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:

- what vectors and matrices are,
- matrix multiplication and transposition, and
- how they are used for coordinate transformations.

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:

- how matrices are used in the solution of linear equations,
- about inverses and their properties, and
- what determinants are and why they matter.

Any of the following resources will cover this:

- The Mathematics course for the Natural Sciences Tripos, part IA, Mathematics for Natural Sciences Tripos. The lecture notes are available via CamTools, course NSTIA 06_07, which is unfortunately not linkable. Note that vectors are taught in the Michaelmas term, and matrices are taught in the Easter term.
- A Level Mathematics for Edexcel: Further Pure FP1 and FP3 (together). A reference to FP1 was given above, and FP3 is ISBN 9780435519223.
- Further Pure Mathematics, Brian and Mark Gaulter, OUP 2001, ISBN 9780199147359.

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.