Much of modern science uses multi-dimensional arrays of numbers to represent vectors, matrices, tensors etc., either individually or as fields. Several courses offered by the University Computing Service teach how to use and to manipulate these in various computer languages (C++, Fortran, Python) and applications (Matlab, Mathematica). However, we only teach the computing element of this and we do require that students of these courses already understand the mathematics.
These topics are no longer part of the core A-level mathematics syllabus. It is essential to learn the basic mathematics before attending courses on using them on a computer. There are two levels of knowledge needed, depending on the course.
For the course Introduction to Modern Fortran , you need to know:
The simplest (and cheapest) reference that we have found that covers this seems to be: A Level Mathematics for Edexcel: Further Pure FP1 (ISBN 9780435519230)
For the course Matlab: Linear Algebra, you need to know:
Any of the following resources will cover this:
There are several other A-level books that include the material, but be careful, because many books cover only the core Mathematics A-level syllabus and not Further Mathematics.