MTH3121 - Algebra and number theory - 2017

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.

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

See also Unit timetable information

Professor Ian Wanless

Applied mathematics

Mathematical statistics

Mathematics

Pure mathematics

One of MTH1020, MTH1030, MTH1035, MAT1830 or ENG1005

MTH2121, MTH2122, MTH3122