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Real and Complex Analysis
The purpose of this course is to learn some foundational results in real and complex analysis. It provides a thorough grounding in parts of modern mathematics that arise from the study of sequences and series of functions, such as: pointwise convergence and uniform convergence, how uniform convergence determines whether the limiting function is continuous and whether a series of functions can be term wise differentiated and integrated, and the precise conditions for a sequence of functions to have a subsequence of functions that converges uniformly on compact sets. In addition, with time permitting, a selection of topics in complex analysis may be covered, such as: Liouville's theorem, open mapping theorem, argument principle, Rouche's theorem, maximum modulus principle, Schwarz's lemma, normal families, Riemann mapping theorem.
Students successfully completing this course should:understand a range of basic concepts in real and complex analysis;have developed a high level of competence at some core analytic skills;be able to confidently apply analytic concepts in practical settings;be able to present clear and logical mathematical arguments.
Subject to approval of the Head of School.
Students must attend one activity from each section.
Freitag, E. , Busam, Rolf;
2nd ed., [2nd English ed.];
Stromberg, Karl Robert;
Introduction to classical real analysis
Wadsworth International Group, 1981.
Domestic fee $1,017.00
International Postgraduate fees
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see
Mathematics and Statistics