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Foundations of Incidence Geometry: Projective and Polar Spaces de Johannes Ueberberg

Foundations of Incidence Geometry: Projective and Polar Spaces: Springer Monographs in Mathematics

Autor Johannes Ueberberg
en Limba Engleză Paperback – 27 noi 2013
Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces.
Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout.
The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.
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  Springer Berlin, Heidelberg – 26 aug 2011 57420 lei  43-57 zile

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Specificații

ISBN-13: 9783642269608
ISBN-10: 3642269605
Pagini: 260
Ilustrații: XII, 248 p.
Dimensiuni: 155 x 235 x 14 mm
Greutate: 0.37 kg
Ediția:2011
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Springer Monographs in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

I Projective and Affine Geometries.- 1. Introduction.- 2. Geometries and Pregeometries.- 3. Projective and Affine Planes.- 4. Projective Spaces.- 5. Affine Spaces.- 6. A Characterization of Affine Spaces.- 7. Residues and Diagrams.- 8. Finite geometries.- II Isomorphisms and Collineations.- 1. Introduction.- 2. Morphisms.- 3. Projections.- 4. Collineations of projective and affine spaces.- 5. Central Collineations.- 6. The Theorem of Desargues.- III Projective Geometry over a Vector Space.- 1. Introduction.- 2. The Projective Space P(V).- 3. Homogeneous Coordinates of Projective Spaces.- 4. Automorphisms of P(V).- 5. The Affine Space AG(W).- 6. Automorphisms of A(W).- 7. The First Fundamental Theorem.- 8. The Second Fundamental Theorem.- IV Polar Spaces and Polarities.- 1. Introduction.- 2. The Theorem of Buekenhout-Shult.- 3. The diagram of a polar space.- 4. Polarities.- 5. Sesquilinear Forms.- 6. Pseudo-quadrics.- 7. The Kleinian Polar Space.- 8. The Theorem of Buekenhout and Parmentier.- V Quadrics and Quadratic Sets.- 1. Introduction.- 2. Quadratic Sets.- 3. Quadrics.- 4. Quadratic Sets in PG(3, K).- 5. Perspective Quadratic Sets.- 6. Classification of the Quadratic Sets.- 7. The Kleinian Quadric.- 8. The Theorem of Segre.- 9. Further Reading.- References.- Index.

Recenzii

“This book provides an introduction into projective and affine spaces as well as polar spaces in the modern language of diagram geometry. … The book is well written and contains many enlightning pictures. It is mainly directed to students.” (Hans Cuypers, Nieuw Archief voor Wiskunde, Issue 4, December, 2015)
“The book under review is a comprehensive monograph devoted to the foundations of incidence geometry … . a clear and good introduction for graduate students who want to learn about modern geometry and is also useful for lecturers who offer courses on this topic. The book may also be of interest for researchers because it contains several results which were previously only available in the original research articles. … At the end of the book the author gives some hints about further reading too.” (Gyӧrgy Kiss, Mathematical Reviews, November, 2013)
“The book contains almost all classical results from projective geometry. It is written in a readable style. Especially the first two chapters can be recommended to those who are interested in a synthetic treatment of projective geometry.” (Boris Odehnal, Zentralblatt MATH, Vol. 1237, 2012)

Textul de pe ultima copertă

Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces.
Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout.
The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.

Caracteristici

The book is a reference in which a lot of classical material is presented in most readable and accessible way Valuable contribution to the literature about a wonderful piece of mathematics Can be used by students, researchers and lecturers