Foundations of Incidence Geometry: Projective and Polar Spaces (Springer Monographs in Mathematics) - Hardcover

Ueberberg, Johannes

 
9783642209710: Foundations of Incidence Geometry: Projective and Polar Spaces (Springer Monographs in Mathematics)
Hardcover
ISBN 10: 3642209718 ISBN 13: 9783642209710
Verlag: Springer, 2011

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Von der hinteren Coverseite

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2011
Sprache
Englisch
ISBN 10 
3642209718
ISBN 13 
9783642209710
Einband
Tapa dura
Anzahl der Seiten
262
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
CMN Printpool Inh. Mathis Neumann
https://www.also.com/ec/cms5/en_6000/6000/index.jsp

Friedrich-Karl-Str. 9
Hamburg
Deutschland

Weitere beliebte Ausgaben desselben Titels

9783642269608: Foundations of Incidence Geometry: Projective and Polar Spaces (Springer Monographs in Mathematics)

Vorgestellte Ausgabe

ISBN 10:  3642269605 ISBN 13:  9783642269608
Verlag: Springer, 2013
Softcover