Module Identifier MA10410 Module Title SYMBOLIC COMPUTATION FOR MATHEMATICIANS Academic Year 2000/2001 Co-ordinator Dr T P McDonough Semester Semester 1 Pre-Requisite A-level Mathematics or equivalent. Course delivery Lecture 11 x 1 hour lectures Practical 11 x 2 hour practical classes Assessment Exam 2 Hours (practical open book examination) 50% Assignment 5 assignments (fortnightly through the course). 50% Resit assessment 2 Hours Continuous assessment passed: same format as above; otherwise 2-hour practical examination (as above). 100%

General description
The aim of this module is to create an awareness of the use of computers in the investigation of mathematical problems. This is achieved through a detailed study of the Maple symbolic algebra system. No prior knowledge of computing is required.

Aims
To create an awareness of the use of computers in the investigation of mathematical problems.

Learning outcomes
On completion of this module, a student should be able to:

• use basic Unix operating system commands;
• create and edit mainframe files;
• use the Maple symbolic algebra system to perform computations involving basic expression manipulation, calculus, linear algebra, equation solving and to obtain graphical output using the high quality graphics capability of Maple.

Syllabus
1. THE COLLEGE COMPUTING NETWORK: The Unix operating system. File creation and editing using edt. Use of the various printer services. Saving data generated by an interactive computing session. Commands with input from a file and output to a file.
2. INTRODUCTION TO MAPLE: Maple as a simple interactive calculator. Basic language entities: numbers, names, strings. Expressions, simplification and evaluation. Assignments.
3. POLYNOMIALS: Expanding, factorising, finding coefficients, remainders and quatients. Sequences, lists and sets. General expression manipulation, substitution.
4. BASIC CALCULUS: Differentiation. Integration, indefinite and definite. Ranges in Maple. Controlling the accuracy of approximate calculations. Taylor expansions.
5. FUNCTIONS AND GRAPHS: Simple one-line functions in Maple. 2-dimensional plotting facilities: X-Maple. Graphs of functions.
6. EQUATION SOLVING: Solutions of algebraic and transcendental equations, exact and approximate.
7. MORE ADVANCED FUNCTIONS: Boolean expressions. Selection statements. Repetition statements. The Maple procedure definition. Recursive procedures.
8. FURTHER TOPICS: Selected functions from Maple packages.