# Natural Sciences

## Mathematics and Computing: Integrative Tools for Natural Sciences (2021/2)

Back
Module Title Credit Value Mathematics and Computing: Integrative Tools for Natural Sciences 30 NSC1002 Dr David Horsell
Duration: Term 1 2 3
No. of weeks 11 11
 Number students taking module (anticipated) 60
Module description

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.

Module aims

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.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

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

SYLLABUS PLAN - summary of the structure and academic content of the module

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

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning and Teaching ActivitiesGuided independent studyPlacement / study abroad
1191810
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
CategoryHours of study timeDescription
Scheduled Learning and Teaching55Lectures (two hours a week in Term 1, three hours a week in Term 2)
Scheduled Learning and Teaching44Programming workshops (two hours a week in Term 1 and in Term 2)
Scheduled Learning and Teaching20Tutorials, surgeries and feedback sessions
ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of assessmentSize of the assessment (eg length / duration)ILOs assessedFeedback method
14 x problem sets  mix of mathematics and computer science questions1 hour per set1-2, 6-9, 11Oral and solutions on ELE
SUMMATIVE ASSESSMENT (% of credit)
CourseworkWritten examsPractical exams
60400
DETAILS OF SUMMATIVE ASSESSMENT
Form of assessment% of creditSize of the assessment (eg length / duration)ILOs assessedFeedback method
Problem set 155 hours1-2, 6-11e/written assessment, then discussed in tutorials/workshops
Problem set 255 hours1-2, 6-11e/written assessment, then discussed in tutorials/workshops
Problem set 355 hours1-2, 6-11e/written assessment, then discussed in tutorials/workshops
Problem set 455 hours1-2, 6-11e/written assessment, then discussed in tutorials/workshops
Problem set 555 hours1-2, 6-11e/written assessment, then discussed in tutorials/workshops
Problem set 655 hours1-2, 6-11e/written assessment, then discussed in tutorials/workshops
Programming exercises1010 x 15 minutes2-5, 7-10, 12in-class marking with oral feedback
Programming project105 hours2-5, 7-10, 12Individual form
Mid-term test101.5 hours1, 3, 5, 7-9, 11Marked, then discussed in tutorials
Final examination402 hours1, 3, 5, 7-9, 11Marked, collective feedback via ELE and solutions
DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original form of assessmentForm of re-assessmentILOs re-assessedTimescale for re-assessment
Problem sets, programming exercisesContinuous assessment (problem sheet with a programming exercise) AllAugust/September assessment period
Final examination and mid-term testWritten examination 1, 3, 5, 7-9, 11August/September assessment period
RE-ASSESSMENT NOTES

If deferred, both forms of re-assessment must take place with the continuous assessment counting for 60% of the overall mark, and the written examination counting for 40% of the marks. If referred in the final exam only, only the written exam must be taken. If referred in all, both re-assessment components must be taken and a mark of 40% achieved in both.

The mark given for a re-assessment taken as a result of referral will be capped at 40%. The mark given for a 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

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of information that you are expected to consult. Further guidance will be provided by the Module Convener

• 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.
Module has an active ELE page?

Yes

Web based and electronic resources
Other resources

 CREDIT VALUE ECTS VALUE 30 15
PRE-REQUISITE MODULES None NSC1003 Foundations in Natural Science, NSC1004 Experimental Science, NSC1005 Frontiers in Science 1
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING? 4 No 01/06/2012 21/06/2017
KEY WORDS SEARCH Mathematics, computing, natural sciences, differential equations, Python