Dear Master's students following the Mathematics Education Programme at UR-CE.This module entitled MEM 6244: STMA was developed for you to explore advanced ideas and concepts of mathematical analysis you missed during undergraduate studies.
This course deals with the geometry of Riemannian and Symplectic manifolds by means of multilinear algebra and Tensor calculus methods.It contains four units.Unit one is focused on tensor algebra, unit two gives an overview of the differential geometry of curves and surfaces in the three-dimensional Euclidean space. Unit three develops basic results about tensor calculus on smooth manifolds and finally the unit four deals with Riemannian and symplectic manifolds and their applications in Relativity theory and Hamiltonian system.