Undergraduate - UnitMTH3150 - Algebra and number theory II

This unit entry is for students who completed this unit in 2014 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

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

Level	Undergraduate
Faculty	Faculty of Science
Organisational Unit	School of Mathematical Sciences
Offered	Clayton Second semester 2014 (Day)
Coordinator(s)	Dr Heiko Dietrich

Synopsis

Rings, fields, ideals, algebraic extension fields. Coding theory and cryptographic applications of finite fields. Gaussian integers, Hamilton's quaternions. Euclidean Algorithm in rings.

Outcomes

On completion of this unit students will be able to:

Appreciate advanced concepts, algorithms and results in number theory;

Use Gaussian integers to find the primes expressible as a sum of squares;

Understand Diophantine equations, primitive roots and the quaternions - the best known skew field;

Appreciate many of the links between algebra and number theory;

Understand the most commonly occurring rings and fields: integers, integers modulo n, rationals, reals and complex numbers, more general structures such as algebraic number fields, algebraic integers and finite fields;

Perform calculations in the algebra of polynomials;

Use the Euclidean algorithm in structures other than integers;

Construct larger fields from smaller fields (field extensions);

Apply field theory to coding and cryptography.

Assessment

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

Chief examiner(s)

Dr Heiko Dietrich

Workload requirements

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

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

Mathematics and statistics

Prerequisites

MTH2121 or MTH3121