# Module MAU34208: Topics in complex analysis II

**Credit weighting (ECTS)**- 5 credits
**Semester/term taught**- Hilary term 2019-20
**Contact Hours**- 11 weeks, 3 lectures including tutorials per week
**Lecturer**- Prof. Andreea Nicoara
**Learning Outcomes**-
On successful completion of this module, students will be able to:

- define concepts, prove theorems, and write down examples and counterexamples;
- understand the properties of harmonic functions and special functions such as the Gamma function and the Riemann-Zeta function;
- work with linear fractional transformations and the Riemann sphere;
- construct meromorphic functions with prescribed zeros and poles as well as elementary Riemann surfaces

- Singularities, the Casorati-Weierstrass Theorem, elementary value distribution theory, and the Picard Theorems
- Harmonic functions and the Dirichlet Problem
- The stereographic projection and the Riemann sphere
- Linear fractional transformations
- Boundary behaviour of the Riemann map
- Divisors, the Mittag-Leffler Theorem, infinite products, and the Weierstrass Theorem on canonical products
- The Gamma Function, the Riemann-Zeta function, and the statement of the Riemann Hypothesis
**Module Prerequisite****Assessment Detail**-
This module will be examined in a 2-hour

**examination**in Trinity term. The final mark is 80% of the exam mark plus 20% continuous assessment consisting of a certain number of homework sets assigned throughout the term. Re-assessments if required will consist of 100% exam.

**Module Content**

MAU23204