Mathematical Concepts

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.

• Algebraic Structure
• Category Theory
• Manifold
• Modal Logic
• Presheave
• Riemannian Geometry
• Scheme
• Simplicial Complex
• Topological Space
• Topos

“This book is an interesting compilation of mathematical concepts and structures. … chapters are stand-alone, allowing readers to pick and choose the subjects they want to explore further. … useful as a supplement to a textbook in a traditional course or for students seeking to learn a little about a particular topic. … for the interested student at the graduate or a very advanced senior undergraduate level, it is a well-written book on independent topics. Summing Up: Recommended. Graduate students.” (S. L. Sullivan, Choice, Vol. 53 (8), April, 2016)

“This book would be an excellent reference for graduate students in just about any area of pure or applied mathematics … . It should also be accessible to researchers in (for instance) chemistry, physics, computer science, and mathematical biology. University libraries should certainly add it to their collections, and many may find a personal copy worth while.” (Robert Dawson, zbMATH 1329.00002, 2016)

• Max Planck Institute for Mathematics in the Sciences, Max Planck Society, Leipzig, Germany

  Jürgen Jost

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