Mathematical Concepts [electronic resource] / by Jürgen Jost.

By: Jost, Jürgen [author.]
Contributor(s): SpringerLink (Online service)
Material type: TextTextPublisher: Cham : Springer International Publishing : Imprint: Springer, 2015Edition: 1st ed. 2015Description: XV, 312 p. 130 illus., 16 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319204369Subject(s): Mathematics | Algebraic geometry | Category theory (Mathematics) | Homological algebra | Algebra | Convex geometry | Discrete geometry | Differential geometry | Biomathematics | Mathematics | Algebraic Geometry | Category Theory, Homological Algebra | General Algebraic Systems | Convex and Discrete Geometry | Differential Geometry | Mathematical and Computational BiologyAdditional physical formats: Printed edition:: No titleDDC classification: 516.35 LOC classification: QA564-609Online resources: Click here to access online
Contents:
Overview and perspective -- Foundations -- Relations -- Spaces -- What is space? -- Spaces of relations -- Structures -- Categories -- Topoi -- A review of examples.
In: Springer eBooksSummary: 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.  .
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Overview 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.  .

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