units

MTH2140

Faculty of Science

# Undergraduate - UnitMTH2140 - Real analysis

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. print version

## 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 First semester 2015 (Day) Coordinator(s) Dr Jerome Droniou

### Synopsis

An introduction to real analysis with a special focus on sequences of real numbers and functions. Topics covered include properties of real numbers (infima/suprema and the axiom of completeness), sequences and series of real numbers (order limit theorem, Cauchy sequences and completeness, compactness), properties of functions over the reals (intermediate value theorem, mean value theorem), sequences and series of functions (pointwise and uniform convergence, the Weierstrass M-test, continuity and differentiability of the limit). Emphasis will be on rigorous mathematical proof and examples will be provided to show how intuition can be misleading.

### Outcomes

On completion of this unit students will be able to:

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

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

1. Understand the basic concepts of analysis including limits of sequences and series (of real numbers or functions), properties of functions over the reals;

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

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

### Assessment

Examination (3 hours): 70%
Assignments and participation in support classes: 30%

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