Synopsis for Exploring Mathematics with MuPAD

Michaelmas Term

Lectures: Week 2.
Demonstrating sessions: Weeks 3–8 of Michaelmas Term and weeks 1–2 of Hilary Term. Each student will have 4 two-hour sessions.

Hilary Term

Lectures: Weeks 1 and 2.
Demonstrating sessions: These continue into the beginning of Hilary Term in weeks 1–2.
Project help sessions: Weeks 3–8 of Hilary Term. Extra sessions run during weeks 5 and 8 of Hilary Term when project submissions are due.

Overview

Mathematicians (like other professionals) use a wide range of generic computer software: email, word processors, web browsers, spreadsheets, database managers and so on. Most, of the students on the Oxford Mathematics courses will have already used some of these packages, and are encouraged to use the facilities available centrally and in colleges to continue to develop their skills with these during their course.

The use by mathematicians of software developed for handling specific sorts of mathematical problems, especially numerical ones, is well-established; lecture courses in later years will, where appropriate, introduce students to some of these applications.

Increasingly, many mathematicians use general purpose mathematical software packages which include tools for both symbolic and numerical computation. Such a package can be used a graphing calculator, as a “scratchpad” for exploring a mathematical concept, as a handbook of mathematical functions and integration rules, or as a tool for verifying the correctness of a calculation done “by hand”.

The virtue of such a system is its flexibility. In this introductory course, students will explore the above ideas using MuPAD, a computer algebra system which makes up part of the popular MATLAB software package.

Learning Outcomes

The aim of the course is to demonstrate the potential of general purpose mathematical packages; to allow students to gain familiarity with one of them (MuPAD); to provide a tool which can be used in the later years of the course.

By the end of Week 2 of Hilary Term students should be able to

1. edit, save, and use MuPAD notebooks;
2. manipulate expressions in MuPAD, and plot simple graphs using MuPAD;
3. write simple programs in MuPAD for solving problems in algebra, calculus, and applied mathematics.

By the end of Hilary Term students should be able to

1. use the“Linalg” Linear Algebra package within MuPAD;
2. complete two or three small projects exploring some mathematical problems using MuPAD;
3. provide reports on the projects in the form of well-commented MuPAD notebooks.

Synopsis

The Michaelmas Term work consists of:

Using the workstation: accounts, passwords, logging in/out. Introduction to computer algebra systems: MuPAD; notebooks. Using MuPAD as a calculator. Manipulation of algebraic formulae. Sets, arrays, tables and lists. Solution of algebraic equations. Approximation. Linear Algebra in MuPAD. Calculus in MuPAD. Simple graphics. Elementary programming in MuPAD. Fourier series in MuPAD, and exploring convergence.

The Hilary Term work is based on a menu of mathematical projects; the list will be printed in the second part of the MuPAD Course Manual.

Access to the system

Undergraduates use the workstations in the Statistics Department Computer Laboratory. For this they will need their university account(the same login details as for their Nexus email account). Arrangements will be made to ensure that, as far as possible, they are allocated an account before MT lectures begin.

Students may also access the system through college or individual computers; for details of how to do this they should consult the computing support at their own college. MuPAD is a part of MATLAB and may also be installed and used on personally-owned computers under the University's site license. Information on downloading MATLAB and MuPAD can be found at http://www.maths.ox.ac.uk/help/software/matlab. To access this page students will need to login to the website using their University account.

Teaching and Assessment

The course deliberately relies heavily on self-teaching through practical exercises. A manual for the course and examples to be worked through will be provided, with a variety of specimen worksheets. You will have access to help and advice from demonstrators.

You will be timetabled for 4 sessions of 2 hours each in the Statistics Department fortnightly in Michaelmas and Hilary Terms. You will work alone on the projects in Hilary Term, demonstrator sessions will be held daily for your assistance.

The Moderators in Mathematics are required, when assessing the performance of candidates, to take into account your work on the MuPAD course. For further information, see the section on examinations in the Undergraduate Handbook.

Academic Honesty

The description of each HT project gives references to books covering the relevant mathematics; if you cannot understand some of this then you are free to consult your tutors or others about it, but not about the project itself. You may discuss with the demonstrators and others the techniques described in the Michaelmas Term Students' Guide, and the commands listed in the Hilary Term Students' Guide or found in the MuPAD Help pages. You may ask the MuPAD Coordinator to clarify any obscurity in the projects. However, it is important that the projects be your own unaided work. You will be asked to make a declaration to that effect when you submit them. At the beginning of the year you will also be asked to sign a declaration stating that the work you will do and submit will be your own unaided work.

Exploring Mathematics with MuPAD: Students' Guide (Mathematical Institute Notes — available from reception).