Learning outcomes and syllabus

Aim of the course

To give the student a sufficient background in basic abstract analysis for further studies in subjects like functional analysis,Fourier analysis,differential equations, dynamical systems, representation theory, differential geometry, topology etc. Knowledge in these areas of mathematics is indispensable in understanding the highly non trivial use of abstract mathematics in the fascinating developments of todays theoretical physics.

Syllabus

Dedekind’s cut, metric and normed spaces, topology, continuity, compactness, Banachs Fixed Point Theorem, derivative, inverse and implicit function theorem, Arsela-Ascoli Theorem, Stone-Weierstrass Theorem, differential forms, Stoke’s Theorem, Lebesque Integrals.