Mathematical Concepts

Description

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. Front Matter....Pages i-xv Overview and Perspective....Pages 1-11 Foundations....Pages 13-67 Relations....Pages 69-87 Spaces....Pages 89-122 What Is Space?....Pages 123-175 Spaces of Relations....Pages 177-219 Structures....Pages 221-229 Categories....Pages 231-259 Topoi....Pages 261-291 A Review of Examples....Pages 293-297 Back Matter....Pages 299-312