Free course

Mathematics for science and technology

Free statement of participation on completion

Maths is intimately entwined with science and technology, whether it is used to analyse data collected on plants in the Amazon rainforest, to calculate the trajectory of a comet or design a bridge to connect two countries. This means that science and technology go hand-in-hand with maths, and that a firm grasp of maths is crucial for studying any science and technology discipline.

This free course, Mathematics for science and technology, will help you build a stronger grip with the maths helping hand. You’ll learn about the power of algebra, get a sense of scientific notation, the beauty of basic trigonometry and why 70 db (decibels) is 10 times more powerful than 60 db. As well as this you will delve into scientific measurement, including the importance of units and the flexibility and practically of the SI – the internationally recognised system of units based on multiples of ten.

Transcript

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The Open University would really appreciate a few minutes of your time to tell us about yourself and your expectations for the course before you begin, in our optional start-of-course survey ⁶⁹. Once you complete the course we would also value your feedback and suggestions for future improvement, in our optional end-of-course survey ⁷⁰. Participation will be completely confidential and we will not pass on your details to others.

This course is accredited by the CPD Standards Office . It can be used to provide evidence of continuing professional development and on successful completion of the course you will be awarded 24 CPD points. Evidence of your CPD achievement is provided on the free Statement of Participation awarded on completion.

Anyone wishing to provide evidence of their enrolment on this course is able to do so by sharing their Activity Record on their OpenLearn Profile, which is available before completion of the course and earning of the Statement of Participation.

Earn this free Open University digital badge if you complete this course! The badge can be displayed, shared and downloaded as a marker of your achievement. The badge is awarded for completing the course and passing the quizzes.

Course learning outcomes

After studying this course, you should be able to:

understand the SI system of measurements, scientific notation and significant figures
understand basic algebra and solve maths equations
apply the basic functions in trigonometry
calculate probability of an outcome, the mean, mode, median and standard deviation for set data
gain an understanding of logarithms.

Enter course

First Published: 13/07/2017

Updated: 20/01/2020

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Course content

Introduction and guidance
- Current section:
  Introduction and guidance
  This free course will give you a better understanding of how algebra, scientific notation and trigonometry is used in science, and the world around us.After studying this course, you should be able to:understand the SI system of measurements, scientific notation and significant figuresunderstand basic algebra and solve maths equationsapply the basic functions in trigonometrycalculate probability of an outcome, the mean, mode, median and standard deviation for a set of datagain an ...
- What is a badged open course?
- How to get a badge
- Acknowledgements
Week1Week 1: Powers and scientific notation
- Current section:
  Introduction
  This first week of the course covers two areas that will give you a firm foundation to build on for the next seven weeks. To start with you will learn the rules used to help manipulate values involving indices (or powers). These will be invaluable when you can to start your study of algebra in Week 3, and logarithms in 5. Leading on from this will be scientific notation, which is commonly used in science and technology. It uses powers of 10 to enable large and small numbers to be written in ...
- 1 Powers
- 2 Large quantities and small quantities – scientific notation
- 3 This week’s quiz
- 4 Summary of Week 1
- Acknowledgements
- Week 1 practice quiz
Week2Week 2: Measurements
- Current section:
  Introduction
  In the UK, two systems of units are in use. Imperial measures for some things: milk is sold in pints and signposts indicate distances in miles. But for many other everyday measurements metric units have been adopted: petrol in litres and sugar in kilogram bags. However, this is, generally, not the case in science. In 1960 an international conference formally approved a standard set of scientific units, thus replacing at a stroke the many different systems of measurement that had been used ...
- 1 Units of measurement
- 2 Scales of measurement
- 3 The logarithmic scale
- 4 How precise are the measurements?
- 5 This week’s quiz
- 6 Summary of Week 2
- Acknowledgements
- Week 2 practice quiz
Week3Week 3: Introduction to algebra
- Current section:
  Introduction
  In mathematics, equations are used a great deal in arriving at a solution to a problem. This week, you will build skills to enable you to solve an equation, or equations, using algebraic techniques. You’ll start by looking at why algebra is so useful, before moving on to simplifying algebraic expressions and changing the subject of an equation. These are both important techniques in preparation for solving equations. In the final section, you will learn how to solve simultaneous equations –...
- 1 Why use algebra?
- 2 Simplifying algebraic expressions
- 3 Changing the subject of an equation
- 4 Solving simple equations with one unknown
- 5 Simultaneous equations
- 6 This week’s quiz
- 7 Summary of Week 3
- Acknowledgements
- Week 3 practice quiz
Week4Week 4: Starting with trigonometry
- Current section:
  Introduction
  Trigonometry is the area of maths that deals with triangles, and how their sides and internal angles are related. The trigonometric functions have very practical applications in science and technology, such as in navigation, bridge design and determining astronomical distances. This week you will work with the three basic functions of sine, cosine and tangent. It is important that you have access to a scientific calculator to carry out the activities. This does not have to be a hand-held ...
- 1 Right angled triangles
- 2 Sine, cosine and tangent
  - 2.1 Right angled triangles – one known side, and two known angles
  - 2.2 Right-angled triangles – two known values, and one unknown value
- 3 Trigonometry in practice
- 4 This week’s quiz
- 5 Summary of Week 4
- Acknowledgements
- Week 4 compulsory badge quiz
Week5Week 5: Logarithms
- Current section:
  Introduction
  In Week 1 you learned about the rules for indices and in Week 2 you were introduced to logarithmic scales. This week uses ideas from both of these weeks, as you turn your attention to logarithms. These were invented in the seventeenth century by John Napier as a way to make calculations involving multiplication and division easier. Before electronic tools were cheaply and commonly available these were an invaluable aid, and this is still the case today. You have already seen how useful a ...
- 1 Logarithms to base 10
- 2 Three log rules
- 3 Natural logarithms
- 4 Change of base
- 5 This week’s quiz
- 6 Summary of Week 5
- Acknowledgements
- Week 5 practice quiz
Week6Week 6: Probability
- Current section:
  Introduction
  Statistical techniques offer ways of dealing with variability, and natural variability is something that scientists and engineers meet all the time. Each time an experiment or a measurement is repeated, a slightly different result may be obtained; in any group of people there will be a variation in height; the count of background radiation at any individual location fluctuates randomly from moment to moment. It is therefore very important to be able to decide with some measure of certainty ...
- 1 Chance and probability
- 2 Calculating probability
- 3 Probability and common sense
- 4 Ways of expressing probability
- 5 Combining probabilities
- 6 This week’s quiz
- 7 Summary of Week 6
- Acknowledgements
- Week 6 practice quiz
Week7Week 7: Statistics and repeated measurements
- Current section:
  Introduction
  Statistical information is a familiar aspect of modern life, which features routinely in, for example, news reports, sports commentaries and advertising. Scientists who have collected large amounts of data by either counting or measuring quantities also rely on statistical techniques to help them make sense of these data. Suppose you had information collected from, say, three thousand patients, all with the same medical condition but undergoing a variety of treatments. First you would need ...
- 1 Types of data sets
- 2 Repeated measurements
- 3 The distribution of repeated measurements
- 4 Mean and standard deviation for repeated measurements
- 5 Using a calculator for statistical calculations
- 6 This week’s quiz
- 7 Summary of Week 7
- Acknowledgements
- Week 7 practice quiz
Week8Week 8: Statistics and sampling
- Current section:
  Introduction
  Week 8 continues your study of statistics, specifically data from population samples rather than repeated measurements. This type of data is very common in biology, and geography where data from large populations are analysed. In some cases, for sample data, the mean is not the most appropriate average, so you will learn about alternatives. However, the mean will still be important when you are calculating the sample standard deviation. Before exploring averages though, you’ll consider in ...
- 1 How likely are particular results?
  - 1.1 Different types of distribution
- 2 Different types of ‘average’
- 3 Samples and populations
- 4 This week’s quiz
- 5 Summary of Week 8
- Where next?
- Tell us what you think
- Acknowledgements
- Week 8 compulsory badge quiz

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Ayesha Shafique 7 August 2025 2:42PM

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Very good and enjoy learning from this platform.

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Tia Walker 19 June 2025 8:35PM

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Excellent course to refresh and introduce important mathematical processes and formulas. Incredibly informative and easy to understand. Some of the print is very small however and may not be accessible for some people.

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Mathematics for science and technology

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