Undergraduate - UnitMTH2121 - Algebra and number theory

This unit entry is for students who completed this unit in 2013 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.

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6 points, SCA Band 2, 0.125 EFTSL

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Level	Undergraduate
Faculty	Faculty of Science
Organisational Unit	School of Mathematical Sciences
Offered	Clayton First semester 2013 (Day)
Coordinator(s)	Dr Tom Hall

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:

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.

Assessment

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

Chief examiner(s)

Dr Tom Hall

Contact hours

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

Prerequisites

One of MTH1020, MTH1030, MTH1035 or MAT1830

Prohibitions

MTH3121, MTH2122, MTH3122