Reviews (4)

A Masterpiece on Enumerative Combinatorics
I agree with the other reviewers.The book is a masterpiece on enumerative combinatorics.However, I am not so sure that it is a good book for a beginner.If you are a beginner, then you should read another book first, like John Riordan's book on "Combinatorial Analysis."Stanley's book is best suited for an advanced student who has a high level of mathematical mental maturity.The reason I say this is that in a few places Stanley's formalism, which is entirely appropriate for professional exposition, actually obscures the underlying simplicity of the mathematical ideas.We have all seen this in research papers, where a mathematician takes a trivial idea and "obsures" the underlying simplicity with too much formalism.However, for an advanced student, the book has a high density of important ideas and methods.

This is for people who likes to COUNT
Gosh! This is for people who count, what else does a combinatorist do? Before people dismiss me as somebody who don't know hoot about math: I took a class with Prof. Stanley (the author) in college, and I had actually used vol 1 as a text. The material is highbrow (I agree on the 'hardcore' math observation) but the main theme of the book is how to 'count' -- needless to say not in the sense of everyday counting, but in the sense that 'topology' is 'coffee-to-donut transformation' and 'analysis' is 'honors calculus'. You have to know how to count, and comfortable with combinatorial proof to actually learn from this. I like the fact that Prof. Stanley asks for combinatorial proof to some known results, marking them as unsolved -- he really elevates the status of combinatorial proof, a method many dismiss as 'handwaving'. There is a number given to each exercise, according to the level of difficulty: [1] for trivial, [5] unsolved. I saw a professor who worked in differential topology for 40 years refer to this book -- and first year undergrads thumbing through the pages for exercises marked [1] and [2] to solve in spare time. This is a book for all levels of mathematicians: I am sure even the armchair amateur mathematicians can grasp some of the materials after a hard day's thought. I dont see this book as any less than a definitive text on enumerative combinatiorics.

People who like to COUNT?!? People who like hard-core math.
There was an earier review that claimed this book is for "people who like to count." That's a little silly. This book is a rigorous math text. And it's glorious. It's probably my favorite text. But it's not light reading at all.

Reviews (4)

A Masterpiece on Enumerative Combinatorics
I agree with the other reviewers.The book is a masterpiece on enumerative combinatorics.However, I am not so sure that it is a good book for a beginner.If you are a beginner, then you should read another book first, like John Riordan's book on "Combinatorial Analysis."Stanley's book is best suited for an advanced student who has a high level of mathematical mental maturity.The reason I say this is that in a few places Stanley's formalism, which is entirely appropriate for professional exposition, actually obscures the underlying simplicity of the mathematical ideas.We have all seen this in research papers, where a mathematician takes a trivial idea and "obsures" the underlying simplicity with too much formalism.However, for an advanced student, the book has a high density of important ideas and methods.

This is for people who likes to COUNT
Gosh! This is for people who count, what else does a combinatorist do? Before people dismiss me as somebody who don't know hoot about math: I took a class with Prof. Stanley (the author) in college, and I had actually used vol 1 as a text. The material is highbrow (I agree on the 'hardcore' math observation) but the main theme of the book is how to 'count' -- needless to say not in the sense of everyday counting, but in the sense that 'topology' is 'coffee-to-donut transformation' and 'analysis' is 'honors calculus'. You have to know how to count, and comfortable with combinatorial proof to actually learn from this. I like the fact that Prof. Stanley asks for combinatorial proof to some known results, marking them as unsolved -- he really elevates the status of combinatorial proof, a method many dismiss as 'handwaving'. There is a number given to each exercise, according to the level of difficulty: [1] for trivial, [5] unsolved. I saw a professor who worked in differential topology for 40 years refer to this book -- and first year undergrads thumbing through the pages for exercises marked [1] and [2] to solve in spare time. This is a book for all levels of mathematicians: I am sure even the armchair amateur mathematicians can grasp some of the materials after a hard day's thought. I dont see this book as any less than a definitive text on enumerative combinatiorics.

People who like to COUNT?!? People who like hard-core math.
There was an earier review that claimed this book is for "people who like to count." That's a little silly. This book is a rigorous math text. And it's glorious. It's probably my favorite text. But it's not light reading at all.

Reviews (24)

A pourry of combinatorics
I want to start saying that this is a book designed for Engineers, not for Mathematicians. It focuses on the tecniques, not on the arguments. This is not a book about combinatorics, it is a wide raging introduction (it lacks on definitions, and his proofs are a lot far away from mathematical ones). The Enegineers can use this book as a good reference. The Mathematicians can improve their lateral thinking, for them (well: us) it is book about problem-solving strategies.
I will never use this book as a textbook for a graduate/undergraduate course, it can be helpful if used with another book about combinatorics: when you study a combinatorial object, you can read from this book the techniques it involves.
The exercises are extremely exciting, when I read this book I spent a lot of time about its exercises (proportion read:solve = 1:3), and they led me to interesting results.

Steep learning curve, the definitive prerequisite for TAOCP.
Why I got this book:
It's a great feeling to know how computers work, when I decided that I want to make a career and a life out of computers, as its truly a passion for me, I delved deeper, discovering the true beauty in the Science part of Computer Science, so I decided to get Donald Knuth' "The Art of Computer Programming" - to describe that seminal, huge work, it's like biting more than you can chew while trying to drink from a fire hose, moreover, the technical and mathematical prerequisites for the work are sometimes too demanding, they require a huge amount of experience with discrete mathematics, although I had some lectures and read some books, none came close "Concrete Mathematics", it covers, from ground up (though with a dangerously steep learning curve) a lot of discrete mathematics topics, it is by far the most extensive work I've read about Sums and really teaches the algorithmic problem solving thinking skill the authors preach so much about, with small amusing comments written by actual students of this course, a comfortable format, and very good writing skills, you can feel these guys are great professors who enjoy this material and are passionate about teaching it.

Recommended, though some better, less steep, introductionary text books are probably out there.

Enjoy.

Only one problem with this textbook
Basically, I like this textbook. The material is interesting, the way the authors presented the material is inspiring, and they provided a lot of jokes to make even studying for exams not that boring. But there is one big problem which made me decided to rate this book only 3 stars instead of 5 stars: the authors like to use non-standard notations. For example: m\n means "m>0 and n=mk for some integer k". One of the worst thing in scientific world is writing things others cannot read, and the authors did this by introducing many strange notations. These things makes the good work sometimes almost unreadable. This is not computer systems in which we use "cp" for the copy command and "cd" for change directory command.

Reviews (42)

"Check it out"
I borrowed volume 2 to implement a special data structure.It helped me immensely in that task.But it wasn't the only resource I used.I could not justify spending the money on this book.

Short of the mathematical treatment, the knowledge certainly wasn't limited to Knuth.In fact, most (all?) of the Art of Programming is a compilation of ideas, isn't it?

I used a variety of resources.I even used to web.There are some terrific animations that show special case tree rotations for AVL trees or red-black trees out there.

Knuth will be appreciated by academics the most.Very specialized programmers, such as embedded designers, OS authors, or database designers will likely be the next biggest group of fans.Application developers will be next in line.They mostly depend on APIs to implement the topics for them.And Rapid Application Developers will hate the book.Don't care.Don't need to know.And they don't.So figure out where you are in that list and that's how much you need this book.

A modern rewrite would definitely nudge me into buying the book.But I just can't force hand on wallet ... to ... shell ... out ... bucks for a book that's already widely available in a variety of formats for free.

PROS:
Likely the best mathematical treatment of a computer science subject you will find.No one ties the practicality of CS and abstraction of math better than Knuth.

Coverage of many core concepts of computer science such asdata structures, big-O notation and efficiency, bit wise arithmetic algorithms, random number generators, etc.

Classic work.Impress your colleagues by idly leaving the book around.Bonus points:leave it open AND have a copy of Red Dragon nearby.

CONS:
Not enough pictures.Seriously.I am a visually oriented person.Two pages of tree rotation diagrams are far more helpful than ten pages of prose.

The book is type faced as a college text.The typeface is difficult to read.The exercises litter the book and make thumbing through it a bit annoying.

MIX.This is Knuth's solution to describing algorithms in a universal programming language the audience can understand.Unforunately, the language is assembly designed for a fictional computer.So no one can understand it but equally as well.Actually, any popular assembler experience (Motorola/Intel/PIC) should span the gap nicely.But when's the last time you programmed in assembler?How come?I blew past the MIX examples and looked for better psuedocode elsewhere.

My two cents
Yes, using MIX is all wrong.Psuedo-code that's intuitively obvious would save
us so much trouble.But, why not a "TAoCP in FORTRAN-90",
a "TAoCP" in APL, a "TAoCP" in COBOL, a "TAoCP" in BASIC,
a "TAoCP" in LISP, a "TAoCP" in ALGOL, a "TAoCP in Ada", a "TAoCP in C", a
"TAoCP in Java", etc. ??Think of the money to be made re-selling it in every
possible langauge if there's a market for it?I might even do it myself and
make some $.Actually, there's no need for a Visual Basic version, etc. because
I/O, etc. is not the issue.This set is about art, about *algorithms*, so most of
the high level language specific aspects are irrelevant (except for recursion,
details like garbage collect, inheritance, polymorphism...). Equally irrelevant is
worrying about efficient memory usage and the like. Today, memory, disk
space, etc. are not scare resources.While (being from the old school) I don't
believe in wasteful code, all people really want today out of algorithms is
optimal speed.Time and CPU power are the only resources that is still
constraints.Discussions about sort algorithms which optimize for anything
else (memory space, etc.) are pointless if they aren't also the most time
efficient.We don't care!Also, unless you work for the US Census or Social
Security Administration, you don't care about hardware devices like tape drives,
so those algorithms are just theoretical mind games. Anyway, please rewrite
this set in a practical high level psuedo-code with time optimal algorithms
only.But only the timeless (pun-intended) universally necessary algorithms
that are always going to be useful.Stuff like searching, data structures,
hashing,trade offs between techniques. In the future all people will want are
parallel processing algorithms for distributed environments and perhaps
eventually quantum computing algorithms for a language built on a CPU which
only processes QBits. One final thing: wasn't there originally
supposed to be 7 volumes and only these 3 were completed? What ever
happened to the rest?Why were they abandoned? I guess I never heard.

Precisely, but let us keep our logic straight.
From the review by Ekalavya Nishada: "It is true it uses MIX and does not cover the last 20 years of advances in computer science yet but if you cant understand MIX you have no hope of understanding the mathemtical analysis of algorithms in these books nor appreciate a quality book like this."

But this is precisely the point! Indeed, w/o MIX you won't be able to really read TAoCP, right, but let us keep our logic straight. Do you need MIX for anything other than reading this book? Nope. Does it add anything to the subject matter? Nope (in fact, it detracts from it; C would be more illustrative and realistic.) Is learning it so easy as to make the issue unworthy of bringing it up? No, learning it will take quite a bit of effort. Yet it *is* a precondition to being able to read TAoCP. And, btw, it's not that MIX "doesn't cover the advances of the last 20 years" -- I suspect, it simply has nothing in common with reality, whether today or 20 years ago. Is it worth your time to dig into this piece of gratuitous esoterica simply in order to be able to read the book? Is TAoCP *that* great and indispensable? Everyone will decide on one's own, but personally I think not, not today -- there are now quite adequate alternatives that do not tax the reader unnecessarily. Life is short; its demands are many; not everyone's a tenured professor...

Reviews (5)

Not a reference guide
This book is REALLY for coursework : someone who is going to sit down and read and work thru this book sequentially, not randomly like a reference book.
Other than that caveat it does what it promises ably but be aware that it is MATHS heavy and REQUIRES the programme work.

A must have.
I read a lot of books about complexity analysis. And this book is a state of art in the field. Easy to read, and well done.It cover the necessary staff that every new commer to the field should know, can be used as a refference,and it make a good teaching material for graduate student.

Clear and concise
This is an excellent book on the analysis of algorithms.More specifically, it is a book on the mathematics needed for the analysis of algorithms.Quite a few algorithms are presented and analyzed in great detail, but the emphasis is on the analysis techniques rather than on the algorithms.

This is in contrast with Cormen,Leiserson and Rivest, or Sedgewick's own "Algorithms" series which emphasize the algorithms rather than the analysis.

If you're looking for a catalog of algorithms along with explanations, you want a different book, but if you want to know how to analyze that bizarre code (which Fred in the next cubicle wrote) and prove that it works well (or doesn't) then this is an excellent choice.

The book is aimed at advanced undergrads/graduate students and assumes a certain amount of mathematical sophistication - i.e. calculus, discrete math, probability, etc.

Reviews (2)

Excellent
The book is really excellent.
Every combinatorialist or combinatorics lover must have the pearl.

Reviews (1)

Reviews (2)

Excellent
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.

Isbn: 0471866547
Sales Rank: 3178057
Subjects:  1. Discrete Mathematics    2. Mathematics    3. Mathematical foundations   

Reviews (5)

Searching for the book vs. the disk?
The Encyclopedia of Integer Sequences is available in three formats.Sellers often incorrectly match the ISBN to the format.It may be helpful to know the ISBN, rather than to rely on the results of a search by Title/Author.

Hardcover Book: ISBN 0125586302
Macintosh Disk:ISBN 0125586310
MSDOS/IBM Disk:ISBN 0125586329

Also, use the price as a clue to which item you will be receiving - the book sells for $70+, the disk for under $20.

Searching for the book vs. the disk?
The Encyclopedia of Integer Sequences is available in three formats.Sellers often incorrectly match the ISBN to the format.It may be helpful to know the ISBN, rather than to rely on the results of a search using Title/Author.

Hardcover Book: ISBN 0125586302
Macintosh Disk:ISBN 0125586310
MSDOS/IBM Disk:ISBN 0125586329

Also, use the price as a clue to which item you will be receiving - the book sells for [$]+, the disk for under [$].

This is a data disk, not the book
This product is not the Encyclopedia of Integer Sequences as it is portrayed here on Amazon; it is instead an almost useless data disk.The integer sequences are there all right, in lexicograhic order;but they are completely unidentified (except for a code number keyed to the book)!In other words, without the book this very expensive diskette is useless.

Reviews (3)

Good Introduction, too many typos
I am, what Prof. Bollobas would call a hobby mathematician. Some popular science book arouse my interest in graph theory, and the author of that popular science book recommended this book. I feel it was a vey good introduction to the subject, even though the proofs become challenging at times. His motivation for the subject is always concise but precise, one cannot but notice, that a master of the subject is writing about it.

The only distraction are the enormous number of typographical errors: I counted over 60, and this in a third corrected printing!?!

Excellent in content, but somewhat challenging in narrative
Bela Bollobas has the rare gift of having both deep mathematical insights, and the ability to eloquently communicate them in a way that is accessible to the average graduate student. In his book "Modern Graph Theory", Bollobas covers just about every exciting area of the subject, and does so in an up-to-date fashion that gives the reader a big picture of each sub-area of the field. The ability to do this not only seems difficult, but also essential, since he himself has written entire books on two of the chapters (extremal graph theory, and random graphs). Just about every major important theorem (including max-flow/min-cut Theorem, and theorems by Menger, Szemeredi, Kuratowski, Erdos/Stone, and Tutte) can be found here, and thus makes this book indispensable for anyone who does research in graph theory, combinatorics, and/or complexity theory.In my opinion the true highlights of this book are indeed those areas he knows best: extremal graph theory, random graphs, and random walks on graphs, the latter of which may be the best introduction to that subject that one will find in a textbook.

My only complaint, at the cost of perhaps half a star, is that his discussions and proofs often seem difficult to follow, as he will state something that to him seems quite obvious, yet to this reader often seemed a bit subtle, and would hence slow down the reading. Indeed, if these off-handed remarks were included as exercises at the end of each chapter, then the number of excercises would have swelled from the current 600 to well over one thousand ! Speaking of which, these 600+ exercises, although also representing another blessing of this book in that they add another degree of depth, tend to lack "starter" exercises, and go straight to the theory. But this is to be expected froma graduate text.

Finally, for the reader whose research significantly intersects with graph theory, but may not be ready or willing to be initiated by Bollabas into the world of graph theory, I would recommend Dietsel's graduate text on the subject. His book covers similar topics, but may be more clearly and transparently, but with less depth and insight.

A good introduction book
My profile is the following: I am a phD student in theoretical computer science and I needed a good introduction book to graph theory.

Isbn: 0882758292
Sales Rank: 2236299

Isbn: 0521573238
Sales Rank: 220169
Subjects:  1. Algebra - General    2. Combinatorial Analysis    3. Combinatorial enumeration prob    4. Combinatorial enumeration problems    5. General    6. Mathematics    7. Science/Mathematics    8. Combinatorics & graph theory    9. Mathematical theory of computation    10. Mathematics / General   

Reviews (3)

Disappointing
Based on other Amazon reviews I had hopes of breezing through this book.But some problems prevented this.1) Use of outdated symbols, including odd italic script letters some of which are unidentifiable, 2) poor organization of material with a complete lack of overview and a disordered approach, 3) a careless "note to self" style of writing, 4) zero examples to backup formulas.Considering that Euler started the ball rolling in the 1700's, and that the last famous breakthrough was by the long dead Hardy and Ramanujan, partition theory is mature enough to deserve a better book than this.

Basic reference on partitions and q-series
This is *the* classic and most essential reference on the theory ofpartitions and related q-series written by the leading authority on thesubject. It requires almost no technical prerequisites, starts fromscratch, and proceeds in a very clear and orderly manner towards some ofthe more elaborate aspects of the subject. If you (plan to) work on thissubject, buy it.

The book was written in 1976, and as such does not coverthe more recent developments, though the bibliography has been updated (toa limited degree) for the current 1998 paperback edition. However, afterall these years, it remains *the* introduction to the subject (with thepossible exception of chapter 14 on computational methods, which isdefinitely outdated), and can be supplemented only by Gaspar and Rahman's'Basic Hypergeometric Series'. I taught a higher undergraduate level coursebased on chapters 1, 2, 3, 7 and 9, and my students definitely found thesechapters to be highly readable.

My one and only complaint is toCambridge University Press: Dover has shown that paperbacks can be producedin such a way that they can be opened completely flat without beingdamaged, and quite cheaply too. Why can't you adopt the same technology?

Isbn: 9027703809
Sales Rank: 1001733
Subjects:  1. General    2. Mathematics    3. Mathematics / Discrete Mathematics   

Reviews (4)

Improvement!
These new editions have many new and interesting stuff that is not included in the original outdated series. It contains many fresh ideas that the authors recently discovered including those old ones. For old ones the original volume has more to say...

Geniuses and Games
This book is dazzling.It can be pretty tough going but it is
well worth the effort.You can always tell the work of a genius because it illuminates the landscape and shows us things we have never seen before.I design games for a living and this book rocks!Hackenbush, Nimbers, games with 1/2 move advantage.Well illustrated.ONLY PROBLEM: Where are volumes 2-4?

Reviews (3)

Fantastic!
Everyone wants to know what mathematicians do should read this book. Yes, only very few among people can get familiar or endure gorgeous complicated formulas here, But even scan or skim this book one will learn much morethan he predicted. The goal of this book is simple enough: To prove aconjecture (surely when proved, it becomes a theorem) But the structure anddetails are well selected and carefully designed. First it introduces andexplains the original problem, than talk about it's history, how it doesconnect with other branches of math, what these branches is about, and whatthe other mathematicians do on this conjecture, and at last the mostexciting: how these results all bringed together and then solve this20-year-long famous conjecture in combinatorics. There are exercises afterevery chapter. so this is NOT merely a history survey (as most books do).Indeed it is a textbook and contains some very excellent introductions tosome branches(for example, plane partition). And I think this is THEcorrect style to populating mathematics--- Do not afraid of formulas, justshow readers the signs, the terrible formulas, show them how and whatmathematicians study and think! Every student major in mathematics shouldread it, and it surely is a must-have for reseachers in combinatorics.

Amazing book on how mathematical research is done
This book tells the story of one of the moreimportant areas of research in algebraic combinatorics in the last few years.Not only does it tell the story of how the relevant conjectures were proposed, and how they wereeventually proved (including some of the blind alleys and several caseswhere surprising connections were discovered), but it also contains abeautiful exposition of the relevant mathematics, at a level which a readerwith no more than a reasonable background in linear algebra can follow. The history is fascinating and the mathematics is beautiful.If you wantto know what research in mathematics is really like, this is the book toread.

Reviews (6)

Excellent for applications
The book covers the fundamentals of graph theory and combinatorics (enumeration) and is designed for first courses for undergraduates.

The material is presented in a clear, friendly manner. The sections are short and specific and the emphasis is on problem-solving. Many examples are provided and constitute the majority of the book's volume. Each section ends with 20-30 exercises with answers (not full solutions) at the end of the book.

The book is excellent for computer science and applied math majors looking for a clear, application-based introduction to combinatorics and graph theory. It is also excellent for self-study.

The book's main flaw is that the proofs are not rigorous and are sometimes more intuitive than mathematical. For pure math students looking to explore graph theory and combinatorics in a more rigorous manner, other books (e.g. Diestel, "Graph Theory") will serve that purpose better.

An almost ideal introduction book to combinatorics
There have been wonderfully written reviews of this book, but since this is really an excellent textbook, I am urged to praise again. Fully recommended.

This book is easily and clearly written; covers almost every important basic concept and technic in graph theory and enumerative combinatorics, with neatly selected and wonderfully organised exercises.

And I highly suggest the author give the references to those last exercises in every section, since each of them does lead into a theory.

An almost ideal introduction book to combinatorics
There have been wonderfully written reviews of this book, but since this is really an excellent textbook, I am urged to praise again. Fully recommended.

This book is easily and clearly written; covers almost every important basic concept and technic in graph theory and enumerative combinatorics, with neatly selected and wonderfully organised exercises.

Reviews (4)

Excellent Introduction to Combinatorics
A COURSE IN COMBINATORICS covers a great breadth of topics under the label of "combinatorics," including graph theory, enumeration, and some algebra. The book is comprehensive; the instructor can pick-and-choose appropriate material from the huge array provided without detriment to understanding.

Each chapter is written in a friendly, accessible manner: plenty of interesting and instructive examples follow the clear definitions and preliminaries. To give the reader an idea of the topics presented in the book, a list of chapters follows:

1. Graphs
2. Trees
3. Colorings of graphs and Ramsey's theorem
4. Turan's theorem and extremal graphs
5. Systems of distinct representatives
6. Dilworth's theorem and extremal set theory
7. Flows in networks
8. De Bruijn sequences
9. Two (0,1,*) problems: addressing for graphs and a hash-coding scheme
10. The principle of inclusion-exclusion; inversion formulae
11. Permanents
12. The Van der Waerden conjecture
13. Elementary counting; Stirling numbers
14. Recursions and generating functions
15. Partitions
16. (0,1)-Matrices
17. Latin Squares
18. Hadamard matrices, Reed-Muller codes
19. Designs
20. Codes and designs
21. Strongly regular graphs and partial geometries
22. Orthogonal Latin squares
23. Projetive and combinatorial geometries
24. Gaussian numbers and q-analogues
25. Lattices and Mobius inversion
26. Combinatorial designs and projective geometries
27. Difference sets and automorphisms
28. Difference sets and the group ring
29. Codes and symmetric designs
30. Association schemes
31. (More) algebraic techniques in graph theory
32. Graph connectivity
33. Planarity and coloring
34. Whitney duality
35. Embeddings of graphs on surfaces
36. Electrical networks and squared squares
37. Polya theory of counting
38. Baranyai's theorem

The problems in the book are generally very rich and well-written, with helpful hints from the appendix that provide motivation but do not spoil. However, the relative difficulty of the problems is not readily made appparent, so over- or underthinking of problems often occurs with misjudgments.

For the interested high-school student to the beginning graduate, this book is ideal for the study of combinatorics. Truly a nice read that connects many areas of mathematics and combines them into a thing of true beauty.

A nice tour of combinatorics
The first word that comes to my mind when I think of this text is "encyclopedic". It contains around 40 chapters, hitting most of the high points of combinatorics that a graduate student should see. The exposition is generally good with nice examples. The one thing that I fault it for is the number of statements that the authors claim are "obvious". In a way, this is good, because it makes you pay attention and understand the material, but sometimes the statement isn't obvious until you've thought about it for an hour and written out a lengthy proof. At that point, it does become completely obvious and you can't believe that you ever thought it wasn't, so I can understand why van Lint and Wilson fell into the trap so often. (In fact, I've heard that Wilson even stumbles over some of those points in lectures.) This is a great book to have on your shelf if you need somewhere to look up combinatorial ideas.

A gentle introduction to combinatorics
This book was the text for a graduate-level course I took.The presentation is very laid-back, much like the lecturing style of one of the authors (Wilson), and so it was quite readable (unlike many other mathbooks which you have to stop every few pages and pick apart everythingbefore it sinks in).

Combinatorics is a relatively recent development inmathematics, one which is generally easy to explain, but with manydifficult open questions.Van Lint and Wilson do an excellent jobexplaining, but there are a few places where the reader needs to know somebackground to place the particular problem in the appropriate mathematicalcontext.Understandably, if the authors were to include all themathematical machinery needed, the book would be huge!Instead, they havechosen to describe as many facets of the field as possible, and thereforehave written a broad, well-balanced book which approaches the topic in anon-threatening way.

My one criticism, then, is that there is a lack ofdepth in several areas of the book, with further discussion of advancedtopics or open problems.But even so, I can appreciate the omission forthe sake of accessibility.

Editorial Review

Aimed at any serious programmer or computer science student,the new second edition of Introduction to Algorithms builds onthe tradition of the original with a truly magisterial guide to theworld of algorithms. Clearly presented, mathematically rigorous, andyet approachable even for the math-averse, this title sets a highstandard for a textbook and reference to the best algorithms forsolving a wide range of computing problems.

With sample problems andmathematical proofs demonstrating the correctness of each algorithm,this book is ideal as a textbook for classroom study, but its reachdoesn't end there. The authors do a fine job of explaining eachalgorithm. (Reference sections on basic mathematical notation will helpreaders bridge the gap, but it will help to have some math backgroundto appreciate the full achievement of this handsome hardcover volume.)Every algorithm is presented in pseudo-code, which can be implementedin any computer language, including C/C++ and Java. This ecumenicalapproach is one of the book's strengths. When it comes to sorting andcommon data structures, from basic linked lists to trees (includingbinary trees, red-black, and B-trees), this title really shines, withclear diagrams that show algorithms in operation. Even if you justglance over the mathematical notation here, you can definitely benefitfrom this text in other ways.

The book moves forward with moreadvanced algorithms that implement strategies for solving morecomplicated problems (including dynamic programming techniques, greedyalgorithms, and amortized analysis). Algorithms for graphing problems(used in such real-world business problems as optimizing flightschedules or flow through pipelines) come next. In each case, theauthors provide the best from current research in each topic, alongwith sample solutions.

This text closes with a grab bag of usefulalgorithms including matrix operations and linear programming,evaluating polynomials, and the well-known Fast Fourier Transformation(FFT) (useful in signal processing and engineering). Final sections on"NP-complete" problems, like the well-known traveling salesman problem,show off that while not all problems have a demonstrably final and bestanswer, algorithms that generate acceptable approximate solutions canstill be used to generate useful, real-world answers.

Throughout thistext, the authors anchor their discussion of algorithms with currentexamples drawn from molecular biology (like the Human Genome Project),business, and engineering. Each section ends with short discussions ofrelated historical material, often discussing original research in eacharea of algorithms. On the whole, they argue successfully thatalgorithms are a "technology" just like hardware and software that canbe used to write better software that does more, with betterperformance. Along with classic books on algorithms (like DonaldKnuth's three-volume set, The Art of ComputerProgramming), this title sets a new standard for compiling thebest research in algorithms. For any experienced developer, regardlessof their chosen language, this text deserves a close look for extendingthe range and performance of real-world software. --RichardDragan