Module Details
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.
Title NUMBER THEORY
Code MATH342
Coordinator Dr TDH Hall
Mathematical Sciences
T.Hall@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2024-25 Level 6 FHEQ First Semester 15

Aims

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

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

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.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

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