MATH425-23S1 (C) Semester One 2023

Real and Complex Analysis

15 points

Details:
Start Date: Monday, 20 February 2023
End Date: Sunday, 25 June 2023
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 5 March 2023
  • Without academic penalty (including no fee refund): Sunday, 14 May 2023

Description

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.

Learning Outcomes

  • 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.

      • University Graduate Attributes

      This course will provide students with an opportunity to develop the Graduate Attributes specified below:

      Critically competent in a core academic discipline of their award

      Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

Prerequisites

Subject to approval of the Head of School.

Course Coordinator

Ngin-Tee Koh

Textbooks / Resources

Recommended Reading

Freitag, E. , Busam, Rolf; Complex analysis ; 2nd ed., [2nd English ed.]; Springer, 2009.

Stromberg, Karl Robert; Introduction to classical real analysis ; Wadsworth International Group, 1981.

Indicative Fees

Domestic fee $1,045.00

* 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 .

All MATH425 Occurrences

  • MATH425-23S1 (C) Semester One 2023
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