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Please take this page in conjunction with the Part III Guide to Courses Combinatorics section.

Part III Courses

Prerequisites given per Part III course.

Relevant undergraduate courses are:

Part II Graph Theory

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Combinatorics

There are really no prerequisites for this course. Occasionally, it would be useful to have met some terminology from graph theory. Any course in graph theory will contain such terminology, and if you have not done any graph theory course then that is also fine, as the terminology will be minimal and very easy to pick up.

Useful books

A book that gives a lot of the flavour of the course is:

  • Combinatorics, by B.Bollobas, C.U.P. (any edition)

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Ramsey Theory

There are really no prerequisites for this course. If you have already met Ramsey's theorem then that is a help, but the course is designed with the assumption that the audience have not met Ramsey's theorem at all.

Useful books

There is no real `book for the course'. You could dip into the following to see some ideas in Ramsey Theory:

  • Ramsey Theory, by R.Graham, B.Rothschild and J.Spencer, Wiley (any edition)

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Extremal Graph Theory

This is a second course in Graph Theory. Pretty much any first course in Graph Theory will be sufficient, as long as it has some theorems in it and is not just a catalogue of definitions. For example, any course that contains Turan's theorem will be fine. But if you have not done any Graph Theory course at all then you might find this course is not followable.

Reality Check

As a `reality check', have a look at some of the questions on these example sheets:

and see if you can do the first few questions of each sheet.

Useful books

There is no book covering the course, but some of the flavour may be found from the two books below:

  • Modern Graph Theory, by B.Bollobas, Springer-Verlag (any edition)
  • The Probabilistic Method, by N.Alon and J.Spencer, Wiley (any edition)

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