Knuth Art Programming

The Art of Computer Programming is a multivolume work on the analysis of algorithms and has long been recognized as the definitive description of classical computer science. The five volumes published to date—Volumes 1, 2, 3, 4A, and 4B—already comprise a unique and invaluable resource in programming theory and practice. Countless readers have spoken about the profound personal influence of Knuth's writings. Scientists have marveled at the beauty and elegance of his analysis, while practicing programmers have successfully applied his "cookbook" solutions to their day-to-day problems. All have admired Knuth for the breadth, clarity, accuracy, and good humor found in his books.

You might well wonder why TFPC in Practice is a part of the Monographs in Visualization series. However, if you really think about typesetting, especially fine typesetting, you soon realize that in large part it is a visual art as well as a science. 'lEX's algorithms produce in almost all cases aesthetic results of the highest quality. On the other hand, occasionally one may want to insert some additional space before a subscript or superscript, or one may want to adjust the vertical spacing in a fraction. Fortunately Donald Knuth, the author of 'lEX, allows one to program such corrections easily where needed. The four volumes of Stephan von Bechtolsheim's long awaited TFPC in Prac­ tice present a comprehensive view of 'lEX. His thorough discussion of each aspect of 'lEX is liberally laced with cogent illustrative examples. Many of these exam­ ples represent complete, ready to use macros that enhance the capabilities of 'lEX. These examples are of particular interest to both the typesetter and the 'lEX programmer. The typesetter can often solve an immediate problem by ei­ ther using one of the examples directly or by making minor changes to adapt it to the problem at hand. The 'lEX programmer can use the examples, along with Stephan's detailed discussion, to increase both the depth and breadth of his or her knowledge of 'lEX. The value of the text is further enhanced by Stephan's concerted effort to explain the reasoning behind each topic or example.

With the advent of powerful computing tools and numerous advances in math­ ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al­ gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli­ cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc … Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.

The Art of Computer Programming is Knuth's multivolume analysis of algorithms. With the addition of this new volume, it continues to be the definitive description of classical computer science.

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