Springer Undergraduate Mathematics Series / Affine Maps, Euclidean Motions and Quadrics

Affine Spaces.- Affinities.- Classification of Affinities.- Classification of Affinities in Arbitrary Dimension.- Euclidean Affine Spaces.- Euclidean motions.- Euclidean Motions of the Line, the Plane and of Space.- Affine Classification of Real Quadrics.- Orthogonal Classification of Quadrics.- Appendices.

From the reviews:"This is a textbook on Affine and Euclidean Geometry, with emphasis on classification problems ... . any professor will easily find the way to adapt the text to particular whims, discarding technicalities or lightening some lessons. ... students will find a self-contained book containing all they need to catch the matter: full details and many solved and proposed examples. All in all the text is a highly recommendable choice for a course on Affine Geometry, and fills some gaps in the existing literature." (Jesús M. Ruiz, The European Mathematical Society, February, 2012)"The book arose from courses held by the author and his predecessors at the Autonomous University of Barcelona, hence it is, at the one hand, for the advanced undergraduate and beginning graduate students of mathematics, physics, and engineering and, at the other hand, for lecturers of linear algebra. ... The clearly arranged book offers modern concepts and notation, a high level of generality, many examples solved in detail, and a great number of exercises." (Rolf Riesinger, Zentralblatt MATH, Vol. 1222, 2011)"Anyone who ... is particularly interested in how geometry can be developed using the tools of linear algebra will certainly want to look closely at this book, which gives a linear-algebraic definition of affine and Euclidean geometry ... . Tarrida clearly intends for this book to be used primarily as a text, rather than as a reference. It was obviously written with the needs of students in mind. ... There is also a good supply of worked examples and end-of-chapter exercises." (Mark Hunacek, The Mathematical Association of America, October, 2011)

From the reviews:

"This is a textbook on Affine and Euclidean Geometry, with emphasis on classification problems ... . any professor will easily find the way to adapt the text to particular whims, discarding technicalities or lightening some lessons. ... students will find a self-contained book containing all they need to catch the matter: full details and many solved and proposed examples. All in all the text is a highly recommendable choice for a course on Affine Geometry, and fills some gaps in the existing literature." (Jesús M. Ruiz, The European Mathematical Society, February, 2012)

"The book arose from courses held by the author and his predecessors at the Autonomous University of Barcelona, hence it is, at the one hand, for the advanced undergraduate and beginning graduate students of mathematics, physics, and engineering and, at the other hand, for lecturers of linear algebra. ... The clearly arranged book offers modern concepts and notation, a high level of generality, many examples solved in detail, and a great number of exercises." (Rolf Riesinger, Zentralblatt MATH, Vol. 1222, 2011)

"Anyone who ... is particularly interested in how geometry can be developed using the tools of linear algebra will certainly want to look closely at this book, which gives a linear-algebraic definition of affine and Euclidean geometry ... . Tarrida clearly intends for this book to be used primarily as a text, rather than as a reference. It was obviously written with the needs of students in mind. ... There is also a good supply of worked examples and end-of-chapter exercises." (Mark Hunacek, The Mathematical Association of America, October, 2011)