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Metric Number Theory - MAT00049M

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  • Department: Mathematics
  • Module co-ordinator: Prof. Victor Beresnevich
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2017-18

Module will run

Occurrence Teaching cycle
A Autumn Term 2017-18

Module aims

The aim of the module is to continue the development of number theory but also to provide a deeper and more quantitative understanding of the structure of the real numbers through Diophantine approximation. To illustrate the interplay of different branches of mathematics by the use of algebra, probability and basic results from the theory of Lebesgue measure and fractal geometry.

Module learning outcomes

At the end of the module you should be able to:

understand a range of ideas and techniques in Diophantine approximation.

be familar with the basic use of algebraic and probabilistic ideas within metric number theory.

understand the role of fractals within number theory.

understand the interplay between number theory and basic dynamical systems.


Task Length % of module mark
University - closed examination
Metric Number Theory
2 hours 100

Special assessment rules



Task Length % of module mark
University - closed examination
Metric Number Theory
2 hours 100

Module feedback

Information currently unavailable

Indicative reading

G H Hardy and E M Wright, The theory of numbers, Oxford University Press (S 2.81 HAR).

J W S Cassels, An introduction to Diophantine approximation, Cambridge University Press (S 2.81 CAS).

D M Burton: Elementary Number Theory, WCB/McGraw-Hill.

H E Rose: A course in Number Theory, Oxford University Press.

Hua Loo-Keng: Introduction to Number Theory, Springer.

W.J. LeVeque: Elementary Theory of Numbers, Addison Wesley Longman Publishing Co.

W.M. Schmidt: Diophantine Approximation, Springer Verlag.

Y. Bugeaud: Approximation by algebraic numbers, Cambridge University Press.

G. Harman: Metric Number Theory, Oxford University Press.

K. Falconer: Fractal Geometry, John Wiley and Sons Ltd.

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.