2 x 2-hour lectures weekly
1 2 of MATH3702, MATH3711, MATH3712, MATH3731
2 Admission into MSCMT-Master of Science (Mathematics)
Must Satisfy: ((1) or (2))
Assignments; Examination (55%).
Topic description

The topic comprises basics of point set topology, classical metric spaces, compactness, completeness, Hilbert spaces, Banach spaces, linear analysis, functionals and operators, Fourier series and contraction mappings.

Educational aims

This topic aims to provide an understanding of the theoretical underpinnings of advanced applied mathematics.

Expected learning outcomes
On completion of this topic you will be expected to be able to:

  1. Understand the fundamental role of point set topology in Analysis applications
  2. Understand and solve problems in the setting of general metric spaces
  3. Understand classical metric spaces and the specifics of completeness and compactness in those spaces
  4. Understand and apply basic methods in Hilbert spaces and Banach spaces
  5. Identification of fixed points of contraction mappings in Banach spaces