The Number Mysteries (Online)


Based on Marcus du Sautoy's book The Number Mysteries, this course explores the question, how natural is mathematics? Through numerous online activities and 'at home' experiments, you will interact with mathematics as you never have done before.

Today's world is full of technological advances which are only possible due to the huge leaps that science has made over the last few decades: the structure of DNA, the microchip, splitting the atom. Yet, as diverse as these major discoveries may seem, they are all understood through the language of mathematics.

Mathematics has come a long way from its humble origins of notches on a stick and through this ten week course we will take you all the way from the beginning of the number system to the very edges of the universe.

Packed full of diverse activities to suit a wide range of learning styles, The Number Mysteries maths course is for anyone who wants to go on a mathematical odyssey which may change the way they think forever.

For information on how the courses work, please click here.

Programme details

1. The construction of the number system and the human relationship to it.

  • History of the number system
  • Prehistory
  • Babylonians
  •  Egyptians
  •  Greeks
  •  Are we born to count

2. Proofs and prime numbers

  • Prime spotting
  • What comes next?
  • Using algebra to help us
  • Cutting circles
  • Cutting circles continued
  • Over to you
  • Proof
  • Direct proof
  • Proof by contradiction
  • Proof by induction

3. Fractals

  • Uses
  • Creating fractals
  • Where on Earth?
  • Music
  • Dimension
  • Ways of measuring a fractal’s dimension
  • Ruler method
  • Box method
  • Which is the smoothest country

4. Topology

  • Homeomorphism
  • How many sides does a piece of paper have?
  • Illustrating topologies
  • What is a map?
  • Euler’s formula
  • Five neighbours theorem
  • Six colours theorem

5. Probability Theory

  • Setting up the theory
  • Calculating probabilities
  • What do you think?
  • Conditional probability
  • The partition theorem
  • Goats, cars and doors
  • Deadly virus
  • Balls

6. Probabilistic games

  • Nim
  • Derren Brown
  • Penney’s game
  • How to win
  • Using probability theory
  • An alternative approach
  • Kruskal’s count

7. Modulo arithmetic

  • Addition and subtraction
  • Multiplication
  • Modular division
  • Bezout’s lemma
  • Divisibility criterion
  • Division by 2
  • Division by 3 and the rest
  • Codes that use modular arithmetic
  • Can they go wrong?
  • Produce the day of the week

8. Encryption

  • Tell me a story
  • Suggested codes
  • RSA
  • Euclidean algorithm
  • Proof that the Euclidean algorithm leads to the highest common factor
  • Finding d

9. Mechanical System

  • Speed, distance, time
  • Instantaneous speed
  • Acceleration
  • Using the formulae
  • Motion under gravity
  • Tennis and recap
  • Dimensional analysis
  • Dimensional activities

10. Chaos and complex numbers

  • Examples of chaos
  • Lorenz, the weather and butterflies
  • The butterfly effect
  • Lorenz water wheel
  • Chaotic billiards
  • Cobwebs
  • Bifurcations
  • Linking chaos to fractals
  • Complex numbers
  • The quadratic map
  • Maths vs art


Credit Application Transfer Scheme (CATS) points 

To earn credit (CATS points) for your course you will need to register and pay an additional £30 fee for each course you enrol on. You can do this by ticking the relevant box at the bottom of the enrolment form or when enrolling online. If you do not register when you enrol, you have up until the course start date to register and pay the £30 fee. 

See more information on CATS point

Coursework is an integral part of all online courses and everyone enrolled will be expected to do coursework, but only those who have registered for credit will be awarded CATS points for completing work at the required standard. If you are enrolled on the Certificate of Higher Education, you need to indicate this on the enrolment form but there is no additional registration fee. 


Digital credentials

All students who pass their final assignment, whether registered for credit or not, will be eligible for a digital Certificate of Completion. Upon successful completion, you will receive a link to download a University of Oxford digital certificate. Information on how to access this digital certificate will be emailed to you after the end of the course. The certificate will show your name, the course title and the dates of the course you attended. You will be able to download your certificate or share it on social media if you choose to do so. 

Please note that assignments are not graded but are marked either pass or fail. 


Description Costs
Course Fee £385.00
Take this course for CATS points £30.00


Dr Thomas Woolley

Dr Thomas Woolley, applied mathematics lecturer at Cardiff University, studied mathematics at University of Oxford between 2004-2017. Through his education he ended up specialising in mathematical biology, where his doctorate focused on understanding the pattern formation behind fish spots and zebra stripes. Along side this research he now investigates mathematical models of stem cell movement. The hope is that by understanding how stem cells move we can influence them and, thus, speed up the healing process.

When not doing mathematics he is a keen participant in mathematical outreach workshops and has given a variety of popular maths lectures nationally and internationally. He has previously worked for the BBC, illustrated Marcus du Sautoy’s book and worked on the popular maths show “Dara Ó Briain: School of Hard Sums”.  Most recently he was the Fellow of Modern Mathematics at the London Science Museum and helped redesign their mathematics gallery.

Course aims

This course aims to

  • give students a deeper knowledge and understanding of the concepts of number, shape, the role of logic and probability in game play, the role of mathematics in codes and the power of mathematical equations to predict the future;
  • provide students with activities that allow the students to interact with mathematics on a level which they may not considered before;
  • show how mathematics permeates many aspects of our daily lives;
  • aid the intuition of the participants when dealing with probability;
  • show the beauty behind the equations that mathematicians use.

This course will enable students to:

  • have confidence in situations where numerical processes are necessary.
  • question the statistical data that the media presents as fact.
  • organise problems logically, stating their assumptions and understanding their conclusions.

Learning outcomes

By the end of this course students will be expected to understand:

  • mathematics is the language of the universe;
  • mathematics is more than just numbers;
  • intuition may not always be correct;
  • the power of proof;
  • mathematics allows us to explore theoretical systems without the need of physical experiment.

By the end of this course students will be expected to have gained the following skills:

  • Discuss mathematical ideas competently.
  • Suggest possible applicable branches of mathematics to new problems.
  • Clarify and evaluate assumptions based on their applicability.
  • Aid their intuition through mathematical insights.
  • Transform known solutions to new problems.

Assessment methods

You will be set two pieces of work for the course. The first of 500 words is due halfway through your course. This does not count towards your final outcome but preparing for it, and the feedback you are given, will help you prepare for your assessed piece of work of 1,500 words due at the end of the course. The assessed work is marked pass or fail.

English Language Requirements

We do not insist that applicants hold an English language certification, but warn that they may be at a disadvantage if their language skills are not of a comparable level to those qualifications listed on our website. If you are confident in your proficiency, please feel free to enrol. For more information regarding English language requirements please follow this link:


Please use the 'Book' or 'Apply' button on this page. Alternatively, please complete an Enrolment form for short courses | Oxford University Department for Continuing Education

Level and demands

FHEQ level 4, 10 weeks, approx 10 hours per week, therefore a total of about 100 study hours.

IT requirements

This course is delivered online; to participate you must to be familiar with using a computer for purposes such as sending email and searching the Internet. You will also need regular access to the Internet and a computer meeting our recommended minimum computer specification.