Affine and Projective Geometry

An important new perspective on AFFINE AND PROJECTIVEGEOMETRY

This innovative book treats math majors and math education studentsto a fresh look at affine and projective geometry from algebraic,synthetic, and lattice theoretic points of view.

Affine and Projective Geometry comes complete with ninetyillustrations, and numerous examples and exercises, coveringmaterial for two semesters of upper-level undergraduatemathematics. The first part of the book deals with the correlationbetween synthetic geometry and linear algebra. In the second part,geometry is used to introduce lattice theory, and the bookculminates with the fundamental theorem of projectivegeometry.

While emphasizing affine geometry and its basis in Euclideanconcepts, the book:

• Builds an appreciation of the geometric nature of linear algebra

• Expands students' understanding of abstract algebra with itsnontraditional, geometry-driven approach

• Demonstrates how one branch of mathematics can be used to provetheorems in another

• Provides opportunities for further investigation of mathematicsby various means, including historical references at the ends ofchapters

Throughout, the text explores geometry's correlation to algebra inways that are meant to foster inquiry and develop mathematicalinsights whether or not one has a background in algebra. Theinsight offered is particularly important for prospective secondaryteachers who must major in the subject they teach to fulfill thelicensing requirements of many states. Affine and ProjectiveGeometry's broad scope and its communicative tone make it an idealchoice for all students and professionals who would like to furthertheir understanding of things mathematical.

Auteur
M. K. BENNETT is Professor of Mathematics at the University of Massachusetts, Amherst, where she earned her PhD in 1966. She was a John Wesley Young Postdoctoral Research Fellow at Dartmouth College, has authored numerous research articles on lattice theory, geometry, and quantum logics and has lectured on her work around the globe.

Résumé
An important new perspective on AFFINE AND PROJECTIVEGEOMETRY

This innovative book treats math majors and math education studentsto a fresh look at affine and projective geometry from algebraic,synthetic, and lattice theoretic points of view.

Affine and Projective Geometry comes complete with ninetyillustrations, and numerous examples and exercises, coveringmaterial for two semesters of upper-level undergraduatemathematics. The first part of the book deals with the correlationbetween synthetic geometry and linear algebra. In the second part,geometry is used to introduce lattice theory, and the bookculminates with the fundamental theorem of projectivegeometry.

While emphasizing affine geometry and its basis in Euclideanconcepts, the book:

• Builds an appreciation of the geometric nature of linear algebra
• Expands students' understanding of abstract algebra with itsnontraditional, geometry-driven approach
• Demonstrates how one branch of mathematics can be used to provetheorems in another

• Provides opportunities for further investigation of mathematicsby various means, including historical references at the ends ofchapters

  Throughout, the text explores geometry's correlation to algebra inways that are meant to foster inquiry and develop mathematicalinsights whether or not one has a background in algebra. Theinsight offered is particularly important for prospective secondaryteachers who must major in the subject they teach to fulfill thelicensing requirements of many states. Affine and ProjectiveGeometry's broad scope and its communicative tone make it an idealchoice for all students and professionals who would like to furthertheir understanding of things mathematical.

Contenu
Affine Planes.

Desarguesian Affine Planes.

Introducing Coordinates.

Coordinate Projective Planes.

Affine Space.

Projective Space.

Lattices of Flats.

Collineations.

Appendices.

Index.