Module Specification
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
1. Module Title NUMBER THEORY
2. Module Code MATH342
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester First Semester
7. CATS Level Level 6 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Dr TDH Hall Mathematical Sciences T.Hall@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Dr R Nair Mathematical Sciences Nair@liverpool.ac.uk
13. Board of Studies
14. Mode of Delivery
15. Location Main Liverpool City Campus
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
16. Study Hours 36

   20

       56
17.

Private Study

 94
18.

TOTAL HOURS

 150
 
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other
19. Timetable (if known)            
 
20. Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

 
21. Modules for which this module is a pre-requisite:

 
22. Co-requisite modules:

 
23. Linked Modules:

 
24. Programme(s) (including Year of Study) to which this module is available on a mandatory basis:
25. Programme(s) (including Year of Study) to which this module is available on a required basis:
26. Programme(s) (including Year of Study) to which this module is available on an optional basis:
27. Aims
 

To give an account of elementary number theory with use of certain algebraic methods and to apply the concepts to problem solving.
 
28. Learning Outcomes
 

(LO1) To understand and solve a wide range of problems about integers numbers.
 

(LO2) To have a better understanding of the properties of prime numbers.
 

(S1) Problem solving skills
 

(S2) Numeracy
 

(S3) Communication skills
 
29. Teaching and Learning Strategies
 

Material is provided in advance of classes for students to study asynchronously. The contact hours consist of 2 hours of active learning sessions and 2 hours of supported study/drop-in sessions.
 
30. Syllabus
   

Greatest common divisor, congruences, perfect numbers, the prime number counting function, Chebyshev's estimates and the Riemann zeta function, Fermat's theorem, pseudoprimes, Euler's theorem, order of an element, primitive roots, the number and sum of divisors of an integer, primality tests and Carmichael numbers, groups, rings and fields, algebraic methods in number theory, quadratic residues, Legendre symbols, Gauss' reciprocity law, squares in finite fields, quadratic number fields.
 
31. Recommended Texts
  Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
 

Assessment
32. EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  final assessment on campus 60 35
33. CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  Class Test 2 on campus 60 35
  Class Test 1 on campus 60 30