Undergraduate - UnitMTH2140 - Real analysis

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

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.

Outcomes

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%

Chief examiner(s)

Associate Professor Alan Pryde

Contact hours

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

Prerequisites

MTH1030 or MTH1035

Prohibitions

MTH2111, MTH3111, MTH3140