Overview

How is a subway map different from other maps? What makes a knot knotted? What makes the M�bius strip one-sided? These are questions of topology, the mathematical study of properties preserved by twisting or stretching objects. In the 20th century topology became as broad and fundamental as algebra and geometry, with important implications for science, especially physics. In this Very Short Introduction, Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field.

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Bruce Mann, Earphones Award-winning narrator, studied classical acting at the prestigious London Academy of Music and Dramatic Art and has been a successful voice-over artist and actor for over ten years. Richard Earl is Director of Undergraduate Studies in the Mathematical Institute, Oxford University, and senior tutor in mathematics at Worcester College, Oxford. He has taught topology at undergraduate and graduate level, as well as presenting the topic to secondary school students. Richard is the author of Towards Higher Mathematics: A Companion.

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