The book "Selected Papers in Discrete Mathematics" is a compilation of work published (plus some unpublished papers) by Donald E. Knuth, in the area of discrete mathematics. Clearly, the author does not need any introduction, and is well known by his authoritative work in areas such analysis of algorithms and digital typography. However, more than this, Knuth is a great example of good expositor and writer. Thus, even if your interests are not directly related to the more mathematical areas of computer science, it is greatly rewarding to read this book as a way of learning how to write good papers.
Review of Selected Papers in Discrete Mathematics by D. Knuth, CSLI (Center for the Study of Language and Information Publication) paperback, $72.00
computation models in Chapters 6 and 7 are especially nice.) In their preface, the authors suggest that the individual chapters can be read independently, and this really does seem to be the case, since de nitions of terminology and notation are often repeated as needed. In the case of almost every theorem, a full proof is given and its source cited. Various pseudocodes for presenting algorithms are introduced and adhered to consistently at least within any single chapter. The nal section of each chapter is devoted to historical and bibliographical remarks. There are ten to forty exercises, of various degrees of di culty at the end of each chapter. These occasionally include open problems. Finally, there is an extensive bibliography, and the index, mixing symbols and terms, is perhaps adequate for most readers. (There is no name index.) For anyone wishing to get quickly to the forefront of current research with respect to the topics it covers, this book is doubtless a good place to start. On the other hand, the book s tremendous scope means that the demands on the reader are considerable. For instance, the reader will nd only two examples, with diagrams, of Boolean circuits on pages 8 and 436 and they are essentially the same. Our one reservation concerns the organization of the book across chapters: speci cally, the text gives the impression of being, in a sense, not one book but, rather, four. The rst extends over Chapters 1 through 3, covering Boolean functions and complexity classes derived from the Boolean circuit model. In later chapters these ideas do occasionally resurface to be sure. For example, the combinatorial argument for a certain Boolean circuit lower-bound result from Chapter 2 gures in an argument for an exponential lower bound on the size of proofs of a version of PHP within bounded-depth Frege systems. But such connections typically receive no mention within chapter introductions and are, for the most part, buried within...
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Review of Selected Papers in Discrete Mathematics by D. Knuth, CSLI (Center for the Study of Language and Information Publication) paperback, $72.00
Oliveira, Carlos A. S.
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, Volume 35 (4)
Association for Computing Machinery – Dec 1, 2004
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