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.
What you will study
There are eleven 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.
You can find the full content list on the Open mathematics and statistics 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.
There is no formal pre-requisite study, but you must have the required mathematical skills.
You can check you’re ready for MST124 and see the topics it covers here.
You can find out which module is your best starting point in mathematics here.
Talk to an advisor if you’re not sure you’re ready.
You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz here, and follow the advice in the quiz.
The key topics to revise include:
- algebraic manipulation and solving equations
- quadratics and parabolas
- geometry and trigonometry
- exponentials and logarithms.
Discovering mathematics (MU123) is ideal preparation.
Module books and website, including access to computer applications and to optional online tutorials.
You will need
We recommend a basic scientific Casio calculator such as the fx-83 or fx-85 range.
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.
You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11), or macOS (11 'Big Sur' or higher).
Any additional software will be provided or is generally freely available.
To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).
Our module websites comply with web standards, and any modern browser is suitable for most activities.
Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.
It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop as described above.