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.