Based on a well-received course designed for philosophy
students, this book is an informal introduction to mathematical
thinking. The work will be rewarding not only for philosophers
concerned with mathematical questions but also for serious amateur
mathematicians with an interest in the "frontiers" as well as the
foundations of mathematics. In what might be termed a sampler of
the discipline, Konrad Jacobs discusses an unusually wide range of
topics, including such items of contemporary interest as knot
theory, optimization theory, and dynamical systems. Using Euclidean
geometry and algebra to introduce the mathematical mode of thought,
the author then turns to recent developments. In the process he
offers what he calls a "Smithsonian of mathematical showpieces":
the five Platonic Solids, the Mbius Strip, the Cantor Discontinuum,
the Peano Curve, Reidemeister's Knot Table, the plane ornaments,
Alexander's Horned Sphere, and Antoine's Necklace. The treatments
of geometry and algebra are followed by a chapter on induction and
one on optimization, game theory, and mathematical economics. The
chapter on topology includes a discussion of topological spaces and
continuous mappings, curves and knots, Euler's polyhedral formula
for surfaces, and the fundamental group. The last chapter deals
with dynamics and contains material on the Game of Life, circle
rotation, Smale's "horseshoe," and stability and instability, among
other topics.
General
Imprint: |
Princeton University Press
|
Country of origin: |
United States |
Release date: |
August 1992 |
First published: |
August 1992 |
Authors: |
Konrad Jacobs
|
Dimensions: |
229 x 152 x 14mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
264 |
ISBN-13: |
978-0-691-02528-5 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
0-691-02528-2 |
Barcode: |
9780691025285 |
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