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Knots, Molecules, and the Universe
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-dimensi...
When Topology Meets Chemistry
The applications of topological techniques for understanding molecular structures have become increasingly important over the past thirty years. In this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, while learning the role these play in understanding molecular structures. Most of the results that are described in the text are motivated by questions asked by chemists or molecular biologists, though the results themselves often go beyond answering the original question asked. There is no specific mathematical or chemical prerequisite; all the relevant background is provided. The text is enhanced by nearly 200 illustrations and more than 100 exercises. Reading this fascinating book, undergraduate mathematics students can escape the world of pure abstract theory and enter that of real molecules, while chemists and biologists will find simple, clear but rigorous definitions of mathematical concepts they handle intuitively in their work.
My Mathematical Universe: People, Personalities, And The Profession
This is an autobiography and an exposition on the contributions and personalities of many of the leading researchers in mathematics and physics with whom Dr Krishna Alladi, Professor of Mathematics at the University of Florida, has had personal interaction with for over six decades. Discussions of various aspects of the physics and mathematics academic professions are included.Part I begins with the author's unusual and frequent introductions as a young boy to scientific luminaries like Nobel Laureates Niels Bohr, Murray Gell-Mann, and Richard Feynman, in the company of his father, the scientist Alladi Ramakrishnan. Also in Part I is an exciting account of how the author started his research...
Knots, Braids And Mobius Strips - Particle Physics And The Geometry Of Elementarity: An Alternative View
Elementary particles in this book exist as Solitons in-and-of the fabric of spacetime itself. As such they are characterized by their geometry, that is their topology and configuration which lead directly to their physical attributes and behavior as well as to a simplification and reduction of assumptions and the importation of parameter values. The emphasis of the book is thus on that geometry, the algebraic geometry associated with taxonomical issues and the differential geometry that determines the physics as well as on simplifying the results. In itself, however, the process of assembling and developing what eventually went into the book has been a singularly rewarding journey. Along the...
The Edge of the Universe
Exquisite expositions of mathematics taken from the first ten years of the Math Horizons magazine.
How Euler Did It
"The final 35 How Euler Did It columns are all collected in this book. ... They are lightly edited versions of the columns as they actually appeared on MAA Online between March 2007 and February 2010"--
Modern Cryptography and Elliptic Curves
This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, a...
777 Mathematical Conversation Starters
Illustrated book showing that there are few degrees of separation between mathematics and topics that provoke interesting conversations.
A Conversational Introduction to Algebraic Number Theory
Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to mo...
