MTH2140

Real analysis ( 6 points, SCA Band 2, 0.125 EFTSL)

Leader: Dr Leo Brewin

Offered:
Clayton First semester 2005 (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 tutorials: 30%

Contact Hours: Three 1-hour lectures and one 1-hour tutorial class per week

Prerequisites: MTH1030

Prohibitions: MTH2111, MTH3111, MTH3140