This unit provides an introduction to abstract methods in a continuous setting. Topics include topology and geometry from a constructive perspective in dimensions two, three and four. Students investigate, via concrete examples, homeomorphisms and diffeomorphisms of manifolds; curvature; vector bundles; and elements of the machinery for describing space-time in physics. Alternatively, topics may include Banach spaces, Hilbert spaces, projections, compact, self-adjoint, normal and unitary operators, Riesz representation theorem, the Fredholm alternative and applications to solving integral and differential equations from physics. -- Course Website
Instructor: Professor Latchezar Stoyanov
Prerequisites: MATH2031 Introduction to Pure Mathematics
