Course ID 020905

Transferable Skills for Applied Mathematicians

MATH 65740

Credit rating 15 Unit coordinator: Gareth Jones

ECTS credits 7.5

Full year

School of Mathematics Postgraduate Taught

Level 6

FHEQ level ’ Masters/Integrated Masters P4 ’ Marketing course unit overview Note that this course takes place over TWO semesters Hours shown below are contact hours, note that significant work is required outside of these contact hours in order to complete the necessary assignments, etc. Initially students will be taught some essential skills deemed necessary for applied mathematicians. The typesetting language latex will be described and the notion of "How to write mathematics" will be taught and discussed with students carrying out a practical example. A significant proportion of the module will involve working in groups on mathematical modelling problems. Typically these problems will involve one lecture of background material and description of the problem to be modelled. Contact time is then used to work in groups in order to attempt to formulate the problem in mathematical language, do background reading, and then solve the problem by whatever techniques are necessary. In the final session, groups will present their work via a short 15-20 minute presentation. Three modelling problems will be worked on over the duration of the course and students will be assessed on their presentations for each modelling problem. In addition, students will prepare a poster describing their favourite problem. They will present this poster and describe its contents in Semester 2. Speakers invited from industrial collaborators will give lectures focusing on specific aspects of importance to them in their work, e.g. the Fast Fourier Transform, eigenvalue problems, pre-conditioners, non-newtonian fluids, etc. Student will have an opportunity to discuss the mathematics used with the industrial contacts. After students have chosen their research dissertation in the early part of semester 2, their supervisor will provide details of 1 or 2 important papers relevant to their thesis. The student should then study these in detail and write a report on their contents, giving for example a summary of a paper, describing their understanding of the work, describing necessary background material, putting the work in context, describing applications, discussing some simpler examples (e.g. by reducing the dimension of the problem). Codes could also be written, deriving appropriate results and giving examples. In some cases ideas for further work, possible extensions could be proposed.

Course unit overview Note that this course takes place over TWO semesters Hours shown below are contact hours note that significant work is required outside of these contact hours in order to complete the necessary assignments, etc. Initially students will be taught some essential skills deemed necessary for applied mathematicians. The typesetting language latex will be described and the notion of "How to write mathematics" will be taught and discussed with students carrying out a practical example. A significant proportion of the module will involve working in groups on mathematical modelling problems. Typically these problems will involve one lecture of background material and description of the problem to be modelled. Contact time is then used to work in groups in order to attempt to formulate the problem in mathematical language, do background reading, and then solve the problem by whatever techniques are necessary. In the final session, groups will present their work via a short 15-20 minute presentation. Three modelling problems will be worked on over the duration of the course and students will be assessed on their presentations for each modelling problem. In addition, students will prepare a poster describing their favourite problem. They will present this poster and describe its contents in Semester 2. Speakers invited from industrial collaborators will give lectures focusing on specific aspects of importance to them in their work, e.g. the Fast Fourier Transform, eigenvalue problems, pre-conditioners, non-newtonian fluids, etc. Student will have an opportunity to discuss the mathematics used with the industrial contacts. After students have chosen their research dissertation in the early part of semester 2, their supervisor will provide details of 1 or 2 important papers relevant to their thesis. The student should then study these in detail and write a report on their contents, giving for example a summary of a paper, describing their understanding of the work, describing necessary background material, putting the work in context, describing applications, discussing some simpler examples (e.g. by reducing the dimension of the problem). Codes could also be written, deriving appropriate results and giving examples. In some cases ideas for further work, possible extensions could be proposed. Aims To provide the soft skills that are useful and necessary in the working environment both in industry and academia. In particular presentation, writing, communication and teamwork skills. Mathematical modelling skills and practical skills will be gained by working on a variety of applied mathematical problems, experiments and computational problems. Learning outcomes On successful completion of this course unit students will • Be able to write mathematics effectively in latex as both reports and in poster form. • Be able to formulate mathematical models for a variety of problems that arise in the real

world. • Have an understanding and appreciation of how mathematics can be applied and used

in academia, and also the wider scientific world including industry.

. Syllabus • How to write mathematics [4] Lectures on how to present and write mathematics

effectvely. Students will work through a practical example in latex. • What is mathematical modelling? [1] Describes the concept of mathematical modelling.

Formulation of a problem in terms of mathematical language, writing down equations, what to neglect, incorporate?

• Modelling Problem 1 [7] First modelling problem. Lecture given on background material followed by splitting into groups working on formulating the problem (or some aspect of the problem) mathematically and then trying to solve.

• Modelling Problem 2 [7] • Modelling Problem 3 [7] • Invited industry lectures [6] (From various industrial collaborators). Lectures given by

invited speakers on a topic of importance to them. Assessment methods * Individual Poster presentation of one modelling problem: 40%* Paper/literature report: 25%* Modelling group talks: 15%* Attendance: 10%* "How to write mathematics" assignment: 5%* Matlab short project: 5% Feedback methods Tutorials will provide a place for student worked examples to be marked and discussed providing feedback on performance and understanding. Feedback is also provided via return of marked coursework Requisites NONE Available as free choice? N Recommended reading • Handbook of Writing for the Mathematical Sciences, Second Edition, Nicholas J.

Higham, SIAM, 1998 • Learning LaTeX, David F. Griffiths and Desmond J. Higham, SIAM, 1997 • LaTeX: A Document Preparation System, Second Edition, Leslie Lamport,

Addison-Wesley Professional, 1994 • Mathematical Modelling, Jagat Narain Kapur, New Age International Publishers, 1997 • Mathematical modelling: classroom notes in applied mathematics, Murray S. Klamkin,

SIAM, 1987 • Mathematical modelling, John S. Berry and Ken Houston, Edward Arnold, 1995 Scheduled activity hours

Lectures 36

Independent study hours 114 hours

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