MTH3121 - Algebra and number theory - 2017

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


Professor Ian Wanless

Unit guides



  • First semester 2017 (Day)


Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups, cosets and normal subgroups; homomorphisms, isomorphisms and the fundamental homomorphism 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; rings, fields and abelian groups in number theory.


On completion of this unit students will be able to:

  1. Appreciate the beauty and the power of pure mathematics;
  2. Understand the fundamental concepts of algebra and number theory;
  3. Appreciate the notion of proof in mathematics and be able to carry out basic proofs;
  4. Appreciate the beauty of the mathematics of the ancient Greeks, including Euclid and Diophantes;
  5. Appreciate the power of large primes in enabling crypto-systems for banking;
  6. Understand the power of the generality of the concepts in group theory.


As for MTH2121

Examination (3 hours): 70% + Assignments and tests: 30%

Third-year students will be expected to exhibit a higher level of knowledge in this subject.

Workload requirements

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

See also Unit timetable information

Chief examiner(s)

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



MTH2121, MTH2122, MTH3122