Natural Sciences

Mathematical and computational methods play an increasingly important role in understanding the complex observational data that are used to understand problems across the natural sciences, for example developmental biology, biochemistry, physics and medicine. These systems are often best explored using the power of mathematical and computational tools and the purpose of this module is to introduce some of the fundamental techniques and tools that are used to study these problems.

This is a compulsory module for students on the BSc/MSci Natural Sciences, and is not open to students on other programmes.

The intentions of the module are to teach fundamental mathematical and computational techniques and to demonstrate their relevance to the natural sciences through specific examples from biology, biochemistry, physics and medicine throughout the module.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

• 1. Understand and apply a variety of mathematical techniques including linear algebra, calculus and statistics
• 2. Write, compile, test, and debug a computer program
• 3. Explain how a program written in a procedural language is translated into a form that allows it to be executed on a computer
• 4. Document software to accepted standards
• 5. Use a high-level programming language for basic numerical analysis, simulation and data visualisation

Discipline Specific Skills and Knowledge:

• 6. Formulate problems from natural sciences in a mathematically rigorous manner
• 7. Systematically break down a problem into its components
• 8. Understand and choose appropriate programming techniques

Personal and Key Transferable/Employment Skills and Knowledge:

• 9. Apply mathematical and computational methods in a multidisciplinary setting
• 10. Work co-operatively and develop time-management strategies to meet deadlines for work
• 11. Analyse a problem and synthesise a solution
• 12. Use technical manuals and books to interpret specifications and technical errors

In the first part of the module, lectures will be used to introduce the fundamental aspects of mathematics and computing (one for each discipline per week). In the second part of the module you will have sufficient knowledge to cover integrated material. Throughout the module, workshops will introduce the basic tools and environment for programming and tutorials will be used to support the mathematical concepts that are being taught.

Mathematics:

Part I. Introductory material, summary overview and background
Part II. Linear algebra and complex numbers
Part III. Sequences, Series, Limits and Convergence
Part IV. Calculus and Differential Equations
Part V. Multivariable calculus and vector calculus
Part VI. Probability and Statistics

Computing:

Part I. Programming overview and introduction to Python as a language (statements, comments and simple arithmetic operations).
Part II. Variables, scope and data types
Part III. Control flows, conditionals, loops and iterations
Part IV. Functions, debugging and testing
Part V. Input and Output
Part VI. Scientific computing in Python

Deferral – if you have been deferred for any assessment,you will be expected to complete relevant deferred assessments as determined by the Natural Sciences Mitigation Committee. If there are valid reasons why you cannot submit one or more of the original summative assessments, your assessment mark may be set aside or substituted by proxy mark as agreed by the Mitigation Committee and as described in the Mitigation section of the Assessment Handbook. The mark given for re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment.

Referral – if you have failed the module overall (i.e. a final overall module mark of less than 40%) you will be required to undertake both re-assessments as described in the table above. The mark given for a re-assessment taken as a result of referral will count for 100% of the final mark with each re-assessment counting for 50% of the total referred mark. The mark given for a re-assessment taken as a result of referral will be capped at 40%.

Reading list for this module:

• Engineering Mathematics. K. A. Stroud. Palgrave Macmillan
• Advanced Engineering Mathematics. K. A. Stroud. Palgrave Macmillan
• Core Maths for the Biosciences. M. B. Reed. Oxford University Press
• Elementary Statistics. Mario F Triola. Pearson.
• A Primer on Scientific Programming with Python (Texts in Computational Science and Engineering). Hans Petter Langtangen. Springer.

Yes

• ELE page: http://vle.exeter.ac.uk/course/view.php?id=3803