id: 02316801
dt: b
an: 1997b.00695
au: Hilton, P.; Holton, D.; Pedersen, J.
ti: Mathematical reflections. In a room with many mirrors.
so: Springer, New York, NY (ISBN 0-387-94770-1). 367 p. (1997).
py: 1997
pu: Springer, New York, NY
la: EN
cc: A25
ut:
ci:
li:
ab: The purpose of this book is to show what mathematics is about, how it is
done, and what it is good for. Frequent questions lead the reader to
see mathematics as an accessible world of thought, where understanding
can turn opaque formulae into beautiful and meaningful ideas. The text
presents eight topics that serve to illustrate the unity of
mathematical thought as well as the diversity of mathematical ideas.
Drawn from both: pure and applied mathematics, they include: spirals in
nature and in mathematics; the modern topic of fractals and the ancient
topic of Fibonacci numbers; Pascalâ€™s triangle and paper folding - two
topics where geometry, number theory, and algebra meet and interact;
and modular arithmetic and the arithmetic of the infinite. The final
chapter presents some ideas about how mathematics should be done, and
hence, how it should be taught; these ideas are referred to throughout
the text, whenever mathematical strategy and technique are at issue.
rv: