units

MTH2121

Faculty of Science

18 September 2017 31 December 2024

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This unit entry is for students who completed this unit in 2016 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.

Monash University

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

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Professor Ian Wanless

Offered

Clayton

  • First semester 2016 (Day)

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 one 2-hour support class per week

See also Unit timetable information

Chief examiner(s)

Professor Ian Wanless

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

Applied mathematics
Mathematical statistics
Mathematics
Pure mathematics

Prerequisites

One of MTH1020, MTH1030, MTH1035, MAT1830 or ENG1005

Prohibitions

MTH3121, MTH2122, MTH3122