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MA40238: Number theory

Follow this link for further information on academic years Academic Year: 2012/3
Follow this link for further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Follow this link for further information on credits Credits: 6
Follow this link for further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Follow this link for further information on period slots Period: Semester 1
Follow this link for further information on unit assessment Assessment: EX 100%
Follow this link for further information on supplementary assessment Supplementary Assessment: Mandatory extra work (where allowed by programme regulations)
Follow this link for further information on unit rules Requisites: Before taking this unit you must take MA20217
Follow this link for further information on unit content 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.
Follow this link for further information on programme availabilityProgramme availability:

MA40238 is Optional on the following programmes:

Department of Computer Science
  • USCM-AFM14 : MComp (hons) Computer Science and Mathematics (Full-time) - Year 3
  • USCM-AFM14 : MComp (hons) Computer Science and Mathematics (Full-time) - Year 4
  • USCM-AKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 4
  • USCM-AKM14 : MComp (hons) Computer Science and Mathematics with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 5
  • USCM-AAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USCM-AAM14 : MComp (hons) Computer Science and Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 5
Department of Mathematical Sciences
  • USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
  • USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
  • USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
  • USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
  • USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
  • USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
  • USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
  • USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Physics
  • USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 4

Notes:
* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.