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.
School of Mathematical Sciences
- First semester 2019 (On-campus)
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:
- Appreciate the beauty and the power of pure mathematics;
- Recognise the fundamental concepts of algebra and number theory;
- Explain the notion of proof in mathematics and be able to carry out basic proofs;
- Illustrate how thousands of years of pure mathematical developments have enabled secure electronic communication;
- Apply important number theoretic algorithms;
- 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.
Three 1-hour lectures and one 2-hour applied class per week
See also Unit timetable information