# 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. A range of mathematical and statistical techniques, including ordinary differential equations, local stability analysis, coupled differential equations, hypothesis testing, linear and non-linear regression, matrix algebra, basic probability and probability distributions are introduced in the context of biological systems. The lectures are supplemented by practical classes using modern computing methods, focusing on the statistical programming language R.

It is highly desirable that students have continued with mathematics during their sixth form (or equivalent) studies. A certain level of prior knowledge is assumed, particularly a basic knowledge of calculus, which is required to follow the lectures in the Lent term. For students from England, Wales or Northern Ireland this would most likely have been gained by the study of GCE Mathematics at A Level or the International Baccalaureate (at either Standard or Higher Level). Students without an equivalent level of preparation are required to complete 20-40 hours of preparatory work before they arrive in Cambridge. These students are also given alternative teaching and support during the final half of the Michaelmas term in order to develop necessary mathematical skills: these students will have a correspondingly smaller choice in the examination.

Any student who is concerned about their background should discuss this with their Director of Studies before or soon after arriving in Cambridge. In addition to the alternative teaching provided centrally, Colleges should also be able to make extra support available (e.g. extra supervisions). Please note that prior study of probability and/or statistics is not necessary; all necessary concepts are taught from scratch.

# Programme Specification: Part IA Mathematical Biology

This course is taught by the Faculty of Biology and is intended for biologists.

## 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 equations, mathematical modelling, matrix algebra, probability and statistical methods;
- to introduce students to the use of R for the analysis of biological processes and data, including simple computer programming.

## 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 (for aims 1-3 and learning outcomes 1-3);
- two assessed exercises, based on the lectures and practicals (for aims 1-4 and learning outcomes 1-4).

## Courses of Preparation

**Highly Desirable:** 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.