Real Algebraic Geometry

Real Algebraic Geometry (UNITEXT / La Matematica per il 3+2)
This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).

Table of Contents

Chapter 1 Introduction 11
Chapter 2 Geometry of Conic Sections 13
Chapter 3 The Physics of Conic Sections and Ellipsoids 29
Chapter 4 Projective Geometry 42
Chapter 5 Complex Algebraic Curves 63
Chapter 6 A Problem for School Pupils 84