Entry requirements

Analysis MN2 and Linear algebra MN1.

Aims

The course will extend the knowledge of real

analysis obtained in the preceding Analysis MN1

and MN2 courses. It is essential for more

advanced studies in mathematics.

Content

The following

items are treated. Metric properties of real

numbers, normed spaces, metric spaces,

completeness, contractions and Banach's fixed

point theorem, linear spaces of continuous and

differentiable functions, convergence of

sequences and series of functions, the implicit

function theorem.

Instruction

Lectures and problem solving sessions.

Assessment

Written and, possibly, supplementary oral

examination at the end of the course. Moreover,

compulsory assignments may be given during the

course.