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Affine and Projective Geometry, by M. K. Bennett
Free Ebook Affine and Projective Geometry, by M. K. Bennett
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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* Provides opportunities for further investigation of mathematics by various means, including historical references at the ends of chapters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.
- Sales Rank: #2529567 in Books
- Published on: 1995-08-18
- Original language: English
- Number of items: 1
- Dimensions: 9.57" h x .71" w x 6.34" l, 1.18 pounds
- Binding: Hardcover
- 248 pages
From the Publisher
Combines three different approaches to affine and projective geometry--algebraic, synthetic and lattice theoretic. By emphasizing these three perspectives, the author demonstrates how areas of mathematics overlap--in this case, algebra and geometry. Provides a complete, detailed and self-contained description of the coordinatization of (Desarguesian) affine and projective space and a thorough discussion of the lattices of these spaces' flats. Concludes with the Fundamental Theorem of Projective Geometry relating synthetic collineations, lattice and vector space isomorphisms. Includes numerous examples and exercises which enable students to develop their skills.
From the Back Cover
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.
About the Author
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.
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