Explorations in topology : Map coloring, surfaces, and knots / David Gay.

Includes bibliographical references and index.

Acme does maps and considers coloring them -- Acme adds tours -- Acme collects data from maps -- Acme collects more data, proves a theorem, and returns to coloring maps -- Acme's solicitor proves a theorem: the four-color conjecture -- Acme adds doughnuts to its repertoire -- Acme considers the Mobius strip -- Acme creates new worlds: Klein bottles and other surfaces -- Acme makes order out of chaos: surface sums and Euler numbers -- Acme classifies surfaces -- Acme encounters the fourth dimension -- Acme colors maps on surfaces: Heawood's estimate -- Acme gets all tied up with knots -- Where to go from here: projects.