The module covers the basic manipulative skills in mathematics which are required by students studying a scientific discipline. The module begins with a review of arithmetic skills, before illustrating how algebraic expressions can be manipulated and rearranged. This includes exploration of fractions, powers, brackets, factors etc.

The concept of a function is introduced by investigating graphical techniques and then re-enforced by applying many of the algebraic methods introduced at the start of the module. The properties and graphs of a range of functions are analysed including polynomials, exponentials and trigonometric functions, with a range of examples explored.

Prerequisites:  GCSE Mathematics or its equivalent

• Manipulate arithmetical and algebraic expressions, and use these techniques to solve various problems
• Recognise polynomial, reciprocal, exponential and logarithmic functions. Recall and determine some of their important properties and sketch their graphs
• Apply methods from algebra and calculus to sketch graphs of functions, determine inverse functions and to solve additional problems
• Define the trigonometric functions, sketch their graphs and apply their properties to solve a range of mathematical problems.
• Clearly present and communicate mathematical content  relating to science.

22 - 50 minute lectures: Two lectures each week are used to present the theory together with examples and applications

11 - 50 minute tutorials: The weekly tutorials provide further opportunity for students to tackle problems and discuss any aspects of the material introduced during the lectures.

Handouts will be provided containing essential parts of material and students are expected to add their own notes and solutions to examples. Opportunity will be provided to students in lectures to attempt and discuss mathematical problems. Students are also expected to undertake at least 40 hours private study including preparation of worked solutions prior to the tutorial classes. Further resources will also be made available via Learning Central.

Numeracy – Reinforcement of essential foundations of arithmetic

Graphical Representation – Production of accurate graphs of some functions

General problem solving – Application of the mathematics introduced to solve simple problems in science

Communication – To produce clear and accurate written work communicating how results are obtained

Summative assessment for the module will take the form of continuous assessment and written examination.

The continuous assessment will be in two parts:

1. Group Presentation and Report
2. Individual homework exercise

This is designed to be formative, in that feedback will be provided and items discussed to aid progress towards achieving the learning outcomes of the module. Further formative assessment will also be provided via weekly tutorial exercises.

The major component of the summative assessment is the written examination. The examination is structured into two sections of equal weight. Section A contains a number of (short) compulsory questions and is intended to assess a student’s ability on the methods introduced. Section B presents a choice (two from three questions) of more detailed questions and tests both basic skills and their application.

• Numbers
  • integers, rationals and reals.
• Algebra
  • simplification of algebraic expressions.
  • Factorization of polynomials.
  • Functions and formulae including change of subject.

• Functions
  • including linear, quadratic, cubic functions.

• Solving equations
  • including geometrical interpretation of the intersection of lines and curves

• Exponential and logarithmic functions
  • indices, logarithms and their properties.

• Trigonometry
  • definition of trigonometric functions
  • Pythagoras theorem
  • solving trigonometric equations

Foundation Mathematics (3rd Ed), Booth, D. J., Pearson, 1998