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Handbook of Discrete and Combinatorial Mathematics
Manufacturer: CRC
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ASIN: 0849301491 |
Book Description
The importance of discrete mathematics has increased dramatically within the last few years but until now, it has been difficult-if not impossible-to find a single reference book that effectively covers the subject. To fill that void, The Handbook of Discrete and Combinatorial Mathematics presents a comprehensive collection of ready reference material for all of the important areas of discrete mathematics, including those essential to its applications in computer science and engineering. Its topics include: · Logic and foundations · Counting · Number theory · Abstract and linear algebra · Probability · Graph theory · Networks and optimization · Cryptography and coding · Combinatorial designs The author presents the material in a simple, uniform way, and emphasizes what is useful and practical. For easy reference, he incorporates into the text: · Many glossaries of important terms · Lists of important theorems and formulas · Numerous examples that illustrate terms and concepts · Helpful descriptions of algorithms · Summary tables · Citations of Web pages that supplement the text If you have ever had to find information from discrete mathematics in your work-or just out of curiosity-you probably had to search through a variety of books to find it. Never again. The Handbook of Discrete Mathematics is now available and has virtually everything you need-everything important to both theory and practice.
Customer Reviews:
Excellent.......2004-04-16
At the university I am attending Johnsonbaugh's book was a required text for a subject introducing discrete mathematics. Unfortunately, like many others it seems, I was less than impressed with the books ability 'teach', or even reinforce what we had just studied in lectures. I went looking for another book, not so much as a replacement for Johnsonbaugh's book, but as an additional reference/study aid.
Since owning this book I've found myself turning to it for explanations and examples over the required text. Almost every section lists definitions of terms, a bunch of useful facts and fully worked examples. Explanations and examples are clear and concise, while the facts often help to understand the process involved before getting into the examples.
I'd like to stress that this is certainly no replacement for a text book in discrete/combinatorial mathematics, however it is marvelous to have by your side to provide additional help through problem areas.
Amazingly comprehensive.......2000-01-06
This book will occupy a prime spot on my bookshelf. I've had to use a bunch of different books to find this kind of information before. It's nice to see such a wide range of topics from discrete math covered so thoroughly.
Book Description
Adopting a user-friendly, conversational—and at times humorous—style, these authors make the principles and practices of discrete mathematics as stimulating as possible while presenting comprehensive, rigorous coverage. Examples and exercises integrated throughout each chapter serve to pique reader interest and bring clarity to even the most complex concepts. Above all, the book is designed to engage today's readers in the interesting, applicable facets of modern mathematics. More than 200 worked examples and problems, as well as over 2500 exercises are included. Full solutions are provided in the back of the book. More than 150 Pauses—short questions inserted at strategic points—are included. Full solutions to Pauses are included at the end of each section. For educators in area of discrete mathematics.
Customer Reviews:
Bareable Book.......2007-01-04
This book is okay. Not the best but not that bad. If you have choice look for something better. If your stuck with this one then its not too bad.
Too discrete!!!.......2005-10-27
It is one thing to learn math. It is another thing to read it from a textbook. Although discrete mathematics is not meant to be all that numerically focused, I do not recommend using this text at all. There are very few examples to accompany the new content and the explanations are not clear. Also, the section review problems are NOTHING like the material presented. Yes, it is imperative to think like a mathematician, but the problems are worded much too differently than what is taught. Do not expect to do well in a course using this text unless you have a helpful instructor!
An excellent choice for discrete if your emphasis is graphs.......2004-09-25
As a teacher of discrete mathematics, I must constantly scan new books in the never-ending search for the best one with appropriate content and level. The course that I teach is required and early in the computer science major. It also provides the mathematical foundation for all of the later computer science courses. Therefore, any book that I use must demonstrate mathematical proofs, but not at too high a level. Coverage of fundamental topics such as propositional logic, sets, relations and functions; basic combinatorics and induction are a requirement.
This book covers these fundamentals at exactly the level of rigor that I need. There are some proofs, but nothing that is beyond the motivated freshman/sophomore who is receiving the appropriate direction. However, I will not be adopting it because of the large amount of graph theory, which is approximately forty percent of the book. In our class we do cover some graph theory, but prefer to spend less time on it than this book would allow. Our department recently added a course in graph theory, so we only need to touch on the basics of graphs in discrete mathematics.
Therefore, while the book is not suitable for my needs, it would be a perfect fit for anyone teaching discrete mathematics where there was an emphasis on graph theory. In fact, the second half of the book could serve as a starter text for our course in graph theory.
it is satisfactory.......2004-01-19
This text was designed mainly for young university students with the goal of introducing concepts such as induction to as well as, of course, some introductory descrete math and graph theory, with the former (induction, etc.) being as important as the latter. This is not a comprehensive text and was not intended to be so. It is a pleasent bridge to more mathematically correct way of thinking. Proofs are emphasized, not numerical answers (in most sections). Famous proofs are displayed and are incorperated in a non-trivial way. This book is applicable for mathematics and computer science students alike and the questions have a good spread of difficulty. I recommend this book to anyone interested in something more than high school math.
DO NOT BUY THIS BOOK!!!!!!!.......2003-10-13
Discrete math is complex enough for subjects to be explained extensively. That's not at all the case in this book. The explanations are too limited but most importantly, the wide range of expected answers REQUIRES this text to include most of, if not all, the correct answers for its exercises. This should not be a problem in this subject since having the answers would still leave you far from getting shortcuts; you'd still have to know discrete math well to pass a test.
This text was created ONLY to generate profits and lacks of any interest in the student's learning. It even looks like the author cashed-in his check and took a nice long vacation since his companion website is empty.
This book will only waste your money.
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A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems (Nonconvex Optimization and Its Applications)
Hanif D. Sherali , and
W.P. Adams
Manufacturer: Springer
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ASIN: 0792354877 |
Book Description
This book addresses a new method for generating tight linear or convex programming relaxations for discrete and continuous nonconvex programming problems. Problems of this type arise in many economics, location-allocation, scheduling and routing, and process control and engineering design applications. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through an automatic reformulation and constraint generation technique. The contents of this book comprise the original work of the authors compiled from several journal publications, and not covered in any other book on this subject. The outstanding feature of this book is that it offers for the first time a unified treatment of discrete and continuous nonconvex programming problems. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. The book lays the foundation of an idea that is stimulating and that has served to enhance the solubility of many challenging problems in the field.
Audience: This book is intended for researchers and practitioners who work in the area of discrete or continuous nonlinear, nonconvex optimization problems, as well as for students who are interested in learning about techniques for solving such problems.
Book Description
Combining a careful selection of topics with coverage of their genuine applications in computer science, this book, more than any other in this field, is clearly and concisely written, presenting the basic ideas of discrete mathematical structures in a manner that is understandable.
Limiting its scope and depth of topics to those that readers can actually utilize, this book covers first the fundamentals, then follows with logic, counting, relations and digraphs, functions, order relations and structures, trees, graph theory, semigroups and groups, languages and finite-state machines, and groups and coding.
With its comprehensive appendices and index, this book can be an excellent reference work for mathematicians and those in the field of computer science.
Customer Reviews:
Excellent text.......2007-10-01
I am reviewing the 5th edition. This is an excellent text, easy to learn from, with a crystal clear presentation. I've found few errors in this edition and the ones that I have found are non-substantive typos, nothing more. Each chapter is broken out into digestible sections, and each section is followed by a wealth of problems. The problems are progressive, starting out very easy, but none of them are too hard to do: the authors' intent is clearly to build the reader's skill with the material. The problems are a mix of routine computations and some proofs. Answers to all odd numbered problems are given in the back of the book, making the text valuable for self-study.
I disagree with the reviewer who criticized the book on the basis of the institutional affiliations of the authors. The text should be judged on its merits: If you're looking for a terse, densely compacted thicket of mathematical symbolism, then this is not your book. If, on the other hand, you're looking for a clear, solid presentation that flows naturally from one topic to the next, then this is the book you should purchase.
Canned methods, sloppy...........2004-02-28
THe credentials of the authors speak in bounds... Drexel University and Georgia Perimeter College???!?!?! GPC is a 2-year. Anyways, all that aside, the presentation of the material is horrible. Obviously, the background of these authors is that of 1,2,3 methods, with absolutely no concept of any concepts behind the material. The problems/examples are unrelated to the material in the chapters, and no preparation was given to answer them. Our professor even said that he emailed the writer to change the wording in a few questions, the writer agreed wholeheartedly, and yet the question remained in the next edition....
IN the age of Chubb Institute and quickie-degree schools, this book would do fine. Math, in my opinion, while can be learned with these methods, is useless without the knowledge of how it came about, why it is used, and theory or explanation/background. This book provides none of this. I do not recommend it to anyone. ESPECIALLY not one of "beginner" status(...)
A fine and useful book........2002-01-07
I have never been a math wizard, but I really enjoyed this book, and have kept it around because it is so helpful.
I appreciate the organization of the book. If you want to study a chapter out of sequence, the opening page tells you which earlier chapters are necessary to understand the new one. The exercises in each section are progressive - you can understand the topic with the first few problems, and by the time you work through the section you will REALLY understand it.
I used the fourth edition, published in 2000, so perhaps there are some inaccuracies in the earlier edition. I found few examples of wrong answers.
Difficult, Innacurate, but Topical.......1999-04-11
The textbook is difficult to understand and many of the answers in the back of the book are wrong. Also it addresses lots of good topics but mostle hard to understand.
Great Reference for Abstract Algebra and Real Analysis!.......1999-03-11
I thought that it was easy to read, the examples weren't difficult to follow and the definitions and proofs were great! I used it many times as a reference for Abstract Algebra (that book was awful) and Intro to Real Analysis. Great buy and a keeper for all students of Mathematics! Also, there is a reference of mathematical symbols in case you should forget what something means.
Book Description
With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics. Three interesting classes of exercises are provided--theorem/proof, programming exercises, and experimental explorations--ensuring great flexibility in teaching and learning the material. The Combinatorica user community ranges from students to engineers, researchers in mathematics, computer science, physics, economics, and the humanities. Recipient of the EDUCOM Higher Education Software Award, Combinatorica is included with every copy of the popular computer algebra system Mathematica.
Customer Reviews:
Do not buy this book........2007-05-20
This book is very poorly written and lacks any kind of order in which to study the chapters. The explanations of theorums and formulas are just not enough. Another thing that I do not like about this is that the section problems want you to work out precise mathematical concepts that were not explained in the relevant section, thus making you have to re-read the section several times over, and even then it is still not enough. I have completed Calculus II and that textbook was nowhere near as difficult to understand than this one. If you want to get a general idea of what Discret Mathematics is or want to do self study, then get this book. But in my opinion, avoid this book at all cost. Pun intended.
More rigorous and lengthy than other discrete texts, too much for my purposes.......2007-01-17
I will once again be teaching discrete mathematics this summer, so I am searching through the mathematical publishing pathways looking for a suitable textbook. Therefore, that is the context within which I examined this book.
It certainly is the largest discrete book that I have encountered; including the appendices and problem solutions, there are over one thousand pages. Grimaldi has tried to include every topic that falls under the discrete mathematics tent. Therefore, this is a book that could be used for a two semester sequence in discrete mathematics.
When examining discrete books for possible adoption I start with the simple premise that logic, set theory and functions and relations must be covered very early. In my ideal world, they are the first three chapters. Set theory and relations are so fundamental a part of other areas that I am surprised when authors don't cover them first. The first chapter in this book covers basic counting principles. While this doesn't break too much from my ideal sequence, I see no overpowering reason why fundamental counting should be before set theory. Given that the rules of counting for sums and products can easily be related to sets, there is a strong justification for putting set theory first.
The coverage is split into four parts, the first of which consists of the seven chapters:
*) Fundamental principles of counting
*) Fundamentals of logic
*) Set theory
*) Properties of integers: mathematical induction
*) Relations and functions
*) Languages: finite state machines
*) Relations: second time around
In my opinion, the order of the topics should be:
*) Fundamentals of logic
*) Set theory
*) Relations and functions
*) Relations: second time around
*) Fundamental principles of counting
*) The principle of inclusion and exclusion (currently chapter 8)
*) Properties of integers: mathematical induction
*) Generating functions (currently chapter 9)
*) Recurrence relations (currently chapter 10)
*) Languages: finite state machines
The current chapters 8 through 10 make up part two of the book.
Part three is graph theory and applications and part four is modern applied algebra. I have no issues with the order here. The chapter headings for the fourth part are:
*) Rings and modular arithmetic
*) Boolean algebra and switching functions
*) Groups, coding theory and Polya's method of enumeration
*) Finite fields and combinatorial design
With this part being nearly two hundred pages in length, the coverage is extensive.
Grimaldi takes a more rigorous approach than many other authors of discrete texts, while I did not examine every single theorem, I did look at a lot of them and all were accompanied by a proof. The exposition is clear, there are many worked examples, a large number of exercises and solutions to the odd-numbered exercises are included. A summary and historical review of the topic follows each section.
If we offered a two course sequence in discrete mathematics, then I would consider adopting this book. Such a situation would allow me to present the material at a higher level of rigor, where this book excels. However, with a one semester course designed to teach computer science majors the mathematical fundamentals they need, this book is both too long and too deep.
ideal for self study.......2006-01-26
Excellent book, carefully chosen examples, ideal for self study. I like it very much. My advice is not to skip any section or solved examples or you might be lost.
Maybe it's just me.......2005-04-20
I find this book lacks explanation at many points, to where I couldn't understand thw way the author presented a problem, a subject, etc... I almost feel like the target audience is to other college professors, and not students of the subject. I also don't like that a lot of the harder problems at the end of the sections are even numbered, so that you don't have a way to see how they are worked. I don't really feel the book warrants just one star, but since most people in my class don't care much for the book, I am confused to all of the great reviews on this web site and felt I needed to show the contrast that my class experienced with it. I think the book requires a good instructor to help you get through it, in contrast to the comments to others who have said it's good for a self learner. I am also enrolled in Calculus 2 and Linear Algebra, and the books I am using for those courses are FAR superior to this one. and I have missed a few class sessions in those two courses and am still running a high B and a mid A in those courses. I wouldn't dream of missing a class in the Discrete Math class because I feel too dependant on the instructor's explanations.
great book on discrete math.......2005-03-21
This is an excellent book for self study. However, there are parts in this book that must be rearranged or deleted. For example, I think Catalan numbers should be deleted. This might be useful for the matrix chaining problem, but that's in the realms of algorithm design (specifically in dynamic programming). Also, I do not understand why Grimaldi sandwiched in a chapter on Finite State Machines between two chapters on Functions and Relations. Maybe he should make a section on languages for FSMs, but I recommend Sipser's Introduction to the Theory of Computation if you want to learn about FSMs.
Book Description
The book is a concise, self-contained and up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called gems of the theory. A wide spectrum of most powerful combinatorial tools is presented: methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A throughout discussion of some recent applications to computer science motivates the liveliness and inherent usefulness of these methods to approach problems outside combinatorics. No special combinatorial or algebraic background is assumed. All necessary elements of linear algebra and discrete probability are introduced before their combinatorial applications. Aimed primarily as an introductory text for graduates, it provides also a compact source of modern extremal combinatorics for researchers in computer science and other fields of discrete mathematics.
Book Description
This book emphasizes combinatorial ideas including the pigeon-hole principle, counting techniques, permutations and combinations, Pólya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs). The volume provides a complete examination of combinatorial ideas and techniques. For individuals interested in combinatorial concepts.
Customer Reviews:
nice accessable text.......2007-04-15
Most (but not all) of the copious errors in earlier editions have been fixed.
(Brualdi maintains an errata list on his website.) I like this book a lot,
it has a nice, relaxed style of exposition and the choice of topics is good
for an introductory course.
Interesting Problems, Too Many Mistakes.......1999-01-04
I used the book to guide me through a Combinatorics class I took in the summer of 1998. The author has presented some very interesting problems like prove that of any 10 points chosen withen an equlateral triangle of side length 1, there are 2 whose distance apart is at most 1/3 that use some interesting techniques such as the pigeonhole principal. The book, however contained too many mistakes. My professor said on average there is one mistake per page and he wasn't exagerating either. Luckily with his help, we corrected the many mistakes and then were successfully able to use the book. I notice that the author has written a new edition. I hope most of the mistakes have been corrected because when I pay a good sum of money for a book I expect it to be good book without errors.
Book Description
The design of code and cipher systems has undergone major changes in modern times. Powerful personal computers have resulted in an explosion of e-banking, e-commerce and e-mail, and as a consequence the encryption of communications to ensure security has become a matter of public interest and importance. This book describes and analyzes many cipher systems ranging from the earliest and elementary to the most recent and sophisticated, such as RSA and DES, as well as wartime machines such as the ENIGMA and Hagelin, and ciphers used by spies. Security issues and possible methods of attack are discussed and illustrated by examples. The design of many systems involves advanced mathematical concepts and this is explained in detail in a major appendix. This book will appeal to anyone interested in codes and ciphers as used by private individuals, spies, governments and industry throughout history and right up to the present day.
Customer Reviews:
Survey of Ciphers.......2007-01-20
It's a good book if you have an interest in ciphers and haven't read much on the subject. It's not a book on modern cryptography and covers very little in the way of recent breakthrough technology. Based on your level of interest and experience it might or might not be the right book for you. It gets four stars from me because the author presents clear, well researched information.
well written and for all.......2004-08-07
This is not a schoolbook, yet it takes from the format some usefull features for such a book : you have some worked out examples and a few exercises to practice. After all, math is not something you read like a novel, but rather something you DO! The author understands that.
But the book also has an easy going feel to it and is very clear. Mixed in with the math, you have tidbits of history and general culture mixed in. If you compare it to a very good book out there (the code book by Singh), you find out more about the codes and the mechanics of them in this book.
good read!
You learn how some key encryption machines were made.......2002-09-29
The ability to convert data into a form that is readable only by a selected group has been a matter of utmost importance for thousands of years. The fate of entire nations has rested on the ability of a nation to keep their messages secure or accurately unravel the messages of opponents. The most celebrated cases involve instances of war, where the messages sent by the Germans and Japanese were intercepted and decrypted by the allies. While not decisive in the outcome of the war, the knowledge gained was of enormous value and did a great deal to assist in the victory. By far, the most well known case is that of the Enigma machine used by the Germans in world war two. The British were able to break the code and the knowledge they obtained made a significant difference in the early years of the war.
Encryption is now a foundation pillar of modern society. Trillions of dollars are now electronically exchanged over the course of a year, and the entire world economy is now dependent on the ability of computers to exchange data in a manner that is accurate and secure from fraud. While security over the Internet is the most widely cited example, most of the data is exchanged over private lines.
The first documented case of encryption being used in war is when Julius Caesar used a simple substitution cipher to send orders to his troops. That and all similar codes is where the book begins. After that, there is a very detailed examination of the Enigma and Hagelin machines, right down to how the wheels interact. This part of the book was by far the most interesting, as well as the descriptions of how it was possible for the allied cryptographers to break the Enigma code. It turns out that the breaking of the codes was not due to a flaw in the machine, but in the way it was used. The remaining part of the book is filled with a description of public key cryptography and the applications for the Internet.
The sections on the substitution ciphers and public key cryptography are good but fairly standard. Problems are given at the end of each chapter and solutions are in the back of the book. What makes this book unique is the mechanical descriptions of the Enigma and Hagelin cipher machines. If you are interested only in the mathematics of encryption, then you will most likely not find them interesting. However, if you are like me and are interested in the mechanical aspects of the machines, then you will like it.
Book Description
This comprehensive textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. Since the complete book contains enough material for at least four semesters (4 hours a week), one usually selects material in a suitable way. The book contains complete but concise proofs, also for many deep results, some of which did not appear in a book before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization. This third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new sections and further material on various topics. New exercises and updates in the bibliography were added.
From the reviews of the 2nd edition:
"This book on combinatorial optimization is a beautiful example of the ideal textbook."
Operations Resarch Letters 33 (2005), p.216-217
"The second edition (with corrections and many updates) of this very recommendable book documents the relevant knowledge on combinatorial optimization and records those problems and algorithms that define this discipline today. To read this is very stimulating for all the researchers, practitioners, and students interested in combinatorial optimization."
OR News 19 (2003), p.42
Customer Reviews:
Useful yet dense!.......2001-11-13
This is the most comprehensive compilation on combinatorial optiomization I have seen so far.
Usually, Papadimitriou's book is a good place for this material - but in many cases, looking for proofs and theorems - I had to use several books:
(*) Combinatorial Optimization Algorithms and Complexity by Papadimitriou and Steiglitz.
(*) Integer and Combinatorial Optimization by Nemhauser and Wolsey
(*) Theory of linear and integer programming by Schrijver
(*) Combinatorial Optimization by Cook, Cunningham, Pulleyblank and Schrijver
(*)Combinatorial Algorithms by Kreher and Stinson
This book, on the other hand, contains so much information and so many proved theorems - it's the richest resuorce in this topic, in my humble opinion.
Using it as a graduate level textbook for an *introduction* to combinatorial optimization is kind of hard - as although it's richness, some topics are described without enough detail or examples (like the topics on network flow and bipartite graphs) - yet the authors probably assumed some previous knowledge in those topics.
I prefer using this book as a reference rather than and intoduction.
The heavy mathematical notations in this book might scare some readers, but no-fear! You quickly get used to it, and appreciate the greatness in the notations, as they make the theorems more short and to the point. On the other hand - getting back to this book for a quick review on some subject might force you to flip pages for a fwe minutes, just to remember the notation again.
The authors intended this book to be a graduaet level textbook or an up-to-date reference work for current research. I believe they accomplished both targets!
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