Programme Specification: M.Sc./PG Dip Mathematical Modelling and Scientific Simulation Course Outline Advanced scientific computing plays a key role in a vast range of modern scientific and technological developments, from the imaging algorithms in digital cameras to methods for probing oil reservoirs, from design of airfoils and ships hulls to deciding the location for grafts in heart bypass surgery, from molecular modelling techniques for designing drugs to weather prediction and predicting climate change. Simulation opens up an extraordinary virtual laboratory, bringing everything from the nanoscale to the cosmological scale into focus. Excellent careers in both industry and academia await those with the right mix of modelling and computational skills, coupled with understanding at an advanced level of an application area in engineering or science. This degree aims to provide such a balanced perspective by combining specialized training in computational mathematics, parallel computing, and scientific algorithms with a focussed exposure to modern applications research in a choice of several areas.

Pathways The taught part of the programme is identical for all students. Exception can be made for students who have graduated with B.Sc. in Mathematics from Leicester and have taken some of the modules within this programme as part of their undergraduate degree. In this case the students can take an optional module of Advanced Readings in Applied Mathematics instead. Students who satisfactorily complete the taught part will be awarded a Postgraduate Diploma. Students who complete at least half of the taught programme may be awarded Postgraduate Certificate. Those who wish to be awarded the M.Sc. and, after the midsummer examinations, qualify for doing so, can undertake a full-time individual project, leading to the submission of a dissertation by the middle of September. Progression rules are detailed in full below.

Programme Specification M.Sc./PG Dip in Mathematical Modelling and Scientific Simulation Entry requirements: Candidates should have, or expect to gain, at least a good second class honours B.Sc. degree or qualification of equivalent standard recognised by the University in a subject with a substantial element of Mathematics. Because applications are treated on an individual basis, alternative qualifications, including work experience, may be considered.

Aims and Objectives • To teach students a range of fundamental skills in modelling and simulation methodology, numerical methods, algorithms and software usage that will help them to achieve ambitious careers in industry or academia. • To enable students from a variety of backgrounds, including mathematics, computer science, engineering, geosciences, and physics, to develop their own projects on algorithms and scientific computing related to problems in forefront areas such as materials modelling, molecular simulation, computational fluid dynamics, parallel computing, and signal processing. • To secure knowledge and research skills for taking their studies further to do a Ph.D., in case they complete the full M.Sc..

Programme quality indicators QAA subject review [www/qaa.org/.]

Course Content and Structure The course consists of 120 credits of taught material in eight modules of 15 credits each: Semester 1: MA7311 Dynamical Modelling and Simulation MA7521 Wavelets and Signal Processing MA7541 Methods in Molecular Simulation CO7104 C++ Programming and Advance Algorithm Design Semester 2: MA7377 Operational Research MA7511 Computational Methods for Partial Differential Equations MA7522 Data Mining and Neural Networks MA7711 Research Presentation Some of the teaching of these modules will be shared with the corresponding Level 3 and Level 4 modules of the BSc and MMath in Mathematics. Option: Students who have graduated with a B.Sc. in Mathematics from Leicester and have taken some of the modules within this programme as part of their undergraduate degree can take an optional module MA7712 Advanced Readings in Applied Mathematics MA7501 Individual Project (60 credits). After Midsummer examinations, a project is undertaken full-time, leading to an oral presentation and the submission of a dissertation by the middle of September. Typical length of the dissertation is about 15000 words, but no precise minimum length is prescribed, as this will depend on the particular topic chose, the amount of software development involved, and the applications component. The project is expected to contain some element of original work. Students will typically complement the foundational material of the first two terms with practical, applied work during the project.

Subject and Professional Skills Intended Outcomes Knowledge

Teaching Methods

Examinations, coursework, oral presentations, computer demos, project plan, and dissertation.

Lectures, computer practicals, coursework assignments.

Examinations, coursework, oral presentations, computer demos, project plan, and dissertation.

Research Presentation module, lectures and computer labs.

Oral presentations, computer demos, project plan, and dissertation.

Independent research, lectures, coursework in modules.

Oral presentations, participation in group discussions, essays/demos, project plan, and dissertation.

Research Presentation module, and supervision for project.

Oral presentations, computer demos, project plan, and dissertation.

Research Presentation module, lectures, project supervision.

Oral presentations, project plan, and dissertation.

C++ Programming module and computing assignments in other taught modules.

Computer practicals and examinations.

Advanced knowledge of a range of mathematical topics in scientific computing. Integration of knowledge across subjects.

Concepts Computational and mathematical modelling, mathematical abstraction, generalisation, justification, and precision.

Techniques Programming of mathematical algorithms, mastery of research methods, project planning.

Critical Analysis Ability to apply understanding of concepts and techniques with independence, rigour & selfreflectivity.

Presentation Ability to organise research material and or technology demonstration in a manner appropriate to the medium that is to be assessed; to distinguish between relevant and non-relevant material; to write-up and deliver oral reports on findings to a professional standard; to engage in scientific discussion with peers.

Appraisal of evidence Ability to apply a numerical method for the solution of some real world problem. Ability to assess the efficacy of method used, both qualitatively and quantitively. Ability to assess the quality of a presentation, both oral and written.

Programming Mathematical Algorithms Ability to programme sophisticated mathematical algorithms.

How demonstrated

Independent research and lectures

Transferable Skills Intended Outcomes Managing Learning Identifying a credible research project, drawing up a realistic research time-table, reflecting on and ‘writing up’ results

Research Skills Progressive improvement in the ability to locate, organise and marshal evidence, report on findings, analyse complex ideas and construct sophisticated critical arguments.

Working Relationships Knowing how and when to draw on the knowledge & expertise of others.

Data Presentation Ability to present research clearly and effectively using appropriate IT resources.

Communication Skills Ability to deliver oral presentations to professional standard; ability to respond to questioning; ability to write cogently and clearly.

Programming Skills Ability to programme in a high level language.

Teaching Methods

How demonstrated

Individual project and coursework in taught modules.

Oral presentations, completion of coursework, project plan, and dissertation.

Through progressive modes of assessment, through the Research Presentation module, to the project plan, culminating in the dissertation.

Oral presentations, demos, project plan, and dissertation.

Project supervision, lectures, group projects in taught modules.

Project reports, dissertation.

Research Presentation module, presentations during taught modules.

Oral presentations, demos, and dissertation.

Research Presentation module, presentations during taught modules, lectures and seminars.

Oral presentations, demos, project plan, and dissertation.

C++ Programming module, computing assignments in other taught modules, computer labs

Computer practicals.

Progression rules Module Assessment Taught modules are assessed based on the combination of continuous assessment (problem sets and computer projects) and examination. Details of assessment for each module are described in the corresponding module forms. Research Presentation module is assessed Pass/Fail based on continuous assessment. The Individual Project is assessed based on the oral presentation and dissertation. Degree Classification Distinction To be awarded a distinction, a candidate will have achieved the specified learning outcomes of the programme to an excellent or very high standard, displayed a very high command of the subject and technical and analytical skills and demonstrated independence of thinking and excellent research potential. Merit To be awarded a pass with merit, a candidate will have achieved the specified learning outcomes of the programme to a very good standard, displayed a high command of the subject and technical and analytical skills and demonstrated independence of thinking and very good research skills. Pass To be awarded a pass, a candidate will have achieved the specified learning outcomes of the programme to a satisfactory standard and displayed a sound command of the subject and technical and analytical skills and demonstrated independence of thinking and sound research skills. Degree assessment schemes Schemes describe the criteria that normally apply in assessing performance. Board of Examiners retain the right to make decisions notwithstanding the published schemes in exceptional circumstances providing it is to a student’s advantage and notes of any such decisions are made in the minutes of the Exam Board’s proceedings. Masters To be awarded a Master’s Degree a candidate must: (i) obtain a mark of 40% or more in each of the taught modules; (ii) obtain a credit-weighted average mark from 165 credits of not less than 50% and a Pass in Research Presentation; (iii) obtain a mark of 50% or more in the Individual Project; (iv) satisfactorily complete all coursework requirements. To be awarded a Master’s Degree with merit a candidate must: (i) obtain a mark of 40% or more in each of the taught modules; (ii) obtain a credit-weighted average mark from 165 credits of not less than 60% and a Pass in Research Presentation; (iii) obtain a mark of 60% or more in the Individual Project; (iv) satisfactorily complete all coursework requirements. To be awarded a Master’s Degree with distinction a candidate must: (i) obtain a mark of 40% or more in each of the taught modules; (ii) obtain a credit-weighted average mark from 165 credits of not less than 70% and a Pass in Research Presentation; (iii) obtain a mark of 70% or more in the Individual Project; (iv) satisfactorily complete all coursework requirements. Borderline candidates may be awarded a distinction at the discretion of the Board of Examiners. Borderline candidates are defined as those with a credit-weighted average of between 67.5% and 70%

Postgraduate Diploma To be awarded a Postgraduate Diploma a candidate must: (i) obtain a mark of 40% or more in each of the taught modules; (ii) obtain a credit-weighted average mark from 105 credits of not less than 50% and a Pass in Research Presentation; (iii) satisfactorily complete all coursework requirements. To be awarded a Postgraduate Diploma with merit a candidate must: (i) obtain a mark of 40% or more in each of the taught modules; (ii) obtain a credit-weighted average mark from 105 credits of not less than 60% and a Pass in Research Presentation; (iii) satisfactorily complete all coursework requirements. To be awarded a Postgraduate Diploma with distinction a candidate must: (i) obtain a mark of 40% or more in each of the taught modules; (ii) obtain a credit-weighted average mark from 105 credits of not less than 70% and a Pass in Research Presentation; (iii) satisfactorily complete all coursework requirements. Borderline candidates may be awarded a distinction at the discretion of the Board of Examiners. Borderline candidates are defined as those with a credit-weighted average of between 67.5% and 70% Postgraduate Certificate To be awarded a Postgraduate Certificate a candidate must: (i) obtain a credit-weighted average from 60 credits of not less than 50%; (ii) satisfactorily complete all coursework requirements.

Rules for re-sits and resubmissions At the discretion of the Board of Examiners, students may be permitted to re-sit any module where they have obtained less than 40%. Students who have passed the taught component of the M.Sc. as specified above will not be allowed to re-sit any module. A student may re-sit a module only once. A re-sit/resubmission of the coursework component of a module will normally not be allowed. When deciding whether a student, who has re-sat some modules, has passed the taught component of the M.Sc., the Board of Examiners will use the higher of the marks in each of the two attempts at a re-sat module as the mark for that module. Notwithstanding the above, on the candidate's final transcript, the mark reported for a re-sat module will be capped to a maximum of 50%. If the re-sit mark is less than 50% then the higher of the marks in each of the two attempts at a re-sat module will be reported. Re-sits may only be taken when the exam for the module to be re-sat is offered in the following academic year. Following the submission of the dissertation of the Individual Project a candidate may: (i) be awarded the M.Sc. degree; (ii) be deferred for presentational reasons, which usually means that, when any recommended changes are completed to the satisfaction of the Board of Examiners, the M.Sc. is conferred; (iii) be failed and invited to redo a project in the following year with substantial revision or, more likely, a complete change of topic.

2011/12

Department of Mathematics

M.Sc./Postgraduate Diploma in Mathematical Modelling in Biology Period of Registration: One year full-time or two years part-time. Entry Requirements: Candidates should normally have at least a good second class honours degree or its equivalent in mathematics, physics, engineering or computer science. Compulsory

Module Code MA7012 MA7031 MA7032 MA7061 MA7011 MA7022 MA7003 MA7032 MA7001

*

Module Title Scientific Computing Applied Dynamical Systems Generalized Linear Models Topics in Mathematical Biology Computational Methods for Partial Differential Equations Data Mining and Neural Networks Research Presentation Equations of Mathematical Physics Individual Project

Credits 15 15 15 15 15 15 15 15 60

* Compulsory only for degree of M.Sc. Curriculum: In addition to the taught modules candidates for the Masters degree also undertake a dissertation or project on an approved topic. Assessment: The pass mark at postgraduate level is 50%. The details of the assessments for individual modules are set out in the relevant Module descriptions. All programmes within the Department of Mathematics follow Scheme B of the Postgraduate Scheme of Assessment. Qualifications Awarded: (i)

Candidates who accumulate 60 credits from the taught modules and satisfy the examiners in each of the modules will be awarded a Postgraduate Certificate.

(ii)

Candidates who accumulate 120 credits from the taught modules and satisfy the examiners in each of the modules will be awarded a Postgraduate Diploma.

(iii)

Candidates who accumulate 180 credits, satisfy the examiners in each of the modules and submit a satisfactory dissertation/project will be awarded a Masters degree.

Notes: (i) (ii)

Candidates may only be awarded the Postgraduate Certificate, Postgraduate Diploma or the Masters degree. No candidate may be awarded more than one of the above qualifications. The Masters degree may be awarded with merit or distinction in accordance with the relevant scheme of assessment.