A textbook for a two-semester advanced undergraduate course for students of mathematics and math education, especially those intending to teach high school. The first part demonstrates the correlations between synthetic geometry and linear algebra; the second uses geometry to introduce lattice theory. The fundamental theorem of projective geometry is also explained. Annotation copyright Book News, Inc. Portland, Or.
An important new perspective on AFFINE AND PROJECTIVE GEOMETRY
This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view.
Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory, and the book culminates with the fundamental theorem of projective geometry.
While emphasizing affine geometry and its basis in Euclidean concepts, the book:
* Builds an appreciation of the geometric nature of linear algebra
* Expands students' understanding of abstract algebra with its nontraditional, geometry-driven approach
* Demonstrates how one branch of mathematics can be used to prove theorems in another
* Provides opportunities for further investigation of mathematics by various means, including historical references at the ends of chapters
Throughout, the text explores geometry's correlation to algebra in ways that are meant to foster inquiry and develop mathematical insights whether or not one has a background in algebra. The insight offered is particularly important for prospective secondary teachers who must major in the subject they teach to fulfill the licensing requirements of many states. Affine and Projective Geometry's broad scope and its communicative tone make it an ideal choice for all students and professionals who would like to further their understanding of things mathematical.
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