Lecture Notes

This is my own collection of work in progress lecture notes, which correspond to the courses that I have taken whilst doing Mathematics at Cambridge. These notes are not direct transcriptions of the lectures, and tend to be heavily modified after the lectures (typically to suit my own tastes).

It is likely that there are errors, which can be assumed to be mine. I welcome all feedback, and I can be contacted at ak2316@srcf.net.

Part IA

• Groups – Dr A. Khukhro (Michaelmas 2020)
• Numbers and Sets – Prof I. B. Leader (Michaelmas 2020)
• Analysis I – Prof G. Paternain (Lent 2021)
• Dynamics and Relativity – Prof P. Haynes (Lent 2021), Condensed Notes

Part IB

• Methods – Prof. E. P. S. Shellard (Michaelmas 2021)
• Markov Chains – Dr P. Sousi (Michaelmas 2021)
• Analysis and Topology – Dr A. Zsák (Michaelmas 2021)
• Linear Algebra – Prof. P. Raphael (Michaelmas 2021)
• Quantum Mechanics – Dr M. Ubiali _(Michaelmas 2021)
• Variational Principles – Dr M. Dunajski (Easter 2021)

Part II

• Graph Theory – Dr J. Sahasrabudhe (Lent 2021)

Part III

• Combinatorics – Prof I. B. Leader (Michaelmas 2021)

Handouts

These are some short handouts which I have written for various reasons. Hopefully you will find them useful, and as always, feedback is appreciated.

• Recognizing Direct Products – IA Groups
• Quotient Groups & The Isomorphism Theorem – IA Groups
• A Crash Course in Integration in $\mathbb{R}^2$ and $\mathbb{R}^3$ – IA Vector Calculus
• Qubits and Quantum States – II Quantum Information & Computing
• Walkthrough of Bertrand’s Postulate – II Number Theory
• Hall’s Theorem – II Graph Theory