In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make...

This text aims to show that mathematics is useful to virtually everyone. And it seeks to accomplish this by offering the reader plenty of practice in elementary mathematical computations motivated by real-world problems. The prerequisite for this book is a little algebra and geometry-nothing more than entrance requirements at most colleges. I hope that users-especially those who "don't like math"-will complete the course with greater confidence in their ability to solve practical problems (without seeking help from someone who is "good at math"). Here is a sampler of some of the problems to...

This book is an introduction to information and coding theory at the graduate or advanced undergraduate level. It assumes a basic knowledge of probability and modern algebra, but is otherwise self- contained. The intent is to describe as clearly as possible the fundamental issues involved in these subjects, rather than covering all aspects in an encyclopedic fashion. The first quarter of the book is devoted to information theory, including a proof of Shannon's famous Noisy Coding Theorem. The remainder of the book is devoted to coding theory and is independent of the information theory...