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# Category Archives: Lecture notes

## A week in Vienna

Last week, in the second week of Spring break in St Andrews, I was in Vienna, giving a course of lectures to the PhD students, at the invitation of Tomack Gilmore, a Queen Mary undergraduate now finishing his PhD with … Continue reading

## A crash course on group theory

I have just finished a crash course on group theory at Universidade de Lisboa. The notes are here. From the preface: On a visit to Universidade de Lisboa in November 2016, I was asked to give a “crash course” in … Continue reading

Posted in Lecture notes
Tagged Classification of Finite Simple Groups, finite groups, first-order logic, groups of prime power order, infinite groups, Jordan-Holder Theorem, locally finite groups, oligomorphic permutation groups, periodic groups, profinite groups, residually finite groups, Sylow's theorem, topology
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## Advanced Combinatorics: the St Andrews lectures

Three years ago, when I joined the School of Mathematics and Statistics at the University of St Andrews, it was suggested that I might like to give a final year MMath module on “Advanced Combinatorics”. No compulsion. Well, of course … Continue reading

Posted in Lecture notes
Tagged Catalan numbers, chromatic polynomial, cycle index, doocot principle, enumeration, formal power series, Friendship Theorem, Gaussian coefficients, generalised line graphs, generalised quadrangles, IBIS groups, line graphs, Mathieu groups, matroid, Moebius inversion, orbit-counting lemma, projective planes, root systems, strongly regular graphs, symmetric Sudoku, triangle property, Tutte polynomial, weight enumerator
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## G. C. Steward lectures 2008

While I was uploading lecture notes, I also put on the page the notes from my G. C. Steward lectures at Gonville and Caius College in 2008. You can find them here. I spent the first half of 2008 in … Continue reading

Posted in history, Lecture notes, Neill Cameron artwork
Tagged automata, bagali polo, Euler, Latin squares, line graphs, magic squares, Moebius inversion, OEIS, On-line Encyclopedia of Integer Sequences, parking functions, partitions, root systems, statistics, Sudoku, synchronization, Tehran
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## Notes on moonshine

A recent conversation reminded me that I had a set of notes on a talk I gave, based on an extended talk by V. Nikulin to the London Algebra Colloquium, about Borcherds’ proof of the moonshine conjecture (for which he … Continue reading

## Lecture notes

I have decided to follow Dima’s suggestion and post my collection of lecture notes here. You will find them from the page “Lecture notes” on the menu bar at the bottom of the picture at the top of the blog. … Continue reading

Posted in Lecture notes
Tagged abstract algebra, combinatorics, enumerative combinatorics, groups, linear algebra, number theory, probability, rings
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