Concrete mathematics: a foundation for computer science / Ronald. L. Graham It was a dark and stormy decade when Concrete Mathematics was born. PDF Drive is your search engine for PDF files. As of today we have 78,, eBooks for you to download for free. No annoying ads, no download limits, enjoy . Concrete Mathematics: A Foundation for Computer Science (2nd Edition) 2 edition (March 10, ); Hardcover pages; eBook PDF ( pages, MB) .

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DOWNLOAD PDF When DEK taught Concrete Mathematics at Stanford for the rst time, he explained the somewhat strange title by saying that it was his. The course title “Concrete Mathematics” was originally intended as an antidote to When DEK taught Concrete Mathematics at Stanford for the first time. Concrete mathematics: a foundation for computer science / Ron- ald L. Graham It was a dark and stormy decade when Concrete Mathematics was born.

List of Tables. About fifty students have taken it each year juniors and seniors, but mostly graduate students - and alumni of these classes have begun to spawn similar courses elsewhere. Thus the time seems ripe to present the material to a wider audience including sophomores. It was dark and stormy decade when Concrete Mathematics was born. Long-held values were constantly being questioned during those turbulent years; college campuses were hotbeds of controversy. The college curriculum itself was challenged, and mathematics did not escape scrutiny. John Hammersley had just written a thought-provoking article "On the enfeeblement of mathematical skills by 'Modern Mathematics' and by similar soft intellectual trash in schools and universities" ; other worried mathematicians even asked, "Can mathematics be saved? So he introduced a new course, teaching what he wished somebody had taught him. The course title "Concrete Mathematics" was originally intended as an antidote to "Abstract Mathematics," since concrete classical results were rapidly being swept out of the modern mathematical curriculum by a new wave of abstract ideas popularly called the "New Math. But its adherents had become deluded that the rest of mathematics was inferior and no longer worthy of attention. The goal of generalization had become so fashionable that a generation of mathematicians had become unable to relish beauty in the particular, to enjoy the challenge of solving quantitative problems, or to appreciate the value of technique. Abstract mathematics was becoming inbred and losing touch with reality; mathematical education needed a concrete counterweight in order to restore a healthy balance. When DEK taught Concrete Mathematics at Stanford for the first time he explained the somewhat strange title by saying that it was his attempt to teach a math course that was hard instead of soft.

Hungarian translation by S. Fridli, J. Gonda, A. Lakatos, and Cs.

Greek translation by Christos A. Kapoutsis Athens: Klidarithmos , , pp. Insight Press , , pp. Croatian translation Zagreb: Golden Marketing , in preparation. Macedonian translation Skopje: Ars Lamina , in preparation. Introduction to the mathematics that supports advanced computer programming and the analysis of algorithms.

An indispensable text and reference not only for computer scientists the authors themselves rely heavily upon it but for serious users of mathematics in virtually every discipline. The second edition includes important new material about the revolutionary Gosper-Zeilberger algorithm for mechanical summation.

Complete answers are provided for more than exercises. Available from the publisher, Addison-Wesley Publishing Company. For a list of corrections to known errors in the pre printings of the second edition, you may download the errata file in compressed PostScript format 74K bytes. This file was generated by the TeX file errata Errata lists for various printings of the first edition can also be found there. And here is a list of all nits that have been picked so far since the 27th printing May The college curriculum itself was challenged, and mathematics did not escape scrutiny.

So he introduced a new course, teaching what he wished somebody had taught him.

But its adherents had become deluded that the rest of mathematics was inferior and no longer worthy of attention. The goal of generalization had become so fashionable that a generation of mathematicians had become unable to relish beauty in the particular, to enjoy the challenge of solving quantitative problems, or to appreciate the value of technique.

Abstract mathematics was becoming inbred and losing touch with reality; mathematical education needed a concrete counterweight in order to restore a healthy balance. Several students from the civil engineering department got up and quietly left the room.

Although Concrete Mathematics began as a reaction against other trends, the main reasons for its existence were positive instead of negative.

Meanwhile, independent con rmation for the appropriateness of the name came from another direction, when Z. Melzak published two volumes entitled Companion to Concrete Mathematics []. The material of concrete mathematics may seem at rst to be a disparate bag of tricks, but practice makes it into a disciplined set of tools.

Indeed, the techniques have an underlying unity and a strong appeal for many people. When another one of the authors RLG rst taught the course in , the students had such fun that they decided to hold a class reunion a year later. But what exactly is Concrete Mathematics? It is a blend of continuous and discrete mathematics.

More concretely, it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. Once you, the reader, have learned the material in this book, all you will need is a cool head, a large sheet of paper, and fairly decent handwriting in order to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data.

You will be so uent in algebraic techniques that you will often nd it easier to obtain exact results than to settle for approximate answers that are valid only in a limiting sense.

The emphasis is on manipulative technique rather than on existence theorems or combinatorial reasoning; the goal is for each reader to become as familiar with discrete operations like the greatest-integer function and nite summation as a student of calculus is familiar with continuous operations like the absolute-value function and in nite integration. But the presentation in those pages is quite terse, so another author OP was inspired to draft a lengthy set of supplementary notes. Melzak [] Concrete Mathematics is a bridge to abstract mathematics.

Free the group. Nuke the kernel. Power to the n. I have only a marginal interest in this subject. This was the most enjoyable course I've ever had. But it might be nice to summarize the material as you go along.

Some of the more advanced parts have been omitted; on the other hand, several topics not found there have been included here so that the story will be complete. The authors have enjoyed putting this book together because the subject began to jell and to take on a life of its own before our eyes; this book almost seemed to write itself.

Moreover, the somewhat unconventional approaches we have adopted in several places have seemed to t together so well, after these years of experience, that we can't help feeling that this book is a kind of manifesto about our favorite way to do mathematics. Since this book was born in a university setting, we have tried to capture the spirit of a contemporary classroom by adopting an informal style.

Some people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we aren't ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive. The joys and sorrows of mathematical work are re ected explicitly in this book because they are part of our lives.

Some of these marginal markings are merely corny, some are profound; some of them warn about ambiguities or obscurities, others are typical comments made by wise guys in the back row; some are positive, some are negative, some are zero.

But they all are real indications of feelings that should make the text material easier to assimilate. Typical of the pseudointellectualism around here.

Somehow it seems appropriate to mix the words of Leibniz, Euler, Gauss, and others with those of the people who will be continuing the work. Mathematics is an ongoing endeavor for people everywhere; many strands are being woven into one rich fabric. Answers to all the exercises appear in Appendix A, often with additional information about related results. Readers are encouraged to look at the answers, especially the answers to the warmup problems, but only after making a serious attempt to solve the problem without peeking.

Mathematicians have unfortunately developed a tradition of borrowing exercises without any acknowledgment; we believe that the opposite tradition, practiced for example by books and magazines about chess where names, dates, and locations of original chess problems are routinely speci ed is far superior.

However, we have not been able to pin down the sources of many problems that have become part of the folklore. If any reader knows the origin of an exercise for which our citation is missing or inaccurate, we would be glad to learn the details so that we can correct the omission in subsequent editions of this book.

The typeface used for mathematics throughout this book is a new design by Hermann Zapf [], commissioned by the American Mathematical Society and developed with the help of a committee that included B. Beeton, R.

Boas, L.