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From the Introduction: "On a more elementary and didactic note: I often had the occasion to use profitably what I had learned in school, sometimes spiced up with a bit of algebra, in preparing lessons for the candidates to the
Aggrégation on the topics of projective geometry, conics and quadrics, and Möbius transformations. I had been considering the task of systematizing those somewhat scattered notes, made of bits and pieces, when my friend Francis Hirsch presented me with a good opportunity to do so by asking me to teach at the ENSET a course in algebra and geometry, primarily designed to expound the parts of the program that the prospective teachers knew less well, while at the same time enlarging their horizons. And the parts of the program that caused them most trouble were exactly those where algebra was applied to geometric situations that they were not very familiar with: projective, and sometimes affine, geometry; projective transformations, cross-ratios, conics, quadrics, and other curves or surfaces. The former situation had been reversed (following Jean Dieudonné's 'down with Euclid'), and it seemed that geometry was no longer taught in high school (even to those preparing for the Ecole Polytechnique), or even in college. Thus I tried to share with those students the fun I had had in school, and to systematize the lectures I had been giving.
"The present book is the result of this effort, and I very much enjoyed writing it. I decided to take this book a bit further than I had taken the course at the ENSET, where I had lots of things to teach that had nothing to do with projective geometry."
CHAPTERS
- Projective Spaces
- One-Dimensional Projective Geometry
- Classification of Conics and Quadrics
- Polarity with Respect to a Quadric
The
Appendix is entitled "(2, 2)-Correspondence" and the book concludes with the sections
Bibliography,
Index of Symbols and Notations, and
Index.
