# Mathematics

## Module summary

**Module code: **MATH0647

**Level: **0

**Credits: **15

**School: **Engineering and Science

**Department: **Science

**Module Coordinator(s): **

## Specification

### Aims

This course aims to:-

provide foundation Mathematics to support the study of various scientific disciplines;

develop the skills and confidences of students to apply mathematical approaches to scientific problem analysis.

### Learning outcomes

On completing this course successfully you will be able to:

demonstrate a level of confidence and competence in basic numeracy;

evaluate arithmetic expressions using electronic calculators;

demonstrate an awareness of rounding and truncation errors and the use of significant figures and standard form; have used basic ideas of algebra;

transpose algebraic equations; recognise simple equations and be able to construct and solve them for simple problems;

have a working knowledge of logs and indices;

represent data using fine charts, bar charts and histograms;

use statistics and probability in elementary problem solving;

demonstrate a level of competence in basic numerical and statistical techniques.

### Indicative content

1.Basic Number Work

Carry out addition, subtraction, multiplication and division on integers, directed numbers, proper fractions, mixed number and decimal fractions - using electronic calculators or computer where appropriate; apply the priority rules of arithmetic; understand how accuracy is affected in calculations by rounding and truncation, and the use of significant figures, decimal places and standard form; use the calculator to evaluate arithmetic expressions involving adding, subtracting, multiplying and dividing, raising to powers, reciprocals, square roots, numbers in standard form, integer, fractional and negative indices; use the calculator to evaluate scientific formulae and equations.

2. Algebra

Understand the basic ideas and uses of algebra, and the rules of arithmetic as applied to manipulating algebraic terms, algebraic functions and expressions; understand the use of formulae for expression relationships, and manipulate and evaluate such formulae; recognise simple equations, construct and solve them for simple problems; recognise common factors, the HCF, and group terms, using brackets, to identify a common factor; factorise quadratic expressions, and recognise the difference of two squares' expressions; solve a quadratic equation by the method of factorisation; know and use the formula for finding the roots of a quadratic equation; sketch a quadratic function; find its maximum or minimum by graphical means, recognise from its graph whether the roots of a quadratic are real and distinct, equal or complex; understand the meaning of 3n, where n is an integer, and be familiar with the laws of indices; interpret 3q where q is a rational number, and simplify expressions involving roots or rational indices; define a logarithm to any base; convert a simple indicial relationship to a logarithmic relationship and vice versa; interpret the laws of indices as laws of logarithms and change a logarithm from one base to another; apply the rules of logarithms, (and indices) to solve simple logarithmic and indicial equations; solve linear simultaneous equations in two unknowns; solve simultaneously a linear, and a quadratic equation by substitution or graphical means.

3. Functions

Relations and Graphs recognise the occurrence of functions in specified mathematical and physical situations; understand the terms axes and co-ordinates and the identification between number pair and points in a plane; sketch the graph of the functions y = f(x) where f(x) is a linear, quadratic or cubic function; interpret and extract information from graphs of functions modeling physical situations; recognise, in particular, examples of linear functions; define gradient and interpret, and determine their values for a given straight line, and vice versa; explain the effects on straight lines of altering the parameters for gradient and/or intercept; plot and interpret linear and quadratic graphs, graphs of experimental data and practical situations including examples of direct and inverse variation.

4. Statistics representation of data - pie charts, bar charts, frequency distributions and histograms, cumulative frequency curves and median quartiles and percentiles. Introduction to simple statistics - measures of central tendency mean, median, mode, measure of dispersion, frequency curves, ranges, mean deviation and standard deviation; probability, equiprobable events, coin and dice throwing, theoretical/experimental probability, addition of probability. Conditional probability, independent events, multiplication exclusive events, multiplication and use of tree diagrams and probability space.

### Teaching and learning activity

Students will be introduced to concepts in lectures and tutorials but much of the learning will centre round workshops with student-centred work supported by tutors. Lectures/Tutorials will constitute 60% of T & L activity, Workshops 40%.

Learning Time (1 credit = 10 hours)

Contact Hours:

lectures 10

seminars

practical sessions

tutorials 20

other

Private Study 117

Assignments: course work and other forms of assessment:

coursework

laboratory work

examinations 3

other

### Assessment

Short Phase Tests - 60%

6 x 30 mins - GCC

3 x 60 mins - Bromley

A minimum of 3 x 60 mins - NYC, Athens

Coursework - 40%

A minimum of 3 x 60 mins - GCC/Bromley

Scientific Applications.

Homework assignments (a set of exercises to be worked at home and discussed in tutorials) - NYC, Athens.

Pass mark - 40% overall