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SCAFFOLDING
Reacting to criticism concerning the lack of motivation in his writings, Gauss remarked that
architects of great cathedrals do not obscure the beauty of their work by leaving the scaffolding in
place after the construction has been completed. His philosophy epitomized the formal presentation
and teaching of mathematics throughout the nineteenth and twentieth centuries, and it is still
commonly found in mid-to-upper-level mathematics textbooks. The inherent efficiency
and natural beauty of mathematics are compromised by straying too far from Gauss' viewpoint.
But, as with most things in life, appreciation is generally preceded by some understanding seasoned
with a bit of maturity, and in mathematics this comes from seeing some of the scaffolding.
The challenge in teaching applied linear algebra is to expose some of
the scaffolding while conditioning students to appreciate the utility and beauty of the subject.
Effectively meeting this challenge and bridging the inherent gaps between
basic and more advanced mathematics are primary goals of this book.
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