Fourier Transform The Fourier Transform and the associated Fourier series is one of the most important mathematical tools in physics. Physicist Lord Kelvin remarked in 1867: “Fourier’s theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly […]

Non Euclidean Geometry – An Introduction It wouldn’t be an exaggeration to describe the development of non-Euclidean geometry in the 19th Century as one of the most profound mathematical achievements of the last 2000 years. Ever since Euclid (c. 330-275BC) included in his geometrical proofs an assumption (postulate) about parallel lines, mathematicians had been trying […]

The Telephone Numbers – Graph Theory The telephone numbers are the following sequence: 1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496… (where we start from n=0). This pattern describes the total number of ways which a telephone exchange with n telephones can place a connection between pairs of people. To illustrate this […]

Happy Numbers Happy numbers are defined by the rule that you start with any positive integer, square each of the digits then add them together. Now do the same with the new number. Happy numbers will eventually spiral down to a number of 1. Numbers that don’t eventually reach 1 are called unhappy numbers. As […]

Give your university applications a headstart on other students with Coursera. Applying for university as an international student is incredibly competitive – for the top universities you’ll be competing with the best students from around the world, and so giving yourself a competitive advantage to make your university application stand out is really important. […]

Statistics to win penalty shoot-outs With the World Cup upon us again we can perhaps look forward to yet another heroic defeat on penalties by England. England are in fact the worst country of any of the major footballing nations at taking penalties, having won only 1 out of 7 shoot-outs at the Euros and […]