, including its application. Assignments are provided to assist further development of understanding. These assignments are marked and returned to students typically within one week with individual feedback. Model solutions to these assignments are made available to students for additional self-study.

Methods of Assessment

This is tested in particular in the project modules, as this is where outside applications may primarily appear. Modules in applied mathematics and statistics may demonstrate application in physics, medicine, business and finance.
The hierarchical nature of mathematics means that all mathematical modules are based on previous mathematical knowledge, and so this understanding is implicitly assessed in any examination.

Demonstrate understanding, and application of this understanding, within an extended range of more specialist optional topics to include statistics and /or operational research

Teaching/Learning Methods and Strategies

Lectures provide the core method for the presentation of the knowledge required for students to be successful. Each lecture-based module has associated tutorials, and, where appropriate, practical classes to assist the student with the development of understanding of the core contents, including its application. Assignments are provided to assist further development of understanding. These assignments are marked and returned to students typically within one week with individual feedback. Model solutions to these assignments are made available to students for additional self-study.

Methods of Assessment

Formal exams, class tests, small reports, presentations

Understand and appreciate the importance of mathematical logic

Teaching/Learning Methods and Strategies

Lectures provide the core method for the presentation of the knowledge required for students to be successful. Each lecture-based module has associated tutorials, and, where appropriate, practical classes to assist the student with the development of understanding of the core contents, including its application. Assignments are provided to assist further development of understanding. These assignments are marked and returned to students typically within one week with individual feedback. Model solutions to these assignments are made available to students for additional self-study.

Methods of Assessment

Formal exams, class tests, small reports, presentations
This appreciation is of particular importance to the project modules, as mathematical logic is critical to arrive at appropriate mathematical conclusions

Use these fundamental concepts and techniques in a range of application areas, including, for example, partial differential equations, mechanics, numerical analysis, statistics and operational research

Teaching/Learning Methods and Strategies

Lectures provide the core method for the presentation of the knowledge required for students to be successful. Each lecture-based module has associated tutorials, and, where appropriate, practical classes to assist the student with the development of understanding of the core contents, including its application. Assignments are provided to assist further development of understanding. These assignments are marked and returned to students typically within one week with individual feedback. Model solutions to these assignments are made available to students for additional self-study.

Methods of Assessment

Formal exams, class tests, small reports, presentations

Application of the fundamental concepts is also of importance to any of the project modules, as deeper understanding will result in higher marks

Demonstrate understanding of the fundamental concepts and techniques of calculus, analysis, algebra, linear algebra, statistics and operational research

Teaching/Learning Methods and Strategies

Lectures provide the core method for the presentation of the knowledge required for students to be successful. Each lecture-based module has associated tutorials, and, where appropriate, practical classes to assist the student with the development of understanding of the core contents, including its application. Assignments are provided to assist further development of understanding. These assignments are marked and returned to students typically within one week with individual feedback. Model solutions to these assignments are made available to students for additional self-study.

Methods of Assessment

Formal exams, class tests, small reports, presentations

Learning Outcomes: Subject Specific

On the completion of this course successful students will be able to:

Present sophisticated mathematical findings through oral and written means to a range of audiences

Teaching/Learning Methods and Strategies

Communication through reports and/or oral presentations forms a compulsory part of many modules across the entire range of modules offered.

Methods of Assessment

These skills are primarily assessed through compulsory reports and presentations within many modules.

Use a range of mathematical and statistical software for the solution of mathematical and statistical problems

Teaching/Learning Methods and Strategies

Basic skills are developed through the mathematical modelling module and the computer algebra module. Numerical analysis and statistics oriented modules have associated computer practicals, using appropriate specialist software.

In the project modules, further opportunities to use mathematical software may be available.

Methods of Assessment

These skills are primarily assessed through reports and presentations associated with work carried out using mathematical software.

Apply a wide range of analytic and/or numerical mathematical and statistical techniques within well-defined contexts, and to formulate and solve complex problems in more loosely defined contexts

Teaching/Learning Methods and Strategies

Each lecture-based module has associated tutorials, and, where appropriate, practical classes to assist the student with the development of understanding and application of logical mathematical arguments and/or analytic/numerical mathematical techniques. Assignments also assist the development of understanding in these areas.

The project modules allow students to spend time on a more extended problem, which will enable a more in-depth development of mathematical arguments and application mathematical techniques

Methods of Assessment

Assessment is mainly through formal examination and class tests for lecture-based modules. This assessment is supplemented through written reports and oral presentations. For project modules, the latter is the main method of assessment.

Demonstrate advanced understanding of logical mathematical arguments, including mathematical proofs and their construction, and apply these arguments appropriately

Teaching/Learning Methods and Strategies

Each lecture-based module has associated tutorials, and, where appropriate, practical classes to assist the student with the development of understanding and application of logical mathematical arguments and/or analytic/numerical mathematical techniques. Assignments also assist the development of understanding in these areas.

The project modules allow students to spend time on a more extended problem, which will enable a more in-depth development of mathematical arguments and application mathematical techniques

Methods of Assessment

Assessment is mainly through formal examination and class tests for lecture-based modules. This assessment is supplemented through written reports and oral presentations. For project modules, the latter is the main method of assessment.

Learning Outcomes: Transferable Skills

On the completion of this course successful students will be able to:

Oversee extended projects

Teaching/Learning Methods and Strategies

Project work associated with modules at each Level are the prime method for development. The increase in level of complexity of such projects throughout the programme, in line with student’s overall development, will implicitly develop the students’ skills in project management.

Methods of Assessment

These skills are assessed implicitly as part of any project component to a module. A higher level of skill in time management will provide student with greater opportunity to present a well thought-through report, which allows the students to better highlight their achievements.

Manage their time

Teaching/Learning Methods and Strategies

Project work associated with modules at each Level are the prime method for development. The increase in level of complexity of such projects throughout the programme, in line with student’s overall development, will implicitly develop the students’ skills in project management.

Methods of Assessment

These skills are assessed implicitly as part of any project component to a module. A higher level of skill in time management will provide student with greater opportunity to present a well thought-through report, which allows the students to better highlight their achievements.

Present findings for complex problems through oral communication

Teaching/Learning Methods and Strategies

Any assignment or coursework or project work involves the communication of mathematical ideas, and these skills are thus embedded indirectly in any module.
Any report or presentation will provide an explicit learning opportunity, where the increase in mathematical difficulty at higher levels will provide a means for communication skill development

Methods of Assessment

The assessment of communication skills takes place through the reports and presentations, where higher skill levels will result in higher overall marks

Present findings for complex problems through written reports

Teaching/Learning Methods and Strategies

Any assignment or coursework or project work involves the communication of mathematical ideas, and these skills are thus embedded indirectly in any module.
Any report or presentation will provide an explicit learning opportunity, where the increase in mathematical difficulty at higher levels will provide a means for communication skill development

Methods of Assessment

The assessment of communication skills takes place through the reports and presentations, where higher skill levels will result in higher overall marks

Communicate high-level mathematical and statistical ideas and concepts clearly

Teaching/Learning Methods and Strategies

Any assignment or coursework or project work involves the communication of mathematical ideas, and these skills are thus embedded indirectly in any module.
Any report or presentation will provide an explicit learning opportunity, where the increase in mathematical difficulty at higher levels will provide a means for communication skill development

Methods of Assessment

The assessment of communication skills takes place through the reports and presentations, where higher skill levels will result in higher overall marks

Use computer technology efficiently for a variety of purposes

Teaching/Learning Methods and Strategies

Basic computer modelling skills are developed through the mathematical modelling module and the computer algebra module. Numerical analysis and statistics oriented modules have associated computer –oriented tasks, where students can develop skills in the use of appropriate specialist software.
In the project modules, further opportunities to use mathematical software may be available.
Written reports develop skills in the use of word-processing software, while the presentations can develop skills in the use of presentation software

Methods of Assessment

Computer modelling skills are primarily assessed through reports and presentations associated with work carried out using mathematical software.
The main test in Computer Algebra takes place through a direct assessment of their use of appropriate software
Computer skills in word-processing and presentation development are assessed implicitly in the project and presentation assessment

Adopt an analytic approach to problem solving

Teaching/Learning Methods and Strategies

Analytic thinking is part of any module in mathematics, and is therefore cultivated through the tutorials, practicals and assignments associated with each lecture-based module, including all the project components.

It is also a critical skill developed during the project modules

Methods of Assessment

Analytic thinking is embedded implicitly in every assessment within mathematics.
Problem solving skills will be assessed through an extended range of project work, culminating in the final-year project modules

Module Information

Stages and Modules

Module Title Module Code Level/ stage Credits

Availability

Duration Pre-requisite

Assessment

S1 S2 Core Option Coursework % Practical % Examination %
Set Theory PMA3014 3 20 YES 12 weeks N YES 30% 0% 70%
Stochastic Processes and Risk SOR3012 3 20 YES 12 weeks Y YES 40% 0% 60%
Mathematical Reasoning MTH1015 1 10 YES 12 weeks N YES 65% 35% 0%
Methods of Operational Research SOR2003 2 20 YES 12 weeks Y YES 20% 10% 70%
Mathematical Methods 1 MTH1021 1 30 YES YES 24 weeks N YES 15% 0% 85%
Investigations AMA3020 3 20 YES 12 weeks N YES 80% 20% 0%
Survival Analysis SOR4007 4 20 YES 12 weeks N YES 20% 10% 70%
Algorithmic Thinking MTH1025 1 10 YES 12 weeks N YES 80% 20% 0%
Mathematical Methods for Quantum Information Processing MTH4023 4 20 YES 12 weeks N YES 30% 0% 70%
Quantum Theory MTH3032 3 20 YES 12 weeks N YES 30% 0% 70%
Statistics Project SOR4001 4 40 YES YES 24 weeks N YES 80% 20% 0%
Introduction to Statistical and Operational Research Methods SOR1021 1 10 YES 12 weeks N YES 100% 0% 0%
Introduction to Probability & Statistics SOR1020 1 30 YES YES 24 weeks N YES 0% 10% 90%
Topology MTH4011 4 20 YES 12 weeks N YES 30% 0% 70%
Financial Mathematics MTH3025 3 20 YES 12 weeks N YES 20% 10% 70%
Modelling and Simulation MTH3024 3 20 YES 12 weeks N YES 100% 0% 0%
Mathematical Investigations PMA3013 3 20 YES 12 weeks N YES 90% 10% 0%
Metric Spaces MTH2013 2 20 YES 12 weeks N YES 30% 0% 70%
Introduction to Algebra and Analysis MTH1011 1 30 YES YES 24 weeks N YES 0% 0% 100%
Statistical Mechanics MTH4332 4 20 YES 12 weeks N YES 25% 20% 55%
Statistical Mechanics MTH4332 3 20 YES 12 weeks N YES 25% 20% 55%
Metric and Normed Spaces PMA3017 3 20 YES 12 weeks N YES 10% 10% 80%
Linear Models SOR3004 3 20 YES 12 weeks Y YES 20% 10% 70%
Statistical Inference SOR2002 2 20 YES 12 weeks Y YES 20% 10% 70%
Employability for Mathematics MTH2010 2 0 YES 12 weeks N YES 100% 0% 0%
Integration Theory PMA4004 4 20 YES 12 weeks N YES 30% 0% 70%
Dynamical Systems MTH3021 3 20 YES 12 weeks N YES 30% 0% 70%
Rings and Modules MTH3012 3 20 YES 12 weeks N YES 30% 0% 70%
Numerical Analysis MTH3023 3 20 YES 12 weeks N YES 50% 0% 50%
Analysis MTH2012 2 20 YES 12 weeks Y YES 25% 0% 75%
Mathematical Methods 2 MTH2021 2 20 YES 12 weeks Y YES 40% 0% 60%
Statistical Data Mining and Machine Learning SOR3008 3 20 YES 12 weeks N YES 40% 0% 60%
Practical Methods for Partial Differential Equations MTH4024 4 20 YES 12 weeks N YES 30% 0% 70%
Functional Analysis MTH4311 4 20 YES 12 weeks N YES 30% 0% 70%
Functional Analysis MTH4311 3 20 YES 12 weeks N YES 30% 0% 70%
Applied Algebra and Cryptography MTH4021 4 20 YES 12 weeks N YES 20% 0% 80%
Group Theory MTH2014 2 20 YES 12 weeks Y YES 30% 0% 70%
Discrete Mathematics MTH3022 3 20 YES 12 weeks N YES 30% 0% 70%
Linear & Dynamic Programming SOR3001 3 20 YES 12 weeks Y YES 20% 10% 70%
Linear Algebra MTH2011 2 20 YES 12 weeks Y YES 30% 0% 70%
Topological Data Analysis MTH4322 4 20 YES 12 weeks N YES 25% 0% 75%
Topological Data Analysis MTH4322 3 20 YES 12 weeks N YES 25% 0% 75%
Classical Fields MTH3031 3 20 YES 12 weeks N YES 30% 0% 70%
Classical Mechanics MTH2031 2 20 YES 12 weeks Y YES 20% 0% 80%
Information Theory MTH4022 4 20 YES 12 weeks N YES 30% 0% 70%
Advanced Quantum Theory MTH4031 4 20 YES 12 weeks N YES 0% 20% 80%

Notes

At Stage 1, Students are required to take the SIX compulsory modules listed

At Stage 2, Students must take six modules, including MTH2011, MTH2012, MTH2013 and SOR2002. In choosing their optional modules, students should take note of pre-requisites for Level 3 Mathematics modules, and it is recommended that MTH2021 and SOR2003 are taken. Students must take at least 80 CATS of SOR modules over Levels 2 and 3. In addition, students planning to take a placement year must take MTH2010..

At Stage 3, Students must take a combination of six Level 3 modules, with MTH4332, MTH4311 and MTH4322 also available. The choice of modules must include SOR3004 and SOR3008, plus either PMA3013 or AMA3020, but not both. Students must take 80 CATS of SOR modules over Levels 2 and 3.

At Stage 4, Students must take SOR4001 and SOR4007 plus three other modules, totalling 120 CATS.