• Student home
• Things to know this week
• Student news
• Student events
• New students' welcome
• Studying at York
  • Semesters
  • Teaching hours
  • Enrolment
  • Manage your studies
    • Enrol or re-enrol
    • Your student record
    • Your timetable
    • Change your plan
    • Programmes and modules
      • Programme specifications
      • Studying beyond your department
      • Module catalogue
    • University study spaces
  • Student Visa holders
  • Study skills
  • Assessment and examination
  • Academic progress issues
  • Graduation
• Support and advice
• Health and wellbeing
• Work, volunteering and career planning
• Study and work abroad
• Accommodation
• IT and online services
• Finance
• Student life in York
• If things go wrong
• Student Centre

Number Theory - MAT00076H

« Back to module search

• Department: Mathematics
• Module co-ordinator: Prof. Sanju Velani
• Credit value: 10 credits
• Credit level: H
• Academic year of delivery: 2021-22
  • See module specification for other years: 2022-23

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	Autumn Term 2021-22

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.

Assessment

Task	Length	% of module mark
Online Exam -less than 24hrs (Centrally scheduled) Number Theory	2 hours	100

Special assessment rules

Pass/fail

Reassessment

Task	Length	% of module mark
Online Exam -less than 24hrs (Centrally scheduled) 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.