 # Mark Coleman

Dr

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## Personnal

I am Director of Studies in the School of Mathematics

## Research Group(s)

• Number Theory

## Teaching for 2018/19

For 2018/19 will be teaching the following three courses.

MATH20101 Real and Complex Analysis; The first half of the course describes how the basic ideas of the calculus of real functions of a real variable (continuity, differentiation and integration) can be made precise and how the basic properties can be developed from the definitions. It builds on the treatment of sequences and series in MATH10242. Important results are the Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration.

MATH20132 Calculus of Several Variables

MATH4\61022 Analytic Number TheoryWe start by giving two proofs of the infinitude of primes. The methods are elementary but poor in that they do not tell us the truth of how many primes there are. Stronger tools are introduced, improving the results until we can indicate, at least in outline, a proof of the Prime Number Theorem

### Biography

I am a Senior Lecturer and the Director of Studies in the School of Mathematics, University of Manchester.

My undergraduate degree was from Imperial College, London. This was followed by a Certificate of Advanced Study (also known as Part III) from Cambridge University. I then did a PhD with Alan Baker, FRS and Fields medal winner. My thesis had the catch-all title of Topics in the Distribution of Primes. Following a two year post-doc back at Imperial College I came north to UMIST in 1989.

### Research interests

Analytic Number Theory with special interest in the "geometric" distribution of ideals in number fields and, in particular, the distribution of Gaussian primes in the plane. The (almost certainly false?) conjecture in this area is that one can walk from the origin of the plane out to infinity with steps of bounded length stepping only on the Gaussian primes.

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