These were part of a short series of seminars given by myself and Paul Cooper, another graduate student at Warwick at the time, aiming to explain the connections between Mechanics and Geometry.

The original series was three lectures, of which I gave the first and third. Later, I gave two more seminars on similar themes.

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May 4th 1999

Mechanics to Manifolds I. An Introduction to Mechanics

The purpose of this seminar was to give a simple introduction to the basics of the theory mechanics with a particular emphasis on those concepts that feed most naturally in to geometry. It was aimed at mathematics graduate students familiar with the basics of geometry but without assuming any particular background knowledge in physics.

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June 7th 1999

Mechanics to Manifolds III. Quantum Mechanics

The purpose of this seminar was to show how problems in Quantum mechanics can give rise to problems in geometry. The problems that I considered in this were how to think of an electron (or other half-integer spin particle) in geometrical terms, and how path integrals arise.

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October 11th 1999

Mechanics to Manifolds, the Revenge: An Introduction to Quantum Mechanics

This is basically a rewrite of Mechanics to Manifolds I.

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October 19th 1999

The Harmonic Oscillator

The Harmonic Oscillator is a fairly unique type of problem in mathematical physics. It is simple enough to be solved exactly. It involves no major simplification of the physical problem. It is very instructive as to the techniques of Quantum Theory. And finally, if you want to understand anything about Quantum Field Theory then you have to understand the Harmonic Oscillator first since QFT says that all fields are infinite collections of Harmonic Oscillators.

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