# Subject Summary: Part IA Mathematical Biology

This course provides an introduction to mathematical biology. It involves mathematical, statistical, and computing methods, and is designed to approach these three elements from an integrated biological point of view. The underlying theme is the modelling and analysis of populations of molecules, cells, and organisms. The principal biological topics are: growth and decline of populations; physiological modelling, statistical methods, matrix algebra and ecological and epidemiological modelling. A range of mathematical and statistical techniques, including ordinary differential equations, local stability analysis, coupled differential equations, hypothesis testing, linear regression, and probability distributions are introduced in the context of biological systems. The lectures are supplemented by practical classes using modern computing methods.

Mathematical Biology is designed for students who have continued with mathematics during their sixth form (or equivalent) studies, and a certain level of prior knowledge is assumed. For students from England, Wales or Northern Ireland this would most likely have been gained by the study of GCE Mathematics at A Level. Students who have only taken mathematics as far as AS Level would be well advised to carefully consider taking Elementary Mathematics for Biologists.

Experience proves that students with other qualifications can perform very well on this course. In particular students who have studied the International Baccalaureate, Scottish Highers, the German Abitur and other similar qualifications have all performed outstandingly in the past. However students who do not have a thorough grounding in calculus (including differentiation of polynomials and other simple forms such as trigonometric functions; the product and quotient rules; the chain rule; and integration at least as far as integration by substitution and parts) and algebra (including exponentials and logarithms) are unlikely to succeed.

Any student who is concerned about their background should discuss this with their Director of Studies soon after arriving in Cambridge. In borderline cases it is possible that their College will be able to make extra support available (e.g. extra supervisions). Students can also discuss their background with the lecturer and/or practical demonstrators during the first week or two of term. Please note that prior study of statistics is definitely NOT necessary for this course; statistics is less than a quarter of the material you will be learning, and we teach all necessary concepts from scratch.

# Programme Specification: Part IA Mathematical Biology

This course is taught by the Faculty of Biology and is intended for biologists who have taken mathematics at A level (or have an equivalent level of preparedness, including a grounding in calculus).

## Aims

- to introduce students to the application of mathematical modelling in the analysis of biological systems including populations of molecules, cells and organisms;
- to show how mathematics, statistics and computing can be used in an integrated way to analyse biological systems;
- to develop students' skills in algebraic manipulation, the calculus of linear differential and difference equations, mathematical modelling, matrix algebra and statistical methods;
- to introduce students to the use of mathematical and statistical computer packages for the analysis of biological processes.

## Learning outcomes

At the end of the course, students should:

- have an enhanced knowledge and understanding of mathematical modelling and statistical methods in the analysis of biological systems;
- be better able to assess biological inferences that rest on mathematical and statistical arguments;
- be able to analyse data from experiments and draw sound conclusions about the underlying processes using their understanding of mathematics and statistics;
- be aware of the use of computers to assist them in studying mathematical functions and carrying out statistical tests.

## Teaching and Learning Methods

These include lectures, supervisions, and computer practicals.

## Assessment

Assessment for this course is through:

- one unseen written examination, based on lecture material and the computer workshops (for aims 1-3 and learning outcomes 1-3);
- two assessed exercises, based on the lectures, examples classes and practicals (for aims 1-4 and learning outcomes 1-4).

## Courses of Preparation

**Essential:** A Level Mathematics. (For 2017 entry A Level Mathematics will be Highly Desired. Students without A Level Mathematics will need to develop their skills to follow this course. Supporting provision will be made, although applicants should note self-stufy of mathematical topics will be required. 20-40 hours of self-study is estimated.)

## Additional Information

Further information is available on the Course Websites pages.