This course is intended both for mathematics students continuing to honours work and for other students using mathematics at a high level in theoretical physics, engineering and information technology, and mathematical economics.

Topics to be covered include:

Complex differentiability, conformal mapping; complex integration, Cauchy integral theorems, Taylor series representation, isolated singularities, residue theorem and applications to real integration. Topics chosen from: argument principle, Riemann surfaces, theorems of Picard, Weierstrass and Mittag-Leffler.

Note: This is an HPC. It emphasises mathematical rigour and proof and develops the material from an abstract viewpoint.

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of complex analysis and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of complex analysis techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from complex analysis
4. Apply problem-solving using complex analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts.

Assessment will be based on:

• Assignment 1 (30%; LO 1-4)
• Assignment 2 (30%; LO 1-4)
• Take home exam (40%; LO 1-4)

36 lectures, tutorials by arrangement

A mark of 60 or more in MATH3320.