Short Course Online

Analytic Number Theory I

The Open University UK

9 months
1705 GBP/full
1705 GBP/full
Tuition fee
Apply date
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In this Analytic Number Theory I course from The Open University UK you’ll study number theory using techniques from analysis, in particular, the convergence of series and the calculus of residues.

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The Analytic Number Theory I course at The Open University UK is based on readings from T.M. Apostol’s Introduction to Analytic Number Theory.

What you will study

The Greeks were the first to classify the integers and it is to them that the first systematic study of the properties of the numbers is attributed.

There are a large number of unsolved problems in number theory that are easy to state and understand - for example:

  • Is every even number greater than two the sum of two primes?
  • Are there infinitely many ‘twin primes’ (primes differing by 2), such as (3, 5) or (101, 103)?
  • Are there infinitely many primes of the form n 2 + 1?
  • Does there always exist a prime between n 2 and (n + 1)2 for every integer n > 1?

Programme Structure

You will learn

  • Successful study of this module should enhance your skills in understanding complex mathematical texts, working with abstract concepts, thinking logically and constructing logical arguments, communicating mathematical ideas clearly and succinctly, and explaining mathematical ideas to others.

Key information


  • Part-time
    • 9 months

Start dates & application deadlines


30 alternative credits



Academic requirements

We are not aware of any academic requirements for this programme.

Other requirements

General requirements

  • You must declare the MSc in Mathematics (or another qualification towards which the module can count) as your qualification intention. 
  • You should normally have a minimum of a 2:2 honours degree in mathematics or a 2:1 honours degree in a subject with a high mathematical content. If you don't have such a qualification, your application will be considered and you may be asked to complete an entry test. Non-graduates will not normally be admitted to M823 unless as part of another Open University qualification. Students already registered for a qualification of which M823 is a constituent part will normally be admitted to M823.
  • You should have a good background in pure mathematics, with some experience in number theory and analysis. An adequate preparation would be our undergraduate-level modules Pure mathematics (M208) and Further pure mathematics (M303). 

Tuition Fee

To alway see correct tuition fees
  • International

    1705 GBP/full
    Tuition Fee
    Based on the tuition of 1705 GBP for the full programme during 9 months.
  • National

    1705 GBP/full
    Tuition Fee
    Based on the tuition of 1705 GBP for the full programme during 9 months.


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Analytic Number Theory I
The Open University UK


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