New Scientific Applications of Geometry and Topology

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American Mathematical Soc., 1992 - Mathematics - 250 pages
Geometry and topology are subjects generally considered to be ``pure'' mathematics. Recently, however, some of the methods and results in these two areas have found new utility in both wet-lab science (biology and chemistry) and theoretical physics. Conversely, science is influencing mathematics, from posing questions that call for the construction of mathematical models to exporting theoretical methods of attack on long-standing problems of mathematical interest. Based on an AMS Short Course held in January 1992, this book contains six introductory articles on these intriguing new connections. There are articles by a chemist and a biologist about mathematics, and four articles by mathematicians writing about science. All are expository and require no specific knowledge of the science and mathematics involved. Because this book communicates the excitement and utility of mathematics research at an elementary level, it is an excellent textbook in an advanced undergraduate mathematics course.
 

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Contents

Implications for its Biological Roles
1
Geometry and Topology of DNA and DNAProtein Interactions
17
Knot Theory and DNA
39
Topology of Polymers
73
Knots and Chemistry
97
Knots and Physics
131
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Page 4 - To conclude, it must be emphasized that the complex topology of DNA is essential for the life of all organisms. In particular, it is needed for the process known as DNA replication, whereby a replica of the DNA is made and one copy is passed on to each daughter cell. The most direct evidence for the vital role played by DNA topology is provided by the results of attempts to change the topology of DNA inside cells. Two related questions arise immediately from the recognition that DNA topology is essential...

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