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.
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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
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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.
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These notes were not subjected to the usual scrutiny reserved for formal publications.
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synchronisation algorithms
Lecture notes supporting an undergraduate level course concerning the algorithms used by operating systems in order to schedule multiple threads and processes.
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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
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These notes were not subjected to the usual scrutiny reserved for formal publications.
