Module MATH40515: Mathematical Tools

Department: Mathematical Sciences

MATH40515: Mathematical Tools

Prerequisites

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Corequisites

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Excluded Combination of Modules

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Aims

• To introduce the basic framework of numerical analysis, enabling the student to solve a variety of problems and laying the foundation for further investigation of particular areas in the life sciences; to describe the basic ingredients of decision theory, for individuals and for groups, and to apply the theory to a variety of interesting and relevant problems in the life sciences.

Content

• Introduction: The need for numerical methods.
• Statement of some problems which can be solved by techniques described in this module.
• What is Numerical Analysis? Non-linear equations.
• Errors.
• Polynomial interpolation.
• Numerical differentiation.
• Introduction to decision analysis: utility.
• Uncertainty.
• Statistical decision theory: Bayes decisions

Learning Outcomes

• Utility, value of money, multi-attribute utility.
• Use of data in decision making, statistical decision theory.
• Bisection, Newton-Raphson and Aitken’s methods.
• Rounding and truncation errors.
• Well conditioned and ill-conditioned problems.
• Lagrange form with truncation error. Chebyshev polynomials. Runge’s example of divergence of interpolation sequence.
• Richardson extrapolation

• Specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling and computation.

• Problem solving.
• Self-organisation, self-discipline and self-knowledge.
• Ability to learn actively and reflectively and to develop intuition, the ability to tackle material which is given both unfamiliar and complex.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures will provide the means to give concise, focussed presentation of the relevant subject matter of the module. They will be supported by reference to suitable text books and where appropriate by the distribution of written material or through links on DUO (on-line learning resource).
• Workshops based on the concepts presented will be used as support teaching.
• Problem sheets will be given regularly in lectures to help students gain an understanding of the concepts presented. These will be assessed formatively.
• Problem classes and tutorials based on the application of the concepts presented will be used as support teaching.
• Practicals in which students use the computer package Maple to implement the numerical methods introduced in the lectures.
• Student performance will be assessed summatively through examination.
• Formative assessments will provide the means for the student to demonstrate their acquisition of subject knowledge and the development of their problem solving skills. The tests will also provide opportunities for feedback, for students to gauge their progress, and for the Management Committee to monitor progress throughout the duration of the module.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Problem sheets distributed in lectures.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University