units

MTH3150

Faculty of Science

# Undergraduate - UnitMTH3150 - Algebra and number theory II

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.

## 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.

 Level Undergraduate Faculty Faculty of Science Organisational Unit School of Mathematical Sciences Offered Clayton Second semester 2015 (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:

1. Appreciate advanced concepts, algorithms and results in number theory;

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

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

1. Appreciate many of the links between algebra and number theory;

1. 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;

1. Perform calculations in the algebra of polynomials;

1. Use the Euclidean algorithm in structures other than integers;

1. Construct larger fields from smaller fields (field extensions);

1. Apply field theory to coding and cryptography.

### 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