Monash University Handbook

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:

Appreciate and develop mathematical proofs and the use of rigorous mathematical arguments;
Appreciate the rich mathematical structure of the real numbers;
Understand the basic concepts of analysis including limits of sequences and series (of real numbers or functions), properties of functions over the reals;
Appreciate the applicability of mathematical ideas to other areas of science;
Identify areas of mathematics where the intuition is unreliable.

Assessment

End of semester examination (3 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for both the end-of-semester examination and continuous assessment components.