Relational Mathematics

Gunther Schmidt (Universität der Bundeswehr München)

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English

Cambridge University Press
04 November 2010

Mathematical logic; Maths for scientists; Database design & theory

Series: Encyclopedia of Mathematics and its Applications

Relational mathematics is to operations research and informatics what numerical mathematics is to engineering: it is intended to help modelling, reasoning, and computing. Its applications are therefore diverse, ranging from psychology, linguistics, decision aid, and ranking to machine learning and spatial reasoning. Although many developments have been made in recent years, they have rarely been shared amongst this broad community of researchers. This comprehensive 2010 overview begins with an easy introduction to the topic, assuming a minimum of prerequisites; but it is nevertheless theoretically sound and up to date. It is suitable for applied scientists, explaining all the necessary mathematics from scratch using a multitude of visualised examples, via matrices and graphs. It ends with tangible results on the research level. The author illustrates the theory and demonstrates practical tasks in operations research, social sciences and the humanities.

By: Gunther Schmidt (Universität der Bundeswehr München)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 132
Dimensions: Height: 234mm, Width: 156mm, Spine: 32mm
Weight: 990g
ISBN: 9780521762687
ISBN 10: 0521762685
Series: Encyclopedia of Mathematics and its Applications
Pages: 582
Publication Date: 04 November 2010
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Preface; 1. Introduction; Part I. Representations of Relations: 2. Sets, subsets and elements; 3. Relations; Part II. Operations and Constructions: 4. Algebraic operations on relations; 5. Order and function: the standard view; 6. Relations and vectors; 7. Domain construction; Part III. Algebra: 8. Relation algebra; 9. Orders and lattices; 10. Rectangles, fringes, inverses; 11. Concept analysis; Part IV. Applications: 12. Orderings: an advanced view; 13. Preference and indifference; 14. Aggregating preferences; 15. Relational graph theory; 16. Standard Galois mechanisms; Part V. Advanced Topics: 17. Mathematical applications; 18. Implication structures; 19. Power operations; Appendix A. Notations; Appendix B. Postponed proofs of Part II; Appendix C. Algebraic visualization; Appendix D. Historical annotations; Table of symbols; References; Index.

Gunther Schmidt was a Professor in the Faculty for Informatics of the Universität der Bundeswehr München before his retirement in 2004.

Reviews for Relational Mathematics

'The author illustrates the mathematical theory and demonstrates practical tasks in operations research, social sciences and the humanities with graspable results at the research level. The multitude of examples is visualized using matrices and graphs. The book is suitable for applied scientists and the broad community of researchers in various fields who use relations in their scientific work.' Zentralblatt MATH This book is an important contribution to the literature on relational algebra, especially for English speakers. Much of the work in the field has been done in German, or else maybe in English but scattered among individual papers or in volumes of proceedings. It is good to have a comprehensive, albeit very theoretical, book in English. Anthony J. Duben, Computing Reviews This text is deliberately encyclopedic, extremely precise and detailed, and the results aimed toward applications in areas such as psychology, linguistics, decision analysis and machine learning. S.I. Gendler, Mathematical Reviews