Algebraic and geometric foundation of mathematical physics (Q2865665)

This book provides an annual course of author's lectures which have been read in 2007. It contains two chapters.NEWLINENEWLINEThe first chapter ``Algebraic minimum'' outlines (without proofs, but with a lot of examples) the main algebraic objects, structures and constructions which are most frequently used in modern mathematical physics. The main part of this chapter is rather standard. But there are some novelties (for such texts) -- this chapter begins with the theory of categories and ends with an examination of homology and spectral sequences. For the convenience of readers each section of this chapter supplied by a list of recommended reading for a more complete study of the subject.NEWLINENEWLINEChapter Two named as ``Elements of differential geometry''. It is written in the expository form (with some proofs). This chapter begins with smooth manifolds, fibrations and concludes with Lie groups and connections. There are no classic differential geometry and no Riemannian geometry here.