Overview
- Authors:
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Thomas Banchoff
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Department of Mathematics, Brown University, Providence, USA
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John Wermer
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Department of Mathematics, Brown University, Providence, USA
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Table of contents (25 chapters)
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- Thomas Banchoff, John Wenner
Pages 1-2
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- Thomas Banchoff, John Wermer
Pages 3-22
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- Thomas Banchoff, John Wermer
Pages 23-28
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- Thomas Banchoff, John Wermer
Pages 29-38
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- Thomas Banchoff, John Wermer
Pages 39-48
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- Thomas Banchoff, John Wermer
Pages 49-59
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- Thomas Banchoff, John Wermer
Pages 60-73
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- Thomas Banchoff, John Wermer
Pages 74-83
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- Thomas Banchoff, John Wermer
Pages 84-95
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- Thomas Banchoff, John Wermer
Pages 96-110
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- Thomas Banchoff, John Wermer
Pages 111-125
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- Thomas Banchoff, John Wermer
Pages 126-129
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- Thomas Banchoff, John Wermer
Pages 130-134
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- Thomas Banchoff, John Wermer
Pages 135-144
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- Thomas Banchoff, John Wermer
Pages 145-162
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- Thomas Banchoff, John Wermer
Pages 163-174
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- Thomas Banchoff, John Wermer
Pages 175-189
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- Thomas Banchoff, John Wermer
Pages 190-201
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- Thomas Banchoff, John Wermer
Pages 202-206
About this book
In this book we lead the student to an understanding of elementary linear algebra by emphasizing the geometric significance of the subject. Our experience in teaching beginning undergraduates over the years has convinced us that students learn the new ideas of linear algebra best when these ideas are grounded in the familiar geometry of two and three dimensions. Many important notions of linear algebra already occur in these dimensions in a non-trivial way, and a student with a confident grasp of these ideas will encounter little difficulty in extending them to higher dimensions and to more abstract algebraic systems. Moreover, we feel that this geometric approach provides a solid basis for the linear algebra needed in engineering, physics, biology, and chemistry, as well as in economics and statistics. The great advantage of beginning with a thorough study of the linear algebra of the plane is that students are introduced quickly to the most important new concepts while they are still on the familiar ground of two-dimensional geometry. In short order, the student sees and uses the notions of dot product, linear transformations, determinants, eigenvalues, and quadratic forms. This is done in Chapters 2.0-2.7. Then the very same outline is used in Chapters 3.0-3.7 to present the linear algebra of three-dimensional space, so that the former ideas are reinforced while new concepts are being introduced.
