Notices of the American Mathematical Society

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. April 2016, Front Cover MCA 2017 Become an AMS Life Member AMS Epsilon Fund April 2016 Table of Contents Front Matter Gauge Invariance of Degenerate Riemannian Metrics, Alice Barbara Tumpach AMS Blogs Mathematics Awareness Month MathSciNet AMS Exemplar Program Award Call for Nominations AMS Spring Sectional Sampler Mathematical Imagery About the Cover Modeling Ebola at the Mathematical and Theoretical Biology Institute (MTBI), C. Castillo Chavez, K. Barley, D. Bichara, D. Chowell, E. Diaz Herrera, B. Espinoza, V. Moreno, S. Towers, and K.E. Yong Call for Nomiations Frank and Brennier Morgan AMS-MAA-SIAM Prize New Applied Math Titles from SIAM/AMS Bookstore email Alert JMM Photos Arlie Petters Interview What Is?..a Quandle, Sam Nelson Graduate Student Blog Find the Graduate Program Report on 2014-2015 Academic Recruitment, Hiring, and Attrition, William Yslas Velez, Thomas H. Barr, and Colleen A. Rose Call for Nomiations for Bocher, Cole, and Conant Prizes 2015-2016 Faculty Salaries Report AMS Graduate Student Blog New Directions in Numerical Computation, Tobin A. Driscoll, Endre Suli, and Alex Townsend, Editors Alexandre Grothendieck 1928-2014, Part 2 Tsinghua University/Tsinghua Sanya International Mathematics Forum Letters to the Editor New from Princeton University Press 2016 Leroy P. Steele Prizes 2016 Chevalley Prize in Lie Theory 2016 Levi L. Conant Prize 2016 E.H. Moore Research Article Prize 2016 Oswald Veblen Prize in Geometry 2016 David P. Robbins Prize 2016 Award for Distinguished Public Service 2016 Frank and Brennie Morgan Prize for Outstanding Research 2016 Norbert Wiener Prize in Applied Mathematics Birds and Frogs: Selected Papers, 1990-2014, A Book Review by Gerald B. Folland Bookshelf Mathematics People Mathematics Opportunities Inside the AMS Classified Advertisements New Publications Offered by the AMS STML Mathematics Calendar Meets & Conference of the AMS Table of Contents Meetings & Conferences of the AMS The Back Page Call for Applications for Director of Washington Office AMS Bookstore