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MA40238: Number theory

Follow this link for further information on academic years Academic Year: 2016/7
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period:
Semester 1
Further information on unit assessment Assessment Summary: EX 100%
Further information on unit assessment Assessment Detail:
  • Exam (EX 100%)
Further information on supplementary assessment Supplementary Assessment:
Mandatory extra work (where allowed by programme regulations)
Mandatory extra work (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA20217
Further information on descriptions Description: NB. This unit is only available in academic years starting in an even year.
Aims:
To introduce the students to some of the main ideas of modern number theory.

Learning Outcomes:
After taking this unit, students will be able to solve problems involving elementary number theory and to demonstrate understanding in a range of more advanced topics in number theory.

Skills:
Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials).

Content:
Elementary number theory: congruences, Chinese Remainder Theorem, Euler phi function, Mobius inversion, quadratic residues. The quadratic reciprocity theorem. Further topics to be taken from: quadratic fields, Pells's equation, quadratic forms, cyclotomic fields, rings of integers, failure of unique factorization, p-adic numbers, Hasse principle.
Further information on programme availabilityProgramme availability:

MA40238 is Optional on the following programmes:

Department of Computer Science
  • USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
  • USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
  • USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
Department of Mathematical Sciences

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