Adavya’s Talk on the Fourier Series

Adavya (Lower Eighth), who has recently been selected to represent the UK at the International Mathematical Olympiad in Australia this summer, gave a talk to the senior problem solving society this week on Fourier series and their application to the Basel problem.

Fourier series give a way to express any periodic function (that is, something which repeats regularly, such as a waveform) as a linear combination of different frequencies of cosine and sine functions. This area of mathematics has far reaching application in mathematics, physics and engineering including acoustics, quantum mechanics, signal processing and partial differential equations, to name but a few.

The Basel problem, on the other hand, considers the sum of the reciprocals of the square numbers, that is

Which converges, rather enigmatically to 

To discover the link between the two, you are encouraged to watch the video of Adavya’s talk, which will appear on the Mathematics department website soon.