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Erica Flapan, ""

In this superb topology text, the readers not only learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, but also their role in understanding molecular structures. Most results described in the text are motivated by the questions of chemists or molecular biologists, though they often go beyond answering the original question asked. No specific mathematical or chemical prerequisites are required. The text is enhanced by nearly 200 illustrations and 100 exercises. With this fascinating book, undergraduate mathematics students escape the world of pure abstract theory and enter that of real molecules, while chemists and biologists find simple and clear but rigorous definitions of mathematical concepts they handle intuitively in their work.

Summary: Mathematics used to explain how biological molecules achieve their activity

Rating: 4

As someone who earned undergraduate majors in mathematics and chemistry and has gone on to teach mathematics at the college level, my first glimpse of this book immediately generated a desire to read it. The one overriding fact of organic and biochemistry is that it is the three-dimensional structure of molecules that gives them their ability to carry out biological activity. It is also not the mere presence of the components in the molecule that matter, but the sections that appear in the active regions.

To truly understand this and appreciate the complexity, some basic understanding of three-dimensional folding or knot theory as applied to molecules is needed. This book will not disappoint you if you are a chemist and want to learn the mathematical basis of the structure of large molecules. While it is impossible to cover such topics without using some advanced mathematical details, Flapan keeps it to a minimum. Anyone who has completed a two-course sequence in calculus should be able to leverage their fundamental understanding of the molecules into reaching an understanding.

Mathematics has many uses; in this case it is effectively applied to explain how large molecules reach their final shapes. It is also used to answer some fundamental questions regarding how life manages to perform the wondrous and routine activities that allow it to exist.

Published in Journal of Recreational Mathematics, reprinted with permission

Summary: How can topology be applied to chemistry?

Rating: 4

This question is answered in a remarkable new book by Erica Flapan, knot theorist and professor of mathematics at Pomona College. Stereochemistry, the study of the three-dimensional structure of molecules, is a recurring theme in chemistry and related fields. Topology, the study of geometrical properties which are invariant under continuous transformations, is a similarly popular area for mathematicians. While it is not immediately obvious that the two fields have anything in common, both fields owe a debt to the other. Although she initiates her book with a historical perspective and detailed expository on basic aspects of low dimensional topology (e.g., stereoisomers, chirality, nonrigid symmetries, knot and link types, three-dimensional manifolds, and link polynomials) she does proceed into more advanced subject matter in later chapters including Möbius ladders, symmetries of embedded graphs, and hierarchies of automorphisms. Of particular interest to the molecular biologist, the final chapter is devoted entirely to the topology of DNA and includes topological considerations of supercoiling, toroidal winding, enzyme action, and tangle theory. The arguments are clearly presented within the framework of interesting and relevant molecular structures, yet there is enough mathematical rigor to satisfy dyed-in-the-wool mathematicians as well. Although there will likely be something of interest to the average working chemist, the supramolecular scientist, organic chemist, molecular biologist, and biophysicist, in particular, stand to gain the most by the contents of this book.

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Rating:
2.5 out of 5 by Book123