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.
Faculty
Organisational Unit
School of Mathematical Sciences
Chief examiner(s)
Coordinator(s)
Unit guides
Synopsis
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.
Outcomes
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.
Assessment
Examination (3 hours): 60% (Hurdle)
Continuous assessment: 40%
Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.
Students enrolled in MTH3121 will be expected to exhibit a higher level of knowledge in this subject than those enrolled in MTH2121.
Workload requirements
Three 1-hour lectures and one 2-hour support class per week
See also Unit timetable information