Programme Specification
MSci Mathematics
Academic Year 2022/23
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 | Final Award (exit route if applicable for Postgraduate Taught Programmes) |
Master in Science | |||||||||||
| Programme Code | MTH-MSCI | UCAS Code | G103 | HECoS Code |
100403 - Mathematics - 100 |
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| ATAS Clearance Required | No | |||||||||||||
| Mode of Study | Full Time | |||||||||||||
| Type of Programme | Undergraduate Master | Length of Programme |
Full Time - 4 Academic Years |
Total Credits for Programme | 480 | |||||||||
| Exit Awards available | No | |||||||||||||
Institute Information
Teaching Institution |
Queen's University Belfast |
School/Department |
Mathematics & Physics |
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Quality Code Higher Education Credit Framework for England |
Level 7 |
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Subject Benchmark Statements The Frameworks for Higher Education Qualifications of UK Degree-Awarding Bodies |
Mathematics, Statistics and Operational Research (2019) |
Accreditations (PSRB) |
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Institute of Mathematics and its Applications |
Date of most recent Accreditation Visit 04-06-13 |
Regulation Information
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Does the Programme have any approved exemptions from the University General Regulations No |
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Programme Specific Regulations Students will not be permitted to register for Stage 2 unless they have passed all their core Level 1 modules. |
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Students with protected characteristics N/A |
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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
Learning Outcomes
Learning Outcomes: Cognitive SkillsOn the completion of this course successful students will be able to: |
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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. |
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Conduct an advanced mathematical investigation 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 |
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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. |
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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 & UnderstandingOn the completion of this course successful students will be able to: |
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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. |
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Demonstrate some understanding of the connection between different areas of mathematics and/or between mathematics 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. |
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Demonstrate understanding, and application of this understanding, within an extended range of more specialist optional topics |
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 |
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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 |
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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 |
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Demonstrate understanding of the fundamental concepts and techniques of calculus, analysis, algebra, linear algebra and numerical methods |
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 SpecificOn the completion of this course successful students will be able to: |
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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. |
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Use a range of mathematical software for the solution of mathematical 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. Methods of Assessment These skills are primarily assessed through reports and presentations associated with work carried out using mathematical software. |
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Apply a wide range of analytic and/or numerical mathematical 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. 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. |
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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. 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 SkillsOn the completion of this course successful students will be able to: |
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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. |
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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. |
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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. 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 |
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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. 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 |
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Communicate high-level mathematical 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. 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 |
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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. Methods of Assessment Computer modelling skills are primarily assessed through reports and presentations associated with work carried out using mathematical software. |
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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. Methods of Assessment Analytic thinking is embedded implicitly in every assessment within mathematics. |
Module Information
Stages and Modules
| Module Title | Module Code | Level/ stage | Credits | Availability |
Duration | Pre-requisite | Assessment |
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
| S1 | S2 | Core | Option | Coursework % | Practical % | Examination % | ||||||
| Introduction to Statistical and Operational Research Methods | SOR1021 | 1 | 10 | -- | YES | 12 weeks | N | -- | YES | 20% | 10% | 70% |
| Mathematical Methods 1 | MTH1021 | 1 | 30 | YES | YES | 12 weeks | N | YES | -- | 15% | 0% | 85% |
| Introduction to Algebra and Analysis | MTH1011 | 1 | 30 | YES | YES | 12 weeks | N | YES | -- | 0% | 0% | 100% |
| Algorithmic Thinking | MTH1025 | 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% |
| Mathematical Reasoning | MTH1015 | 1 | 10 | YES | -- | 12 weeks | N | YES | -- | 65% | 35% | 0% |
| Metric Spaces | MTH2013 | 2 | 20 | -- | YES | 12 weeks | N | YES | -- | 30% | 0% | 70% |
| Methods of Operational Research | SOR2003 | 2 | 20 | YES | -- | 12 weeks | Y | -- | YES | 20% | 10% | 70% |
| Employability for Mathematics | MTH2010 | 2 | 0 | YES | -- | 12 weeks | N | -- | YES | 100% | 0% | 0% |
| Group Theory | MTH2014 | 2 | 20 | -- | YES | 12 weeks | Y | -- | YES | 30% | 0% | 70% |
| Analysis | MTH2012 | 2 | 20 | YES | -- | 12 weeks | Y | YES | -- | 10% | 0% | 90% |
| Linear Algebra | MTH2011 | 2 | 20 | YES | -- | 12 weeks | Y | YES | -- | 30% | 0% | 70% |
| Mathematical Methods 2 | MTH2021 | 2 | 20 | -- | YES | 12 weeks | Y | YES | -- | 40% | 0% | 60% |
| Statistical Inference | SOR2002 | 2 | 20 | -- | YES | 12 weeks | Y | -- | YES | 20% | 10% | 70% |
| Classical Mechanics | MTH2031 | 2 | 20 | YES | -- | 12 weeks | Y | -- | YES | 20% | 0% | 80% |
| Numerical Analysis | MTH3023 | 3 | 20 | YES | -- | 12 weeks | Y | -- | YES | 50% | 0% | 50% |
| Measure and Integration | MTH3011 | 3 | 20 | YES | -- | 12 weeks | N | YES | -- | 30% | 0% | 70% |
| Fourier Analysis and Applications to PDEs | MTH4321 | 3 | 20 | -- | YES | 12 weeks | N | -- | YES | 30% | 0% | 70% |
| Classical Fields | MTH3031 | 3 | 20 | YES | -- | 12 weeks | Y | -- | YES | 30% | 0% | 70% |
| Stochastic Processes and Risk | SOR3012 | 3 | 20 | YES | -- | 12 weeks | N | -- | YES | 55% | 0% | 45% |
| Rings and Modules | MTH3012 | 3 | 20 | YES | -- | 12 weeks | Y | -- | YES | 30% | 0% | 70% |
| Discrete Mathematics | MTH3022 | 3 | 20 | -- | YES | 12 weeks | N | -- | YES | 30% | 0% | 70% |
| Statistical Data Mining and Machine Learning | SOR3008 | 3 | 20 | -- | YES | 12 weeks | N | -- | YES | 40% | 0% | 60% |
| Financial Mathematics | MTH3025 | 3 | 20 | -- | YES | 12 weeks | N | -- | YES | 20% | 10% | 70% |
| Mathematical Investigations | PMA3013 | 3 | 20 | -- | YES | 12 weeks | N | YES | -- | 90% | 10% | 0% |
| Linear Models | SOR3004 | 3 | 20 | YES | -- | 12 weeks | Y | -- | YES | 20% | 10% | 70% |
| Modelling and Simulation | MTH3024 | 3 | 20 | -- | YES | 12 weeks | N | -- | YES | 100% | 0% | 0% |
| Quantum Theory | MTH3032 | 3 | 20 | YES | -- | 12 weeks | N | -- | YES | 30% | 0% | 70% |
| Investigations | AMA3020 | 3 | 20 | -- | YES | 12 weeks | N | YES | -- | 80% | 20% | 0% |
| Dynamical Systems | MTH3021 | 3 | 20 | -- | YES | 12 weeks | N | -- | YES | 30% | 0% | 70% |
| Geometry of Optimisation | MTH4323 | 3 | 20 | YES | -- | 12 weeks | N | -- | YES | 20% | 0% | 80% |
| Quantum Fields | MTH4331 | 3 | 20 | -- | YES | 12 weeks | N | -- | YES | 20% | 20% | 60% |
| Advanced Quantum Theory | MTH4031 | 4 | 20 | YES | -- | 12 weeks | N | -- | YES | 0% | 20% | 80% |
| Topology | MTH4011 | 4 | 20 | YES | -- | 12 weeks | N | -- | YES | 30% | 0% | 70% |
| Mathematical Methods for Quantum Information Processing | MTH4023 | 4 | 20 | -- | YES | 12 weeks | N | -- | YES | 30% | 0% | 70% |
| Quantum Fields | MTH4331 | 4 | 20 | -- | YES | 12 weeks | N | -- | YES | 20% | 20% | 60% |
| Project | AMA4005 | 4 | 40 | YES | YES | 24 weeks | N | YES | -- | 80% | 20% | 0% |
| Survival Analysis | SOR4007 | 4 | 20 | YES | -- | 12 weeks | N | -- | YES | 30% | 10% | 60% |
| Fourier Analysis and Applications to PDEs | MTH4321 | 4 | 20 | -- | YES | 12 weeks | N | -- | YES | 30% | 0% | 70% |
| Practical Methods for Partial Differential Equations | MTH4024 | 4 | 20 | YES | -- | 12 weeks | N | -- | YES | 30% | 0% | 70% |
| Geometry of Optimisation | MTH4323 | 4 | 20 | YES | -- | 12 weeks | N | -- | YES | 20% | 0% | 80% |
| Integration Theory | PMA4004 | 4 | 20 | YES | -- | 12 weeks | N | -- | YES | 30% | 0% | 70% |
| Applied Algebra and Cryptography | MTH4021 | 4 | 20 | -- | YES | 12 weeks | N | -- | YES | 20% | 0% | 80% |
| Project | PMA4001 | 4 | 40 | YES | YES | 24 weeks | N | YES | -- | 80% | 20% | 0% |
| Bayesian Statistics | SOR4008 | 4 | 20 | -- | YES | 12 weeks | N | -- | YES | 20% | 10% | 70% |
| Information Theory | MTH4022 | 4 | 20 | -- | YES | 12 weeks | N | -- | YES | 30% | 0% | 70% |
Notes
At Stage 1 Students are required to take MTH1011,MTH1021, MTH1015 and MTH1025 PLUS two other modules which may be chosen from any of those offered elsewhere in the University. It is recommended that these modules should be SOR1020 and SOR1021.
At Stage 2 Students must chose six Level 2 modules to include MTH2011, MTH2012, MTH2013 and MTH2021. Students should note the importance of taking MTH2031 Classical Mechanics or MTH2014 Group Theory or SOR2002 Statistical Inference, as they are prerequisites for a number of modules at Stage 3.
MTH2010 must be taken by students planning on taken a placement year.
At Stage 3, students must take a combination as approved by the AoS of six Level 3 modules. The choice must include MTH3011 plus either PMA3013 or AMA3020.
Students intending to pursue the Analysis stream should take MTH3021, MTH4321 and PMA3013.
Students intending to pursue the Algebra stream should take MTH3012, MTH3022 and PMA3013.
Students intending to pursue the Quantum stream should take MTH3032 and AMA3020.
Students intending to pursue the Modelling stream should take MTH3023 and AMA3020.
Stage 4, students must take a combination as approved by the AoS of Level 4 modules to include either project module AMA4005 or PMA4001 PLUS FOUR other optional modules, the combination of which is dependant on the Analysis. Algebra, Quantum or Modelling stream as indicated in further information provided by the school each year.
Further information on pre-requisites can be found on Qsis course catalogue.