The Mathematical Beauty that led to Quantum Physics

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This course showcases the beautiful mathematics that, in the late 19th century/ early 20th century, led to the discovery of a revolutionary branch in physics: Quantum Mechanics. Planck postulated that the energy of oscillators in a black body is quantized. This postulate was introduced by Max Planck in the derivation of his law of black body radiation in 1900. This assumption allowed Planck to derive a formula for the entire spectrum of the radiation emitted by a black body (we will also derive this spectrum in this course). Planck was unable to justify this assumption based on classical physics; he considered quantization as being purely a mathematical trick, rather than (as is now known) a fundamental change in the understanding of the world. Calculus and Multivariable Calculus are a prerequisite to the course; other important mathematical tools (such as Fourier Series, Parseval’s theorem, binomial coefficients, etc.) will be recalled, with the emphasis being put on mathematical and physical insights rather than abstract rigour.