Number Theory - MAT00023H

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  • Department: Mathematics
  • Module co-ordinator: Prof. Sanju Velani
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2018-19

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Module will run

Occurrence Teaching cycle
A Autumn Term 2018-19

Module aims

  • To deepen and broaden the study of number theory initiated in the “Introduction to Number Theory” course as part of Pure Mathematics/Pure Mathematics Option 1.

  • To exhibit the unusually wide variety of methods and proofs which appear in number theory.

  • To introduce an important modern application of number theory: cryptography.

  • To give students the opportunity to tackle a range of number theoretic problems.

Module learning outcomes

  • Understand and appreciate the unusually wide variety of methods and proofs which appear in number theory.

  • Understand RSA encryption.

  • Competently tackle a range of number theoretic problems.

Module content

[Pre-requisite modules: students must have taken either Pure Mathematics or Pure Mathematics Option 1.]

  • Arithmetical functions: Dirichlet series and Euler products.

  • Sums of Squares: Waring’s problem.

  • The elementary theory of the distribution of primes: Tchebychef's Theorem.

  • Algebraic and transcendental numbers.

  • Continued fractions.

  • Quadratic forms.

  • Diophantine equations.

  • Ellipitic curves: Mordell-Weil Theorem.

  • Cryptography: the RSA code.

Assessment

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

Special assessment rules

None

Reassessment

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

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

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



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.