# Introductory Computer Algebra

## Overview

The Department wants students to work towards being
independent learners. As part of the redesign of the
undergraduate programme, it has therefore incorporated the use
of computer
algebra in its teaching.

Computer algebra software can help you learning and doing
mathematics. It may be used to reduce the tedium of extended
calculations, to verify the correctness of hand calculation
and also for exploration of a new topic. It is

*not*a substitute for mathematical thinking. Think about it: if a computer program could solve all mathematical problems, there would be no jobs for people with maths degrees. Note that computer algebra software usually, but not always, gets the right answer.
Computer algebra is embedded in many modules and is used by
lots of lecturers for demonstrations and to ease calculations.
All students studying a Mathematics degree have to do a
project in their
final year, and by learning how to use computer algebra at
an early stage you are more likely to fix concepts practically
and benefit from what it has to offer before you get to your
final year.

## Structure of this module

There will be an initial supervised/guided session at the
beginning of the year, where students will go through a
worksheet showing how computer algebra may be used in the
context of some A-level topics. During the remainder of the
year, from time to time lecturers will demonstrate ways in
which computer algebra may be used to check calculations,
carry out more difficult computations and gain insight into
the material being studied. Lecturers may also set problems to
be solved by students using computer algebra.

## Guides and Lecture notes

CIS Guide 65 - Basic Maple: a Beginner's
GuideThis is the CIS beginner's guide to Maple with a brief overview of how the system works. |

Introduction to Computer AlgebraNotes to get you started, using Maple to illustrate the type of problems you can tackle with computer algebra. |

Finally, the best thing you can do to learn a computer algebra
system is to simply experiment with one of them.

## Getting computer algebra software

There are several general purpose computer algebra systems
available, some for free
(e.g. Maxima
and the graphical
version wxMaxima)
and others for a substantial price
(e.g. Mathematica).
At Durham University we have a site licence for
Maple,
which is available to use on all IT service networked
computers; for more information see
the CIS Maple
page. Once registered and in possession of a campus card,
students who wish to purchase Maple for their own computers
can do so from the CIS service desk for the substantially
discounted price of £15.

These "three M's" can all handle algebra, calculus, linear
algebra, plotting and so on, and have a varying degree of
built-in knowledge about special functions, differential
equations and other more advanced topics. So they will most
likely get you through a lot of material of the first few
years of a maths degree. However, sometimes you may run into a
problem for which none of these general purpose tools are any
good; feel free to contact me if you want to know more about
other options.

## Sample notebooks/worksheets

notebook | Maple | Mathematica | wxMaxima |
---|---|---|---|

tutorial | tutorial.mw | tutorial.nb | tutorial.wxm |

## Which Durham modules use computer algebra?

In Mathematical
Sciences teaching we use Maple in a number of modules,
listed below. Some modules also use MapleTA through DUO.

Core A | MATH1012 |

Data analysis, modelling & simulation | MATH1711 |

Single mathematics A | MATHS1561 |

Core Mathematics B2 | MATHS1041 |

Numerical Analysis II | MATHS2051 |

Differential Geometry III | MATHS3021 |

Approximation Theory & Solutions of ODEs III | MATHS3081 |

Electromagnetism III | MATHS3181 |

Solitons III | MATHS3231 |

Solitons IV | MATHS4121 |

Approximation Theory & Solutions of ODEs IV | MATHS4221 |