units

MTH2140

Faculty of Science

Undergraduate - Unit

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.

print version

6 points, SCA Band 2, 0.125 EFTSL

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LevelUndergraduate
FacultyFaculty of Science
Organisational UnitSchool of Mathematical Sciences
OfferedClayton First semester 2013 (Day)
Coordinator(s)Dr Jerome Droniou

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

On completion of this unit students will be able to:

  1. Appreciate the rich mathematical structure of the real numbers;

  1. Understand a variety of paradoxes of the infinite;

  1. Understand the basic concepts of analysis including limits, derivatives, integrals, sequences and series;

  1. Appreciate the applicability of mathematical ideas to other areas of science;

  1. Identify areas of mathematics where the intuition is unreliable;

  1. Appreciate and develop some simple mathematical proofs and the use of rigorous mathematical arguments;

  1. Apply 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)

Contact hours

Three 1-hour lectures and one 2-hour support class per week

Prerequisites

Prohibitions

MTH2111, MTH3111, MTH3140