# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.08

## Topology

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## ANNOTATED BIBLIOGRAPHY FOR TEACHERS

2. Mathematics, by David Bergamini. A book in Time Life’s “Life Science Library” Series, 1963. “Topology: The Mathematics of Distortion,” pp. 176191. Excellent introduction to the ideas of Topological Transformations, Moebius Strip, Map Coloring, Noncircular Circles and Mazes with No Insides and The Bridges of Koenigsberg. Beautifully illustrated and inspiring.

3. Mathematical Snapshots, by Hugo Steinhaus, Oxford, 1969. Chapter 12, “Platonic Bodies, Crossing Bridges, Tying Knots, Coloring Maps and Combing Hair, pp. 252281. Good for general reading.

4. School Mathematics Project: Book B, Cambridge University Press. Chapter 11. Excellent introduction to Topological Transformations, Simple Closed Curves, Traversable Networks, Inside or Outside, Coloring Regions and the Koenigsberg Bridge problem with lots of examples and illustrations. A must for those who wish to teach topology.

5. School Mathematics Project Book 2, Cambridge University Press. Chapter I. Good introduction to Topological Maps, Topological Transformations, Simple Closed Curves, Traversable Networks and Coloring Regions with examples and illustrations.

6. Experiments in Mathematics, Pearcy and Lewis, Longmans.

Stage I: pp. 4647. Good introduction to the idea of “Inside or Outside” with examples and illustrations. Well worth reading, it deals with how complicated mazes are transformed into simple networks.

Stage 2: pp. 4647. Good introduction to the idea of “The Moebius Band and Other Surfaces.” Good for general reading.

Stage 3: pp. 2021. Good introduction to “Networks and Routes” and solution to the problem of the Seven Bridges of Koenigsberg, pp. 4243. Excellent photographs and introduction to the idea of “Topological Transformations,” with an easytofollow text.