Five More Golden Rules: Knots, Codes, Chaos, and Other Great Theories of 20th Century Mathematics
by John L. Casti
This follow-up explores the intricacies of knot theory, functional analysis, control theory, chaotic systems, and information theory.
Science author John Casti offers an exposition of the origins of five additional interesting modern mathematical theories, with insight on how these discoveries have shaped our lives. As with the first volume, no more background is required than high school math classes.
Knots: Mathematics With a Twist
by Alexei Sossinsky
Ornaments and icons, symbols of complexity or evil, aesthetically appealing and endlessly useful in everyday ways, knots are also the object of mathematical theory used to unravel ideas about the topological nature of space. In recent years, knot theory has been brought to bear on the study of equations describing the weather systems, mathematical models used in physics, and even, with the realization that DNA sometimes is knotted molecular biology. Sossinsky is Professor of Mathematics at the University of Moscow.
The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time
by Keith J. Devlin
In 2000, the Clay Foundation of Cambridge, Massachusetts, announced a historic competition: whoever could solve any of seven extraordinarily difficult mathematical problems, and have the solution acknowledged as correct by the experts, would receive $1 million in prize money. There was some precedent for doing this: in 1900 David Hilbert, one of the greatest mathematicians of his day, proposed twenty-three problems, now known as the Hilbert Problems, that set much of the agenda for mathematics in the twentieth century.
The Millennium Problems are likely to acquire similar stature, and their solution (or lack of one) is likely to play a strong role in determining the course of mathematics in the current century. Keith Devlin, renowned expositor of mathematics, tells here what the seven problems are, how they came about, and what they mean for math and science. He has done an excellent job of providing a historical and mathematical background for each of these problems for the laymen, and in process, reveals how the solutions to these problems would bring an exponential leap for the human knowledge as a whole.
Nine Crazy Ideas in Science: A Few Might Even Be True
by Robert Ehrlich
The author points out that many ideas in science seemed crazy at one time but are now reported as being settled ... as in the case of plate tectonics, which grew out of an earlier "crazy" theory of continental drift.
Some of the crazy ideas relate to our lives: AIDS, gun control, sun and radiation exposure. Others are further out there, such as the double sun theory and the possibility of time travel. For each he examines who the idea's proponents are and what their agendas might be. He looks for internal consistency, misapplication of statistics, how open the proponents are with their data and methods, and more. The book makes several eccentric scientific theories accessible to general readers and, more important, it teaches methods of evaluating new ideas so we can decide for ourselves whether or not they make sense.
Proofs from the Book
by Martin Aigner, Gunter M. Ziegler
The heroes of this book are the perfect proofs: brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives to basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest undergraduate mathematical background.