The Number Mysteries (Online)

Course details

Code
O19P541MAV
Fees
From £280.00
Credit
10 CATS points

Dates
Wed 25 Sep 2019 - Fri 06 Dec 2019

The Number Mysteries (Online)

Overview

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, and a link to our course demonstration site, please click here.

Programme details

Week 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

Week 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
  • Prove it!

Week 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

Week 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

Week 5: Probability Theory

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

Week 6: Probabilistic games

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

Week 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

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

Week 9: Mechanical System

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

Week 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
  • Summary
  • The end (a final word from the author)

Recommended reading

To participate in this course you will need to have regular access to the Internet and you will need to buy the following book:

  • du Sautoy, Marcus; The Number Mysteries [2010], Fourth Estate, Great Britain

Certification

To earn credit (CATS points) for your course you will need to register and pay an additional £10 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 £10 fee.

For more information on CATS point please click on the link below: http://www.conted.ox.ac.uk/studentsupport/faq/cats.php

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.

Assignments are not graded but are marked either pass or fail.

All students who successfully complete this course, whether registered for credit or not, are eligible for a Certificate of Completion. Completion consists of submitting both course assignments and actively participating in the course forums. Certificates will be available, online, for those who qualify after the course finishes.

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.

Fees

EU Fee: £280.00
Non-EU Fee: £300.00
Take this course for CATS points: £10.00

Tutor

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 is 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

Assessment for this course is based on two written assignments - one short assignment of 500 words due half way through the course and one longer assignment of 1500 words due at the end of the course.

Assignments are not graded but are marked either pass or fail.

Application

Please use the 'Book' or 'Apply' button on this page. Alternatively, please contact us to obtain an application form.

Level and demands

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