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.
- 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:
- Appreciate the beauty and the power of pure mathematics;
- Understand the fundamental concepts of algebra and number theory;
- Appreciate the notion of proof in mathematics and be able to carry out basic proofs;
- Appreciate the beauty of the mathematics of the ancient Greeks, including Euclid and Diophantes;
- Appreciate the power of large primes in enabling crypto-systems for banking;
- Understand the power of the generality of the concepts in group theory.
Examination (3 hours): 70%
Assignments and tests: 30%
Three 1-hour lectures and one 2-hour support class per week
See also Unit timetable information
This unit applies to the following area(s) of study
MTH3121, MTH2122, MTH3122