Algebraic Approach to Geometry

Francis Borceux is Professor of mathematics at the University of Louvain since many years. He has developed research in algebra and essentially taught geometry, number theory and algebra courses and he has been dean of the Faculty of Sciences of his University and chairman of the Mathematical Committee of the Belgian National Scientific Research Foundation.

From the book reviews: "The book under review is the second of a trilogy of books discussing the broad sweep of geometry and the various ways of approaching this subject. ... This book ... would give the students not only a new look at geometry but also a renewed appreciation for the power of linear algebra in other branches of mathematics. ... it is certainly something that any instructor interested in geometry or algebra would want to have." (Mark Hunacek, MAA Reviews, January, 2014) "This beautiful, comprehensive, well-written and clearly structured book addresses all those who have to teach or learn geometry at an undergraduate level. More than 110 very aesthetical figures accompany the text and appeal to the geometric intuition of the reader; 41 references are recommended for further reading. The text is divided into 7 chapters, each begins with an overview and ends with problems and exercises." (Rolf Riesinger, zbMATH, Vol. 1298, 2014)

• ​Introduction.- Preface.- 1.The Birth of Analytic Geometry.- 2.Affine Geometry.- 3.More on Real Affine Spaces.- 4.Euclidean Geometry.- 5.Hermitian Spaces.- 6.Projective Geometry.- 7.Algebraic Curves.- Appendices: A. Polynomials Over a Field.- B. Polynomials in Several Variables.- C. Homogeneous Polynomials.- D. Resultants.- E. Symmetric Polynomials.- F. Complex Numbers.- G. Quadratic Forms.- H. Dual Spaces.- Index.- Bibliography.​