# Mathematics Induction

This is a self-guided review of mathematics material that will be useful for the core HetSys training modules, and is designed to be completed at your own pace.

## Objectives

By the end of this session you should be able to:
1. manipulate and carry out operations on vectors
2. manipulate and carry out operations on matrices
3. demonstrate a familiarity with basic linear algebra
4. differentiate and integrate functions
5. solve first-order and higher-order ordinary differential equations
6. solve simple cases of some partial differential equations
7. understand basic ideas of statistics and probability

The material presented here is not intended to be rigorous, but may rather be considered as a pragmatic quick-start guide to the standard of mathematics expected of students enrolled on this course. The Maths for Chemists booklet developed by Birmingham and Leeds also provides a useful refresher (whether or not you consider yourself a chemist!). This list is incomplete, so if while studying you feel you need to brush up on other areas of mathematics, follow the Supporting Material link at the end of the list below.

1. Vectors
2. Matrices
3. Linear vector spaces
4. Differentiation and integration
5. Ordinary differential equations
6. Partial differential equations
7. Probability and statistics
8. Supporting material on other topics can be found from the "Just the Maths" homepage

There is a self-assessment test available to gauge your progress. If you feel sufficiently up-to-date on the maths outlined above, feel free to complete the test now! Otherwise, follow the links to work through each section, and then complete the test.

Acknowledgement: Much of this online material is taken from "Just the Maths", devised by A. J. Hobson, Coventry University. The linear vector spaces and some of the ODE and PDE notes were written by Tiffany Walsh.