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 ISBN: 9780130652478  0130652474
 Cover: Paperback
 Copyright: 8/21/2002
Key Benefit:This book presents a sound mathematical treatment that increases smoothly in sophistication.Key Topics:The book presents utilitygrade discrete math tools so that any reader can understand them, use them, and move on to more advanced mathematical topics.Market:A handy reference for computer scientists.
Preface to the Fifth Edition  xi  
To the Student Especially  xv  

1  (49)  

1  (6)  

7  (9)  

15  (1)  

16  (6)  

22  (6)  

28  (6)  

34  (5)  

39  (11)  

46  (2)  

48  (2)  

50  (45)  

50  (8)  

58  (8)  

66  (5)  

71  (6)  

76  (1)  

77  (9)  

86  (9)  

94  (1)  

95  (33)  

95  (5)  

100  (6)  

106  (6)  

112  (7)  

119  (9)  

127  (1)  

128  (53)  

128  (9)  

137  (8)  

144  (1)  

145  (8)  

153  (7)  

160  (7)  

167  (4)  

171  (10)  

179  (2)  

181  (44)  

181  (8)  

189  (8)  

197  (7)  

204  (9)  

212  (1)  

213  (12)  

220  (5)  

225  (44)  

225  (7)  

232  (7)  

239  (5)  

244  (7)  

251  (6)  

257  (12)  

266  (3)  

269  (49)  

269  (8)  

277  (9)  

286  (12)  

298  (6)  

304  (14)  

315  (3)  

318  (31)  

318  (7)  

325  (8)  

333  (1)  

333  (16)  

347  (2)  

349  (40)  

349  (10)  

359  (7)  

366  (8)  

374  (15)  

387  (2)  

389  (35)  

389  (9)  

398  (7)  

405  (7)  

412  (5)  

417  (7)  

422  (2)  

424  (38)  

424  (9)  

433  (6)  

439  (7)  

446  (6)  

452  (10)  

459  (3)  

462  (53)  

462  (8)  

470  (6)  

476  (11)  

487  (8)  

495  (6)  

501  (14)  

512  (3)  

515  (21)  

515  (7)  

522  (5)  

527  (9)  

534  (2)  
Dictionary  536  (2)  
Answers and Hints  538  (69)  
Index  607 
In writing this book we have had in mind both computer science students and mathematics majors. We have aimed to make our account simple enough that these students can learn it and complete enough that they won't have to learn it again. The most visible changes in this edition are the 274 new supplementary exercises and the new chapters on probability and on algebraic structures. The supplementary exercises, which have complete answers in the back of the book, ask more than 700 separate questions. Together with the many endofsection exercises and the examples throughout the text, these exercises let students practice using the material they are studying. One of our main goals is the development of mathematical maturity. Our presentation starts with an intuitive approach that becomes more and more rigorous as the students' appreciation for proofs and their skill at building them increase. Our account is careful but informal. As we go along, we illustrate the way mathematicians attack problems, and we show the power of an abstract approach. We and our colleagues at Oregon have used this material successfully for many years to teach students who have a standard precalculus background, and we have found that by the end of two quarters they are ready for upperclass work in both computer science and mathematics. The math majors have been introduced to the mathematics culture, and the computer science students have been equipped to look at their subject from both mathematical and operational perspectives. Every effort has been made to avoid duplicating the content of mainstream computer science courses, but we are aware that most of our readers will be coming in contact with some of the same material in their other classes, and we have tried to provide them with a clear,mathematicalview of it. An example of our approach can be seen first in Chapter 4, where we give a careful account of while loops. We base our discussion of mathematical induction on these loops, and also, in Chapter 4 and subsequently, show how to use them to design and verify a number of algorithms. We have deliberately stopped short of looking at implementation details for our algorithms, but we have provided most of them with time complexity analyses. We hope in this way to develop in the reader the habit of automatically considering the running time of any algorithm. In, addition, our analyses illustrate the use of some of the basic tools we have been developing for estimating efficiency. The overall outline of the book is essentially that of the fourth edition, with the addition of two new chapters and a large number of supplementary exercises. The first four chapters contain what we regard as the core material of any serious discrete mathematics course. These topics can readily be covered in a quarter. A semester course can add combinatorics and some probability or can pick up graphs, trees, and recursive algorithms. We have retained some of the special features of previous editions, such as the development of mathematical induction from a study of while loop invariants, but we have also looked for opportunities to improve the presentation, sometimes by changing notation. We have gone through the book section by section looking for ways to provide more motivation, with the result that many sections now begin where they used to end, in the sense that the punch lines now appear first as questions or goals that get resolved by the end of the section. We have added another "Office Hours" section at the end of Chapter 1, this one emphasizing the importance of learning definitions and notation. These sections, which we introduced in the fourth edition, allow us to step back a bit from our role as text authors to address the kinds of questions that our own students have Asked. They give us a chance to suggest how to study the material and focus on what's important. You may want to reinforce our words, or you may wa