Essential mathematics 1
This key introductory module provides a broad and enjoyable foundation for university-level mathematics, but you do require some prior knowledge. It teaches you the essential ideas and techniques that underpin university-level study in mathematics and mathematical subjects such as physics, engineering and economics. You’ll study a range of fundamental topics – including calculus, vectors, matrices and complex numbers – and use mathematical software to solve problems. You’ll also develop your skills in communicating results and defining problems. This is not a module for beginners. Our MathsChoices website (mathschoices.open.ac.uk) contains quizzes, sample material and advice to help you decide if this is the right module for you.
What you will study
There are twelve study units in this module.
In the first two, you’ll revise and extend the basic mathematical knowledge and skills in basic algebra and graphs that should mainly be familiar to you. This revision material should help you identify and fill any gaps in your previous knowledge, and develop your basic mathematical skills to the level that you’ll need in the rest of the module. Much of the material in these two units will be available online, so you can make a start on your revision even before the module begins, if you wish. The first two units also teach you about communicating mathematics, and introduce you to the mathematical software that you’ll use in the module.
In the remaining study units you’ll cover these topics:
- Functions: these provide a means of representing situations where one quantity depends on another. For example, the distance travelled by a car depends on the time that it has been travelling. You need to know about functions before you can study calculus.
- Trigonometry: you’ll revise the relationships between the angles and side lengths of triangles, and the definitions of the trigonometric functions sine, cosine and tangent for angles of any size. You’ll learn many useful properties of these functions, which are used to model a wide range of cyclical phenomena, such as rotating objects, and waves.
- Vectors: these are quantities that have both a size and a direction. You’ll learn about the mathematics of vectors, and how to use them to model a variety of physical quantities, such as speed in a particular direction.
- Calculus: this is one of the most important and widely applicable topics in mathematics. It is concerned with quantities that change continuously, such as the distance travelled by, and the speed of, a moving object. You’ll be introduced to differentiation and integration, and learn how to use calculus to model a range of different situations and to solve problems from areas such as physics and economics.
- Matrices: these are arrays of numbers, which can be manipulated mathematically in various ways. They’re used extensively in both pure mathematics and mathematical applications.
- Sequences: you’ll learn how to work with some commonly occurring types of number sequences, such as those in which each number is obtained by multiplying the previous number by a constant.
- Complex numbers: these form an intriguing set of numbers that includes all the usual numbers, and also many `imaginary’ numbers, such as the square root of minus one. They have many uses in applied mathematics, as well as being the basis of some fascinating pure mathematics.
You’ll work mainly from the module books, which are available in various electronic formats as well as in print. You can view many of the worked examples in the books in an alternative video format, in which tutors work through and discuss the examples. You’ll also use specially-designed software applications to help you understand the concepts taught, and you’ll learn to use a mathematics computer package to solve problems. There are many online interactive practice questions to help you consolidate your learning.
The module includes a large amount of online study material, and requires you to use mathematical software frequently, so you’ll need regular access to a suitable personal computer.
Samples of the study material, including example assessment questions, are available on our MathsChoices website.
You will learn
Successful study of this module should begin to develop your skills in:
- expressing problems in mathematical language
- using mathematical techniques to find solutions to problems
- communicating mathematical ideas clearly and succinctly.
Essential mathematics 1 is designed to be taken either as your first university-level mathematics module or following on from Discovering mathematics (MU123).
Essential mathematics 2 (MST125) is designed to follow on from Essential mathematics 1. Normally, you should have completed this module first. However, if you have plenty of study time and a high level of confidence and fluency with algebraic manipulation you could study both modules in one year.
Alternatively, if you are considering progressing to Mathematical methods (MST224), normally you should have also completed this module.
This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.
This is a key introductory OU level 1 module. OU level 1 modules provide core subject knowledge and study skills needed for both higher education and distance learning, to help you progress to modules at level 2.
Although many of these topics are revised, consolidated and extended in the module, we recommend that you have a working knowledge of:
- arithmetic of whole numbers, decimals and fractions (including negative numbers, powers and roots)
- algebraic manipulation, such as multiplying out brackets, factorising simple expressions, solving linear and quadratic equations, manipulating algebraic fractions and manipulating powers of variables
- percentages, ratio and proportion.
- coordinates of points in the plane, and the equations of straight lines and parabolas.
- geometry of plane figures, such as the sizes of angles, alternate and corresponding angles, the areas of shapes, similar and congruent shapes, and the properties of triangles, rectangles and circles
- geometry of solid figures, such as volumes and other properties of cuboids and cylinders
- simple inequalities
- trigonometric ratios – sine, cosine and tangent
- logarithms and the rules for manipulating them.
A mathematical A-level, or a high grade in GCSE mathematics (or the equivalent), would normally provide this. If you are not familiar with the majority of the topics listed above, we recommend that you study our OU level 1 module Discovering mathematics (MU123) before this module.
Before registering for the module, we recommend you attempt this self-assessment quiz to help assess your prior knowledge and to help you decide if Essential mathematics 1 is the right module for you.
If you have any doubt about the level of study, or about choosing the most suitable mathematics module with which to start, please speak to an adviser or look at our MathsChoices website.
The first two units of the module help you to revise, consolidate and extend the basic mathematical knowledge and skills that are required in the rest of the module. Much of the material in these first two units will be available online before the module begins, and it would be a good idea to start working through it as soon as you can, to make sure that you’re as well prepared as possible for the main work in the module. Working through this material will also help you confirm whether this is a suitable module for you: if you find that most of it is unfamiliar to you, we recommend that you consider taking Discovering mathematics (MU123) first.
If you wish to do some extra preparation before starting on the study material, then we suggest that you work through a GCSE Mathematics Higher Level, or equivalent, text book, which may be available online or in a local library. You could also use a book or website to familiarise yourself with the first core module (C1 – the first pure maths module) of AS-Level Mathematics, or equivalent. This will contain some topics which you are not expected to have studied before you start this module but, if you can do some work on those as well, it may help you to get a head start with your studies. The MathsChoices website contains further suggestions for help on topics you may need to practice, for example algebra and trigonometry.
Module books and website, including access to computer applications and to optional online tutorials.
You will need
We recommend a basic scientific Casio `Natural’ calculator such as the fx-83GT PLUS or fx-85GT PLUS. The module website includes a calculator guide with references to this series of calculator.
Note that the only type of calculator permitted in the final examination is a scientific calculator that does not offer algebraic manipulation, differentiation or integration, language translation or communication with other devices or with the internet. It should also not be programmable, and not have any retrievable information (such as databanks, dictionaries, mathematical formulas or text) stored in it.
A computing device with a browser and broadband internet access is required for this module. Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.
Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.
A desktop or laptop computer with either:
- Windows 7 or higher
- Mac OS 10.7 or higher
The screen of the device must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.
To participate in our online-discussion area you will need both a microphone and speakers/headphones.
Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students.