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.

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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.

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Level 1: Foundations of Physics Tutorials

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

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