Module Identifier MA12510 Module Title INTRODUCTORY MATHEMATICAL TECHNIQUES Academic Year 2000/2001 Co-ordinator Dr R S Jones Semester Semester 1 Pre-Requisite GCSE Mathematics at grade C or above. Mutually Exclusive May not be taken at the same time as, or after, any of MA10020 to MA11410, MA12610, MA13610. Course delivery Lecture 22 x 1 hour lectures Seminars / Tutorials 11 x 1 hour example classes Assessment Exam 2-hour written examination 100% Resit assessment 2-hour written examination 100%

General description
The purpose of this module is to introduce some of the basic ideas of mathematics to students without A-level qualifications in Mathematics but who require mathematics in their main subject. The syllabus includes basic set theory; functions and graphs; indices, exponentials and logarithms; rates of growth; recurrence relations, arithmetic and geometric progressions; matrices and determinants, solution of linear equations and elementary descriptive statistics.

Aims
To introduce students to some of the basic concepts of mathematics and to develop their manipulative skills.

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

• explain the difference between integers, rational and irrational numbers and work in different number bases;
• manipulate numbers and symbols using the operations of algebra;
• simplify algebraic expressions and inequalities;
• solve linear and quadratic equations algebraically;
• define a function and its domain and range;
• differentiate polynomials, logarithmic and exponential functions.

Syllabus
1. REPRESENTATION OF NUMBER: Natural numbers, integers, fractions, decimals, different bases, fixed and floating point, the laws of indices, exponents, logarithms.
2. ALGEBRA: Rules of algebra, simplification of algebraic expressions, factorization, inequalities, the solution of linear and quadratic equations.
3. COMPLEX NUMBERS: Real and imaginary parts, modulus and argument, representation on the Argand diagram.
4. THE CONCEPT OF FUNCTION: Linear and quadratic functions, exponential and logarithmic functions, trigonometric functions and inverse functions.
5. CALCULUS: Introduction to curves, tangents and the derivative of a function, the rules of differentiation, rates of change.