MTH2121 - Algebra and number theory - 2019

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.



Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Professor Ian Wanless


Professor Ian Wanless

Unit guides



  • First semester 2019 (On-campus)


One of MTH1020, MTH1030, MTH1035, MAT1830 or ENG1005


MTH3121, MTH2122, MTH3122


Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups, cosets and normal subgroups; homomorphisms, isomorphisms and the first isomorphism theorem. The Euclidean algorithm, prime factorisation, congruences, the Euler totient function; the theorems of Fermat, Euler and Wilson, and the RSA public key cryptosystem; Chinese remainder theorem; quadratic reciprocity; factorisation and primality testing algorithms.


On completion of this unit students will be able to:

  1. Appreciate the beauty and the power of pure mathematics;
  2. Recognise the fundamental concepts of algebra and number theory;
  3. Explain the notion of proof in mathematics and be able to carry out basic proofs;
  4. Illustrate how thousands of years of pure mathematical developments have enabled secure electronic communication;
  5. Apply important number theoretic algorithms;
  6. Describe the power of the generality of the concepts in group theory.


End of semester examination (3 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for both the end-of-semester examination and continuous assessment components.

Workload requirements

Three 1-hour lectures and one 2-hour applied class per week

See also Unit timetable information

This unit applies to the following area(s) of study