Currently I am teaching (at Durham University Year 2020/2021):

Level 3: Maths Workshop - integral transform.

Lecture notes can be downloaded here (notes will be periodically updated). The figure below shows some applications of Fourier transform in music.


The bottom left panel in the figure above shows the sound wave P(t) from the middle A from the piano. The bottom right panel shows its Fourier transform (modulus squared) |P(ω)|2 as a function of angular frequency ω (in units of Hz). The Fourier transform |P(ω)|2 tells us the frequency spectrum of this particular piano note. |P(ω)|2 shows a peak at ω ≃ 440 Hz. This corresponds to the fundamental frequency of the middle A indeed. However, |P(ω)|2 also shows several other peaks at ω ≃ 880 Hz, 1320 Hz, 1760 Hz and so on. The peak at ω ≃ 880Hz corresponds to the note of high A. The peak at ω ≃ 1320 Hz corresponds to the note of high E. So the middle A note contains a small percentage of E note. Bach et al. discovered that when note A and note E are played together, they sound nice. This is called harmony in music theory. (Plots adapted from M. R. Petersen, The Math. Assoc. of America.)

Level 3: Computing Projects

Some selection of condensed matter projects: hard spheres crystallization, band structure of semiconductors, and Ising model.


Level 1: Foundations of Physics Tutorials

Covers problem solving in mechanics, waves, optics, electromagnetism, quantum mechanics, and relativity.