# MTH2140 - Real analysis

## 6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSL

### Undergraduate Faculty of Science

#### Leader(s): Associate Professor Alan Pryde

#### Offered

Clayton First semester 2009 (Day)

#### Synopsis

Real numbers, countable and uncountable sets, paradoxes of the infinite, the Cantor set; compactness and convergence; sequences and series; continuous and differentiable functions; fixed points and contractions; applications to Markov chains, branching processes and integral equations.

#### Objectives

At the completion of this unit, students will be able to demonstrate understanding of: the rich mathematical structure of the real numbers; a variety of paradoxes of the infinite; some basic concepts of analysis including limits, derivatives, integrals, sequences and series; the applicability of mathematical ideas to other areas of science; and will have developed skills in: identifying areas of mathematics where the intuition is unreliable; appreciating and developing some simple mathematical proofs; the use of rigorous mathematical arguments; applying the tools of real analysis to study discrete dynamical systems.

#### Assessment

Examination (3 hours): 70%

Assignments and participation in support classes: 30%

#### Contact hours

Three 1-hour lectures and one 1-hour support class per week