Complex Analysis
The more classical subject of complex analysis is one of the sources of modern mathematics. Construction of examples or counterexamples using objects in classical real and complex analysis is always the most natural ones. They form a cornerstone for more complicated constructions. Historically, {\it Mittag-Leffler's problem} is the major motivation for the development of cohomology theory. The field of complex numbers is also the most important case in the study of algebraic geometry. The course on {\it Riemann Surface} has given me the chance to see how various fields such as topology, complex analysis, algebraic geometry, and functional analysis come into play at the same time. Although I cannot go deeply into every topic I read, the course does introduce me into the many important concepts such as sheaf, cohomology, holomorphic vector bundle; which are usually omitted in undergraduate study but are commonsense for working mathematicians. Indeed, having insufficient time to have a more thorough study of the historical development of various concepts, I often have to take a purely formal point of view when studying, without knowing the origin of such theories.