units

MTH2121

Faculty of Science

18 September 2017 22 November 2024
Monash University

Undergraduate - Unit

This unit entry is for students who completed this unit in 2015 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

print version

6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

LevelUndergraduate
FacultyFaculty of Science
Organisational UnitSchool of Mathematical Sciences
OfferedClayton First semester 2015 (Day)
Coordinator(s)Dr Norman Do

Synopsis

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.

Outcomes

On completion of this unit students will be able to:

  1. Appreciate the beauty and the power of pure mathematics;

  1. Understand the fundamental concepts of algebra and number theory;

  1. Appreciate the notion of proof in mathematics and be able to carry out basic proofs;

  1. Appreciate the beauty of the mathematics of the ancient Greeks, including Euclid and Diophantes;

  1. Appreciate the power of large primes in enabling crypto-systems for banking;

  1. Understand the power of the generality of the concepts in group theory.

Assessment

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

Workload requirements

Three 1-hour lectures and an average of one 1-hour support class per week

See also Unit timetable information

Chief examiner(s)

Dr Norman Do

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

Mathematics and statistics

Prerequisites

One of MTH1020, MTH1030, MTH1035 or MAT1830

Prohibitions

MTH3121, MTH2122, MTH3122