This unit continues the study of functions of a complex variable introduced in the second year unit Analysis (MATH2023/2923). It is aimed at highlighting certain topics from analytic function theory that have wide applications and intrinsic beauty. By learning about the analysis of functions of a complex variable, you will acquire a very important background for mathematical areas such as dynamics, algebraic and differential geometry, and number theory; and advanced theoretical physics such as quantum mechanics, string theory, and quantum field theory. The unit will begin with a revision of properties of complex numbers and complex functions. This will be followed by material on conformal mappings, Riemann surfaces, complex integration, entire and analytic functions, the Riemann mapping theorem, analytic continuation, and Gamma and Zeta functions. Finally, special topics chosen by the lecturer will be presented, which may include elliptic functions, normal families, Julia sets, functions of several complex variables, or complex manifolds. At the end of this unit you will have received a broad introduction and gained a variety of tools to apply them within your further mathematical studies and/or in other disciplines.
Lecture 3 hrs/week; tutorial 1 hr/week
2 x assessment (30%), final exam worth (70%) (requires pass mark of 50% or more)
Good knowledge of analysis of functions of one real variable, working knowledge of complex numbers, including their topology, for example MATH2X23 or MATH2962 or MATH3068
A mark of 65 or above in 12cp of MATH2XXXProhibitions
MATH4079 or MATH3964