COMBINATORIAL TALES
Lecture notes containing selected results from extremal graph theory and the theory of random graphs. In particular, the following topics are covered.
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Classical results from extremal graph theory starting with the theorems of Mantel and Turán and culminating with various applications of Szemerédi's regularity lemma.
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Classical results from the theory of random graphs:
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Thresholds for the appearance of small graphs.
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The emergence of Hamilton cycles in random graphs.
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Hadwiger's conjecture for random graphs.
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These notes were not subjected to the usual scrutiny reserved for formal publications.
spectral graph theory
Lecture notes containing selected results from spectral graph theory with applications in data science. In particular, the notes cover the following topics.
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Incidence matrices of graphs.
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Adjacency matrices of graphs and their spectrum.
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Laplacians.
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Expansion in graphs (the expander mixing lemma in particular).
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Clustering, Principal component analysis & k-means.
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Random walks.
These notes were not subjected to the usual scrutiny reserved for formal publications.
optimisation
Lecture notes containing selected results from the theory of optimisation & algorithms. In particular, the notes cover the following topics.
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Classical results from graph theory such as
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The Hungarian method & matchings in graphs
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Vertex & edge connectivity (Menger's theorem)
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Hamiltonicity
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Graph colouring
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NP-completeness
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Linear programming
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Approximation algorithms
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Randomised algorithms
These notes were not subjected to the usual scrutiny reserved for formal publications.
elementary number theory
& early group theory
Lecture notes supporting an undergraduate level course in elementary number theory and a mild introduction to group theory. The text commences with proving the cornerstone results of elementary number theory and then reproduces them all using the language of groups.
These notes were not subjected to the usual scrutiny reserved for formal publications.
synchronisation algorithms
Lecture notes supporting an undergraduate level course concerning the algorithms used by operating systems in order to schedule multiple threads and processes.
These notes were not subjected to the usual scrutiny reserved for formal publications.
some programming notes
Various notes accumulated over the years teaching certain programming oriented courses
These notes were not subjected to the usual scrutiny reserved for formal publications.
