Knots, Molecules, and the Universe: An Introduction to Topology by Erica FlapanMy rating: 0 of 5 stars
...This book introduces the elementary mathematics of topology with applications to chemistry and cosmology. Basically self-contained, it does not assume or require any mathematical background beyond the most basic algebra and set theory concepts and notation. Clearly meant to be fun, this can be an enjoyable read for the interested and nontechnical, or used as an undergraduate textbook. There are some ambitious undertakings by the authors, considering the audience, as the second chapter “Visualizing Four Dimensions” and the exploration of the Klein Bottle later in “Part 1: Universes”. Sticking with the material, the reader will have a good understanding of orientability, manifolds, Euler characteristic, and the genus of a surface. Keeping with the theme of assuming no real prior mathematical sophistication on the reader, proving the sidedness of a non-orientable 3-manifold is patiently walked through beginning with defining “if and only if”. This Part concludes with a thorough and enlightening dive info Euclid’s Axioms, since throughout non-Euclidean surfaces must be confronted...
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