
Academic Year:  2016/7 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must take MA20217 
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, padic numbers, Hasse principle. 
Programme availability: 
MA40238 is Optional on the following programmes:Department of Computer Science

 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 3)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
 USMAAFB13 : BSc(Hons) Mathematics (Year 3)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
 USMAAFM14 : MMath(Hons) Mathematics (Year 3)
 USMAAFM14 : MMath(Hons) Mathematics (Year 4)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
 USMAAFB05 : BSc(Hons) Statistics (Year 3)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
Notes:
