W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

    This distinguished little book is a brisk introduction to a series of mathematical concepts, a history of their development, and a concise summary of how today's reader may use them.

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    This brief, accessible introduction describes some of the most interesting research in the field and also enables readers to implement and experiment with genetic algorithms on their own. It focuses in depth on a small set of important and interesting topics--particularly in machine learning, scientific modeling, and artificial life--and reviews a broad span of research, including the work of Mitchell and her colleagues.The descriptions of applications and modeling projects stretch beyond the strict boundaries of computer science to include dynamical systems theory, game theory, molecular biology, ecology, evolutionary biology, and population genetics, underscoring the exciting general purpose nature of genetic algorithms as search methods that can be employed across disciplines.An Introduction to Genetic Algorithms is accessible to students and researchers in any scientific discipline. It includes many thought and computer exercises that build on and reinforce the reader's understanding of the text. The first chapter introduces genetic algorithms and their terminology and describes two provocative applications in detail. The second and third chapters look at the use of genetic algorithms in machine learning (computer programs, data analysis and prediction, neural networks) and in scientific models (interactions among learning, evolution, and culture; sexual selection; ecosystems; evolutionary activity). Several approaches to the theory of genetic algorithms are discussed in depth in the fourth chapter. The fifth chapter takes up implementation, and the last chapter poses some currently unanswered questions and surveys prospects for the future of evolutionary computation.

    The authors' enthusiasm for their subject is compelling as they present abstract concepts in a humorous and easy-to-grasp fashion. Together, these books will open new doors of thought to anyone who wants to find out what computing is really about. The Little Schemer introduces computing as an extension of arithmetic and algebra; things that everyone studies in grade school and high school. It introduces programs as recursive functions and briefly discusses the limits of what computers can do. The authors use the programming language Scheme, and interesting foods to illustrate these abstract ideas. The Seasoned Schemer informs the reader about additional dimensions of computing: functions as values, change of state, and exceptional cases. The Little LISPer has been a popular introduction to LISP for many years. It had appeared in French and Japanese. The Little Schemer and The Seasoned Schemer are worthy successors and will prove equally popular as textbooks for Scheme courses as well as companion texts for any complete introductory course in Computer Science.