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Knots, Molecules, and the Universe: An Introduction to Topology

Erica Flapan Pomona College, Claremont, CA
Available Formats:
Hardcover ISBN: 978-1-4704-2535-7
Product Code: MBK/96
386 pp
List Price: $74.00 MAA Member Price:$66.60
AMS Member Price: $59.20 Electronic ISBN: 978-1-4704-2819-8 Product Code: MBK/96.E 386 pp List Price:$69.00
MAA Member Price: $62.10 AMS Member Price:$55.20
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $111.00 MAA Member Price:$99.90
AMS Member Price: $88.80 Click above image for expanded view Knots, Molecules, and the Universe: An Introduction to Topology Erica Flapan Pomona College, Claremont, CA Available Formats:  Hardcover ISBN: 978-1-4704-2535-7 Product Code: MBK/96 386 pp  List Price:$74.00 MAA Member Price: $66.60 AMS Member Price:$59.20
 Electronic ISBN: 978-1-4704-2819-8 Product Code: MBK/96.E 386 pp
 List Price: $69.00 MAA Member Price:$62.10 AMS Member Price: $55.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$111.00
MAA Member Price: $99.90 AMS Member Price:$88.80
• Book Details

2016
MSC: Primary 57; 92; 94;

This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook.

The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material.

The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details.

Undergraduate students and instructors interested in elementary topology.

• Part 1. Universes
• Chapter 1. An introduction to the shape of the universe
• Chapter 2. Visualizing four dimensions
• Chapter 3. Geometry and topology of different universes
• Chapter 4. Orientability
• Chapter 5. Flat manifolds
• Chapter 6. Connected sums of spaces
• Chapter 7. Products of spaces
• Chapter 8. Geometries of surfaces
• Part 2. Knots
• Chapter 9. Introduction to knot theory
• Chapter 10. Invariants of knots and links
• Chapter 11. Knot polynomials
• Part 3. Molecules
• Chapter 12. Mirror image symmetry from different viewpoints
• Chapter 13. Techniques to prove topological chirality
• Chapter 14. The topology and geometry of DNA
• Chapter 15. The topology of proteins

• Reviews

• [T]his is a wonderful introduction to geometry and topology and their applications to the sciences. The book contains a unique collection of topics that might entice young readers to continue their academic careers by learning more about the world of mathematics.

Claus Ernst, Zentralblatt MATH
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2016
MSC: Primary 57; 92; 94;

This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook.

The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material.

The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details.

Undergraduate students and instructors interested in elementary topology.

• Part 1. Universes
• Chapter 1. An introduction to the shape of the universe
• Chapter 2. Visualizing four dimensions
• Chapter 3. Geometry and topology of different universes
• Chapter 4. Orientability
• Chapter 5. Flat manifolds
• Chapter 6. Connected sums of spaces
• Chapter 7. Products of spaces
• Chapter 8. Geometries of surfaces
• Part 2. Knots
• Chapter 9. Introduction to knot theory
• Chapter 10. Invariants of knots and links
• Chapter 11. Knot polynomials
• Part 3. Molecules
• Chapter 12. Mirror image symmetry from different viewpoints
• Chapter 13. Techniques to prove topological chirality
• Chapter 14. The topology and geometry of DNA
• Chapter 15. The topology of proteins
• [T]his is a wonderful introduction to geometry and topology and their applications to the sciences. The book contains a unique collection of topics that might entice young readers to continue their academic careers by learning more about the world of mathematics.

Claus Ernst, Zentralblatt MATH
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