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Knots, Molecules, and the Universe: An Introduction to Topology
 
Erica Flapan Pomona College, Claremont, CA
Knots, Molecules, and the Universe
Hardcover ISBN:  978-1-4704-2535-7
Product Code:  MBK/96
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
eBook ISBN:  978-1-4704-2819-8
Product Code:  MBK/96.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
Hardcover ISBN:  978-1-4704-2535-7
eBook: ISBN:  978-1-4704-2819-8
Product Code:  MBK/96.B
List Price: $154.00 $116.50
MAA Member Price: $138.60 $104.85
AMS Member Price: $123.20 $93.20
Knots, Molecules, and the Universe
Click above image for expanded view
Knots, Molecules, and the Universe: An Introduction to Topology
Erica Flapan Pomona College, Claremont, CA
Hardcover ISBN:  978-1-4704-2535-7
Product Code:  MBK/96
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
eBook ISBN:  978-1-4704-2819-8
Product Code:  MBK/96.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
Hardcover ISBN:  978-1-4704-2535-7
eBook ISBN:  978-1-4704-2819-8
Product Code:  MBK/96.B
List Price: $154.00 $116.50
MAA Member Price: $138.60 $104.85
AMS Member Price: $123.20 $93.20
  • Book Details
     
     
    2016; 386 pp
    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.

    Readership

    Undergraduate students and instructors interested in elementary topology.

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2016; 386 pp
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.

Readership

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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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