02818nam a22004095i 4500978-3-319-20436-9cr nn 008mamaa150910s2015 gw : s :::: 0:eng d978331920436910.1007/978-3-319-20436-9ENGCHQA564-609516.35 (DDC 23)Online resource: Springer International PublishingJost, Jürgen.1956-Mathematical Concepts[EBook]by Jürgen Jost.1st ed. 2015.Cham :Springer International Publishing,2015.XV, 312 p. 130 illus., 16 illus. in color.online resource.textonline resourceOverview and perspective -- Foundations -- Relations -- Spaces -- What is space? -- Spaces of relations -- Structures -- Categories -- Topoi -- A review of examples.The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detailed than standard mathematical textbooks so that the reader can readily grasp the essential concepts and ideas for individual needs. It will be suitable for advanced mathematicians, postgraduate students and for scientists from other fields with some background in formal reasoning. .Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)Algebraic GeometryCategory theory (Mathematics).Homological algebra.Algebra.Convex geometry.Discrete geometry.Differential GeometryGeneral Algebraic Systems.Convex and Discrete Geometry.Differential Geometry.SpringerLink (Online service)http://dx.doi.org/10.1007/978-3-319-20436-9