Aims at providing a solid foundation in the basic concepts, principles and methods of functional analysis, a study which is mainly concerned with vector spaces and operators acting upon them. The principles learnt from basic calculus and linear algebra will be developed further to the more general setting of abstract infinite-dimensional vector spaces. This provides powerful tools in handling problems in applied mathematics and theoretical physics; also helps the understanding of the development of mathematical theories such as partial differential equations and the theory of operators.

The first part of the course is devoted to the theory of metric spaces, the general setting in which discussions of central concepts such as continuity and convergence can be carried out. This is followed by a detailed study of normed and Banach spaces, inner-product sapaces and Hilbert spaces, with the emphasis on abstract reasoning and proof. The theory of operators forms an important part of the unit; it opens up many avenues of application in a variety of fields (such as quantum mechanics) for further study.