Number Theory - MAT00076H

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Module summary

This is for postgraduate students only

Related modules

Additional information

MSc students should have taken a suitable first course in Pure Mathematics

Module will run

Occurrence	Teaching period
A	Spring Term 2022-23

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

• 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.

Indicative assessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	100

Special assessment rules

Pass/fail

Indicative reassessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	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.