# Essential Mathematics

## Overview

• Credit value: 30 credits at Level 3
• Convenor and tutor: to be confirmed
• Assessment: coursework consisting of frequent short tests and problem-based homework (100%)

## Module description

In this module we will reinforce your knowledge and ability with key mathematical techniques, so that you can enter Year 1 of the BSc programme with a very strong set of skills. The module will revise and extend crucial topics including algebra, functions, logarithms and basic differentiation.

### Indicative syllabus

• Numbers and symbols: fractions, percentages and indexes and weighted average; arithmetic operations on fractions; parentheses in arithmetic expressions; surds; estimation of arithmetic expressions
• Algebra: evaluating algebraic expressions; rules of indices; collecting terms; expansion of brackets; factorizing; simplifying expressions involving rational functions; simplifying radicals; solving quadratics including parametrized equations; solving linear and quadratic inequalities including link with graphs solving simultaneous equations
• Logarithms: computing logs; manipulation of expressions involving logs; solving logarithmic equations; graphs of logarithmic and exponential functions
• Functions: notation of sets; using 'set builder notation'; definitions such as domain and range; evaluating functions including at parameters; graphing; relationship with graph; equations of lines
• Differentiation: derivative of polynomial functions and exponential functions; rules of differentiation; product, quotient and chain rules; idea of derivative as gradient of tangent; interpretation of the first and second derivatives; finding maxima and minima; applications to economics and business

## Learning objectives

By the end of this module, you will have:

• knowledge and understanding of, and the ability to use, essential mathematical techniques
• confidence in manipulating algebraic expressions, particularly simplifying expressions, multiplying out brackets and dealing with exponents
• an ability to solve simultaneous equations and systems of linear equations
• an ability to work with logarithms and exponentials
• an understanding of language around functions, sets and graphs
• an ability to differentiate polynomial expressions and to understand some of the applications of differentiation
• an ability to follow and construct mathematical arguments
• developed a logical and systematic approach to problem solving
• highly developed quantitative skills.