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Popular maths talks

Shape of the cosmos

University of Nottingham (16/03/2010)

Watching the sky, you can see the Sun, moon, planets and stars moving above Earth. It is very intuitive to imagine that you are standing still and the objects you are observing are moving above you and this was the view taken by geocentric models of the cosmos. A Greek model, which was dominant in many parts of the world for hundreds of years, had a spherical Earth at the centre of the universe, with the other heavenly bodies orbiting in perfect circles. This talk will outline problems and challenges to this model, and the developments which followed, through the theory of Copernicus, mathematical treatments by Kepler and Newton and questions of what drives planetary motion.

This talk was recorded for the web as part of the History of Maths and x series.

View video of 'Shape of the cosmos'.
View slides from 'Shape of the cosmos'.

Puzzles

Cardiff University (09/03/2010)

I gave a version of my puzzles talk at a schools outreach event. This included river crossing puzzles, sorites, magic squares and Rubik's cubes.

Chance and Coincidence

University of Leicester, 04/02/2010

How striking are astonishing coincidences? We see that often people are blown away by events that are not that unexpected, or that we even should be expecting to happen. We look at human understanding of large numbers and the effect this has on coincidental events. We look at the way people view coincidences and what this can tell us about predicting the future. We examine the ability of people to draw patterns and derive coincidence from meaningless data, and what effect this has on drawing conclusions from statistical analysis. We look at how people judge random events and how this can help in detecting fraud. Finally, we look at an area of great coincidence - winning the lottery. Using a small lottery machine, we will create a bespoke lottery for this audience with fabulous prizes to be won (in chocolate form); but you make the rules to decide how many people win!

Substitution ciphers: Ancient - Renaissance

University of Nottingham (01/12/2009)

Cryptography is the process by which messages are communicated through secret means. Cipher cryptography converts messages by applying some cipher algorithm with a secret key to a plaintext message, converting it into a ciphertext message that cannot be read by interceptors. Cryptanalysis is the science that attempts to decipher these messages without access to the secret key.

This talk will focus on substitution ciphers and demonstrate the processes of encrypting and breaking some examples of these. The focus is on the battle between cryptographers - who create cipher systems - and cryptanalysts - who attempt to break them. As cryptanalysis develops more ingenious ciphers must be created and this constant struggle evolves from Roman generals, through the Golden Age of Islam to political intrigue in Renaissance Europe.

This talk will provide a gentle introduction and will assume no prior knowledge of cryptography.

This talk was recorded for the web as part of the History of Maths and x series.

View video of 'Substitution ciphers: Ancient - Renaissance'.
View slides from 'Substitution ciphers: Ancient - Renaissance'.

Cryptography

I gave my lecture on Cryptography to a potential South Yorkshire Branch of the IMA at the University of Sheffield on 19/11/09. Abstract:

Cryptography is the process by which messages are communicated through some secret means, often through a process on encrypting a message using some cipher process into an unintelligible sequence. This talk runs through 4 interesting cipher systems from history and demonstrates the processes of encrypting, decrypting and in some cases breaking these - Caesar cipher and frequency analysis, Vigenère cipher, Enigma and Public key cryptography. This talk will provide a gentle introduction and no previous knowledge of cryptography will be assumed. The talk features demonstrations using The Code Book on CD-ROM.

Clement W. Jones Lectures

As University Liaison Officer for the Institute of Mathematics and its Applications, I give the following to university students as Clement W. Jones Lectures:

Careers for mathematics graduates

What do mathematics graduates do? And what skills do employers think they lack? This talk highlights some of the broad range of careers options for mathematics graduates and points to several sources of career inspiration. Following this is information on the skills a maths degree gives you and those it perhaps does not. Looking at what skills employers think mathematics graduates lack will help you in finding a job - when you sit down in a job interview, what skills is the person opposite you expecting that you lack? Being able to surprise them may just get you the job! The talk rounds off with a look at the benefits of professional membership and some information about the Institute of Mathematics and its Applications.

I have given this talk at the following universities: Nottingham Trent University (09/10/2008, twice on 08/10/2009); Greenwich (26/01/2009); Bristol (12/02/2009, 03/03/2010); University of the West of England (12/02/2009, 03/03/2010); Brunel (twice on 19/02/2009; 08/03/2010); Cardiff (20/02/2009, 18/02/2010); Aberdeen (25/02/2009); St. Andrews (25/02/2009); Glasgow (26/02/2009, 25/11/2009); Strathclyde (26/02/2009, 25/11/2009); Heriot-Watt (27/02/2009); Edinburgh (27/02/2009); Edinburgh (27/02/2009); Leicester (05/03/2009); London Met (30/03/2009, 23/02/2010); York (06/05/2009, 10/03/2010); University of East Anglia (07/10/2009); Liverpool John Moores (14/10/2009); Liverpool (15/10/2009); Kingston (21/10/2009); Lancaster (27/10/2009); Manchester Metropolitan (28/10/2009); Bolton (28/10/2009); Kent (04/11/2009); Durham (11/11/2009); Sheffield (19/11/2009); Dundee (23/11/2009); Stirling (25/11/2009); Brighton (02/12/2009); Portsmouth (03/12/2009); Exeter (08/12/2009); Plymouth (09/12/2009); Nottingham (03/02/2010); Imperial College (08/02/2010); Oxford (shortened version 08/02/2010); Swansea (19/02/2010); Keele (24/02/2010); Bath (02/03/2010); Leeds (10/03/2010); Surrey (29/04/2010).

View slides from 'Careers for mathematics graduates'.

Puzzles

There is a long history of puzzles and games and their interaction with mathematics. The talk will include a selection of puzzles through the ages: Starting in the ancient world of Egypt and Greece, going through the Renaissance, Euler's work in recreational mathematics, the popular acceptance of mathematical puzzles in the late 19th C. to the modern age of Rubik's and Sudoku.

I gave this talk at the following universities: York (05/05/2009); Liverpool (15/10/2009); London School of Economics (02/11/2009); Newcastle (10/11/2009); Northumbria (12/11/2009); Edinburgh (26/11/2009).

Spin in Ball Games

Pool is a game in which balls (consider them points) bounce around a rectangle (the table) in two-dimensions. When a ball strikes the edge of the table (the cushion) it will bounce away following "angle of incidence = angle of reflection". Right? Anyone who has played pool will know this is not always true and the interesting aspects come from applying spin to the ball. This talk runs through some of the interesting and sometimes counter-intuitive effects that can be achieved in ball games using spin. This short talk is followed by the chance to play pool, tennis and other games on a Nintendo Wii.

I have given this talk at the following universities: Greenwich (18/02/2009); Leicester (05/03/2009); Newcastle (28/04/2009); Sheffield (29/04/2009); York (11/11/2009).

Cryptography

Cryptography is the process by which messages are communicated through some secret means, often through a process on encrypting a message using some cipher process into an unintelligible sequence. This talk runs through 4 interesting cipher systems from history and demonstrates the processes of encrypting, decrypting and in some cases breaking these - Caesar cipher and frequency analysis, Vigenère cipher, Enigma and Public key cryptography. This talk will provide a gentle introduction and no previous knowledge of cryptography will be assumed. The talk features demonstrations using The Code Book on CD-ROM. Following the talk an activity can be operated whereby groups of students use The Code Book on CD-ROM's encryption and decryption tools to crack each others messages.

I gave this talk at the following universities: Newcastle (25/11/2008); Lancaster (27/10/2009); Aberdeen (24/11/2009); St. Andrews (26/11/2009); Heriot-Watt (27/11/2009); Southampton (03/12/2009); Aberystwyth (19/03/2010); Derby (21/04/2010).