Book Description

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Reviews (18)

Exactly how an undergrad abstract algebra book should be
Pretty much any introductory abstract algebra book on the market does a perfectly competent job of introducing the basic definitions and proving the basic theorems that any math student has to know. Artin's book is no exception, and I find his writing style to be very appropriate for this purpose. What sets this book apart is its treatment of topics beyond the basics--things like matrix groups and group representations. I suppose many introductory books shy away from much of the material on matrix groups in Artin's book because it involves a little analysis (and likewise for the section on Riemann surfaces in the chapter on field theory). However, Artin correctly realizes that a reasonably mathematically mature student--even one who doesn't know much analysis--will be able to profit from and enjoy the relatively informal treatments he gives these slightly more advanced topics. Of course these topics can also be found in graduate-level texts, but I for one would much rather be introduced to them via an example-based approach such as that in Artin than through the diagram-chasing obscurantism in more advanced books. I happened upon this book a little late--in fact, only after I'd taken a semester of graduate-level algebra and already felt like analysis was the path I wanted to take--but I'm beginning to think I would have been more keen on going into algebra if I'd first learned it from a book like this one.

A Bad Text Book
I must read everything from any other text book to understand clearly what Artin is saying in his book. can you believe it? Few definition is described clearly, few theorem is proved in a logic-clear, easy-to-undersatnd way. The most important is that many useful properties of Ring , field are not included in his book, but in the problems you have to find all these totally by yourself in order to solve the problems. Also, the textbook is NOT well- orginized. A typical exmaple, Artin has not yet tell the reader basic informations and properties of Ring Of Polynomial in one variable , but he starts to describe the structure of Ring Of Polynomial in 2 or more variables. The reader's minds would be completely mixed up if he doesn't not have an extremely high IQ. I believe , your knowlege of Ring and Filed will be very limited and very unclear if you use Artin's book only. Abstract Algebra is a hard topic. You should not use a book which is definitely not a help for you but rather a trouble for you!.Artin may be a famous mathematician, but he is not a good educator. He doesn't not know to teach students in a good manner.

Great book for challanging you to think with clarity
Artin's book is probably one of the better books, more because of the way you have to read it to learn it. Artin's book is extremely nonstandard, in the sense that it isn't so "encyclopedic" as you usually encounter with the whole theorem, corollary, proof, proof, proof, example, example sequence. What I think a lot of readers miss is that Artin's book makes you fill in the details he leaves out by using the hints he mentions in words within the text. For example, I was able to expand the two pages of notes on Ch 2, section 5, in Artin into about 8 pages of original notes and theorems, just by digging for the main points. If you want a sample of my notes, please email me and I'll email you a brief PDF sample for you to compare. That being said, assume that you will have to dig a lot in this book, and should you choose to study from it, I suggest the following:

How to read it:

With a cup of coffee, or tea, and a notepad of paper for you to make comments on. Do not take notes; anyone knows that simply rewriting things doesn't do anything for learning. You should do the proofs in different ways, if you can see how, and try to make some of the aside remarks he makes into theorems or more precise ideas (this is not to say that Artin lacks rigor; this is just talking about the general commentary. When he makes commentary, it always seems to be enough to actually dig out exactly what to do after a little scratching). He also leaves a lot of easier proofs to the reader, so do them.

Is non-standard a less-rigorous approach?

No. Artin is definitely doing his own thing here, but I think it works really well. Getting through that book FORCES you to take responsibility for your math education by making you get your hands dirty while also developing an intuitive understanding of algebra.

What about his personal flavor of algebra?

Well, it's fairly clear to all of us that texts seem to have different flavors (being a function of the author's research area, and what was fashionable during the time the book was authored). Artin's book is algebra with light strong hints of geometry throughout, as he is in algebraic geometry. You will find that unlike most authors, Artin loves structures made of matrices when working with examples, as opposed to permutation groups or the ``symmetries of the square group,'' known also as the ``octic group.'' While these things have their place in his book, he changes the emphasis here. That's why I suggest using a companion book so as to have two sharply contrasting flavors of presentation, and Herstein seems to write in such a way that would do this. Artin covers a lot of material extremely quickly, but focuses on the bigger picture in several key areas. For example, the sections 7 and 8 in chapter 2 deal almost exclusively with how one would go about investigating a particular group structure to learn about it, teaching a student how to dig into something they might barely understand.

Advice to make a wondeful course:

Use another book which IS encyclopedic as a reference, since Artin doesn't label theorems and definitions so explicitly. I suggest Herstein's Abstract Algebra, or his book Topics in Algebra.

Personal Charracterization:

I place this book as one of my favorites on the bookshelf, and it sits among others like Rudin, Ahlfors, Sarason's notes, Herstein, though it's obvious to me that Artin is on a very very different path than all those books, very nonstandard (Artin DOES DO all that a usual algebra course does, and more, if you were wondering), but as a result, very very very thorough and very clearly presented. I love this book very much.

Good overall, not consice enough
Artin is a good intro book for casual self-study in a lazy summer afternoon. That is, if you are bored and decide to learn some abstract algebra just for fun, go for Artin. It's very easy to read and the author basically does the thinking you have to do for you in the text. However, if you want to be hardcore and be more involved with the material, I would recommend Dummit and Foote, a more rigorous treatment.

good, solid treatment of algebra
I bought this book for a class that I ended up dropping. In the beginning, I hated this book. I found Herstein's "topics in algebra" much better, and more to the point. It was only when I was getting bored with Herstein that I bothered to pick this up again. I was pleasantly surprised. A lot of the material flowed very smoothly - exactly as if Artin was teaching the material to you. It must however be noted that people tend to love or hate this book. This is predominantly due to the author's writing style. Given how expensive this book is, you might perhaps want to peruse it somewhere before deciding to buy it. But if you do, you'll get a solid exposition on most of the introductory topics in algebra as well as some insight on groups and symmetry, lie groups, representation theory, galois theory and quadratic number fields. And a whole lot of intuition as well, for the more regular topics. Give this book a chance - it's worth the effort and money. ... Read more

Book Description

When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core algebraic concepts – from monomials, inequalities, and analytic geometry to functions and variations, roots and radicals, and word problems – and get the best possible grade.

At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase – and zero in on the essential information you need to succeed. ... Read more

Reviews (6)

Great "Review" Book
This book is the 2nd Algebra book that I bought. I am the type of person who goes beyond what is given to me. This book is a great book for review purposes. I am over half way through the year in Algebra 1 and already know how to do everything that will be taught to me by the end of the year. I have really learned a lot from these books and I will say, that this is a great book for anyone that is studying Algebra.

It Really Helps!
I have only bought this book for learning and for studying before I am gonna go back to school, but I have learn a lot from it! I really explains clearly enough so you can understand what it is talking about or you can do it after its example.

Excellent book for brushing up
This book is an excellent overview for people who may not have had any algebra for a long time, it is clear, and has very good examples and explanations. Unlike many 'learn algebra' type books, this one shows you exactly how to do the problems from start to finish. I believe you could actually teach yourself an entire semester of algebra on your own with only this book as a teacher. I highly reccomend it.

Great Transition!
I got this book recently because I needed a simple small "transition" book to review all the Algebra I had lost from taking Geometry. Well... I really like this book. It is very useful and I hope to be able to easily integrate it with the rest of all my studying materials. I really like how it has such an easy interface and is small. (to fit in small backpack pockets) For these first months of Algebra II, you guys that are too dumb to remember you basic algebra (like me), get this book. It is a great tool for reviewing even the most important sections in Algebra. Thanks Cliff Notes... you allow people to slack at all times of the year. :)

This book REALLY helps!
In school I had a hard time with exponents & terms, etc.But this book put it in english! ... Read more

Book Description

Unique in approach and content, this book presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively.This book covers trusses; axial members, beams, and frames; one-dimensional elements; two-dimensional elements; three-dimensional elements; dynamic problems; design and material selection; design optimization; and more.For Design Engineers in CAE-CAD. ... Read more

Reviews (6)

Good intro, but does not go far enough
I bought this book hoping it would make my job of developing a finite element model using ANSYS easier. But I did not learn much of anything new from this book. I was already familiar with finite element theory and also took the intro to ansys course offered by ANSYS. I had hoped that this book would go beyond what was offered by these two sources, but sadly it does not. Still, for the beginner who knows next to nothing of f.e. methods and ANSYS this is probably helpful.

A good book for begninners in FE.
The book presents the "black box" behind the GUI. The author wrote the book especially for FE beginners. Ansys users will get the maximum benefit out of it. The book starts by explaining the various formulations applied in FEM. Then, 1D, 2D and 3D elements are presented, followed by simple and clear analytical applications in the field of structural, thermal and fluids. In the second half, the book introduces Ansys and then put it at work through a number of examples. The book/author has the merit of keeping the theory and examples simple and to the point. It is probably the only of its kind. This book is a must for beginners in the FEM.

THE RIGHT BOOK TO START WITH
this book is an excellent book for beginners. Unlike other books, this book gives simplified theory and powerful introduction to ANSYS. each chapter has several examples and some of these examples are solved again by ANSYS to verify the analytical results. you can learn the finite element method in any other book of similar size but, you can not learn ANSYS unless you go through the manuals. Therefore, the author did it for the reader. you will learn the FE theory and ANSYS from the same book and in less time than learning FE only from any other book.

It's the most complete book for structural engineers.
Now I'm reading this guide in my work in the university im my MSc programm in str engineering. In a few weeks I'll be able to make deeper analysis.

a good handbook
it's a good book for analyzing finite elememt model,and ansys is a really power tool! some one can write a book using ansys to analyze a bridge or a building.

youngly in taiwan ... Read more

Book Description

Assuming only an elementary background in discrete mathematics, this textbook is an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It includes random sampling, expectations, Markov's and Chevyshev's inequalities, Chernoff bounds, balls and bins models, the probabilistic method, Markov chains, MCMC, martingales, entropy, and other topics. The book is designed to accompany a one- or two-semester course for graduate students in computer science and applied mathematics. ... Read more

Book Description

Many mathematics students have trouble the first time they take acourse, such as linear algebra, abstract algebra, introductory analysis, or discrete mathematics, in which they are asked to prove various theorems.This textbook will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs.The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted.These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs.The author shows how complex proofs are built up from these smaller steps, using detailed "scratchwork" sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets.Numerous exercises give students the opportunity to construct their own proofs.No background beyond standard high school mathematics is assumed.This book will be useful to anyone interested in logic and proofs:computer scientists, philosophers, linguists, and of course mathematicians. ... Read more

Reviews (16)

A good start on writing proofs, but falls short!
I found that this book utilized a little too much set theory for beginning students. If the author could have given more concrete examples, perhaps from group theory or simpler ones from analysis or number theory, it would have been much better. For students wanting a more lucid exposition of proof techniques, I highly recommend, "100% Mathematical Proof" by Rowan Garnier and someone else,whos name escapes me at the moment. "100% Mathematical Proof" is far superior to this book, and it has answers to the exercises which is crucial to the beginning student learning on his/her own. Velleman needs to bring the abstract nearer to the concrete for the beginning student.

An excellent book
This is an excellent book for the early undergraduate student. It is actually two books in one. The first half is a careful review of Logic and the essentials of Set Theory with an emphasis on precise language. Thereafter a structured development of proof techniques is clearly presented using these tools. The second half of the book is a detailed presentation of introductory material about functions, relations, and a few aspects of more advanced set theory. These chapters serve as a wonderful introduction and show applications of the proof techniques developed earlier.
I have referred back to this book often in my own study of analysis and number theory. I recommend it highly. It will be very useful to any undergraduate proceeding through a mathematics curriculum. I recommend studying it early in the first semester, and re-reading it as time goes on.

Starts off good, and then goes off on a tangent.
I bought this book in the hopes that it would help me improve my proof writing skills. Being only a high school graduate (a month ago), I had practically no knowledge of set theory. The initial proof structures were great, and I enjoyed following the proofs from the premises and, through logical steps, to the desired conclusion. However, then the Set Theory came in. I can understand why a certain amount of set theory was necessary in order to be able to talk about certain types of proofs, but he goes so far into set theory in the book, that by a certain point, instead of following the logical flow of the proofs, I was trying to remember abstruse terminology he had mentioned briefly and trying, successfully for the most part, to understand what the actual proof meant, and why it would make sense that it was correct. Its possible that the reason I feel this way is because when I do proofs, I usually need to understand it intuitively first and then go from there, and it could be the case that this isn't possible with more abstract proofs. Overall, it was a good read, but unfortunately, he went a little too far into the set theory than was necessary. Reading it twice would fix that problem though. Another criticism is that there are no solutions to the exercises.

Breakthrough and Original ......
I recall it was a few years back when I encountered this little gem at my first analysis class. In fact this book wasn't assigned and instead we used Analysis by Lay. I didn't get essential proof tactics/strategies out of Lay's so I plunged myself into Library and after looking up one after another, I finally found this book. It is about as title says and not about Analysis. The book does not cover as much as one expects from Analysis books. But many of them I've seen seem to fail on teaching "how to prove" to study Analysis.

Velleman uses structured style as a technique. Two columns are prepared. The left column is Givens and right Goal. By restructuring Givens and Goal using relationships and definitions, some parts of Goal statement is moved to Givens, like peeling skins of onion. This process iterates until one finds the proving obvious. The whole process is a "scratch work" and a reader is able to see how the author structures the proof step by step, both from Goal and Givens viewpoints.

In past, there was only a Macintosh proofing program, but now Java version called Proof Designer is out. So Windows and Linux users alike can now enjoy this little program in conjunction with the book. Two disappointments with Proof Designer are that the output is only in the form of a traditional proof style which does not expose "the scratch work" and that the program does not use the two column style used in the book.

There are additional materials such as supplementary exercises, documentation, and a list of proof strategies (which is also available at the end of the book as a good reminder and reference), all available from author's site for free. [search in google like this: velleman "how to prove it" inurl:amherst]

After completion of this book, don't throw it away! Advance to Rudin's Principles of Mathematical Analysis and keep Velleman aside. Now one can work on complete proof of materials in Rudin with rigor and study how he constructs logical structures step by step in your own "structured" words!

Probably the best book out there but not perfect
A good basic introduction to understanding math proofs by understanding logic first. Only lacking in its connection to math proofs that one might actually see, in other words too basic (which is as much complement as a critcism.) ... Read more

Book Description

Ensure your success! Purchase the value package textbook and Student Solutions manual for the price of the textbook alone!
That's a $32.95 savings!
(Set ISBN: 0471654930)

Textbook: Achieving a fine balance between the concepts and procedures of calculus, this applied Calculus text provides students with the solid background they need in the subject with a thorough understanding of its applications in a wide range of fields ? from biology to economics.

Key features of this innovative text include:

• The text is problem driven and features exceptional exercises based on real-world applications.
• The authors provide alternative avenues through which students can understand the material. Each topic is presented four ways: geometrically, numerically, analytically, and verbally.
• Students are encouraged to interpret answers and explain their reasoning throughout the book, which the author considers a unique concept compared to other books.
• Many of the real-world problems are open-ended, meaning that there may be more than one approach and more than one solution, depending on the student's analysis. Solving a problem often relies on the use of common sense and critical thinking skills. Students are encouraged to develop estimating and approximating skills.
• The book presents the main ideas of calculus in a clear, simple manner to improve students' understanding and encourage them to read the examples.
• Technology is used as a tool to help students visualize the concepts and learn to think mathematically. Graphics calculators, graphing software, or computer algebra systems perfectly complement this book but the emphasis is on the calculus concepts rather than the technology. (Textbook ISBN: 0471207926)

Student Solutions Manual: Provides complete solutions to every odd exercise in the text. These solutions will help you develop the strong foundation you need to succeed in your Calculus class and allow you to finish the course with the foundation that you need to apply the calculus you learned to subsequent courses.
(Solutions Manual ISBN: 0471213624) ... Read more

Reviews (3)

excellent, much faster than I expected
Excellent seller. It arrived much faster than I expected.
Thanks a lot

Teach yourself Calculus
This book is addressed for understanding of the Calculus and not for the traditional teaching that sins for the excess of formalism. It is an excellent book for who wants to understand and to learn Calculus through the application of problems of the Real World. The book also motivates the use of graphic calculators to have a better vision of the problem.

A Bad Math Book
... The layout of the book was confusing and so where theexamples and explanations. If it where not for a great math teacher Iwould have been lost in the class if I was just left to the book alone. I would recommend students and teachers (if your considering this book for your class) to stay away from it... END ... Read more

Reviews (8)

If there was a zero rating, this book would have it.
Incomprehensible is the best word I can find for this book. I'm good at math and I can't understand half this book. It's the worst textbook I have ever had to deal with. Obviously college instructors do not read the reviews.

The authors give one poor example for every problem, work through the sections as if the reader already knows all the methods, and introduce new concepts without so much as a definition. It's BAD BAD BAD!

College instructors: If you want to confuse your students and discourage them from taking any more classes in math, choose this book.

Hire A Tutor
I agree with the other reviews - this is a poor book. Examples are terse, not well explained, and often don't apply to the exercises you have to do. College Algebra is an intimidating class for nonmajors (perhaps for majors too), and this book does not help. I'd encourage any professor with a choice not to use this book.

So what to do if it's required, like it was for me? I'd say buy the book used (lots of low priced options currently), and use the savings to hire a good tutor to help explain what the book doesn't. I did this, and it did help a lot. I really only turned to the book to write the problems down, and ignored the rest, because otherwise I got too frustrated.

Obviously the authors do not pay attention to reviews....
This has to be the most useless math book ever! You would think that by the 8th edition they would have made some changes to enable learning. The only thing that saved me in this class was the great interactive web program (which of course must be purchased separately unless you are buying brand new @ $125.00).

I used to feel that I was fairly good at math. Thanks to this book, I (and the rest of the students in my class) feel like never taking another math class again!!

Why-oh-why does my school use this book?
I'm currently struggling through this book. I've had to supplement my reading with other textbooks. It is exactly as other reviews have stated - it's like the writers expect you to know the material already and skip any explaination. Avoid this book.

How to teach algebra to mathematicians...
This book was not written for students. It was written for those already fluent in algebra. Why this was chosen as the textbook for my college algebra course, I will never know.
The explanations are terse, and if the student does not already posess a natural affinity for mathematics, lead to even greater confusion. Vital steps are glossed over as if the author thinks everyone reading the book instantly understands without explanation or example. ... Read more

Book Description

The Fifth Edition of one of the standard works on number theory, written by internationally-recognized mathematicians. Chapters are relatively self-contained for greater flexibility. New features include expanded treatment of the binomial theorem, techniques of numerical calculation and a section on public key cryptography. Contains an outstanding set of problems. ... Read more

Reviews (4)

good book
This book (5th edition) cover the topics of undergraduate number theory well. The chapters are -
(1)divisibility
(2)congruences
(3)quadratic reciprocity and quadratic forms
(4)some funtions of number theory
(5)some diophantine equations
(6)farey fractions and irrational numbers
(7)simple continued fractions
(8)prime estimates and multiplicative number theory
(9)algebraic numbers
(10)partition funtion
(11)density of sequences of integers.
It also contains basic cryptography, basic group theory and basic elliptical curves in some of the chapters. The authors give notes on the end of each chapter about some research results, which I enjoy reading.

However, the author give too much hints spoling the fun of solving the problems. Eg 32-36, 40-3, 59-53, 108-36, 136-17, 312-8, and most of the problems in chapter 8. The author should put these hints at the back of the book. I suggest you look up IMO (imo.math.ca) for problems suitable for chapter 1-7 because IMO is well-knowned for its excellent number theory problems (especially 1990-3).

Overall this is an excellent book. I give it a rating of 4.5/5, I don't give it 5 because of the author give too much hints to problems instead of putting hints at back of the book.

Comprehensive
This is a fantastic book on number theory. It covers far more ground than most introductory text (comparable to Hardy and Wright in depth with much less concern for the big O). It covers material usually only available in separate texts: Rational points on elliptic curves, the partition function, and Dirchlet series. Quite readable chapters, well motivated theoretically, although the historic motivation for the subject matter comes largely in the end-of-the-chapter notes. It's an excellent refresher and reference for non-specialist who find themselves using an algorithm or formula they've forgotten (number theory now playing a role in physics and CS, like never before). It is well cross-referenced with regards to methods of proofs the can be accomplished in different section by different methods - this again making it an excellent reference.

Alas, it is pre-FLT. So you'll have to look elsewhere for that.

The best intro to the subject!
I have started my studies in Number Theory reading this book from the preface to the last word. It is amazing! I think it is a better introduction to the subject than the classical Hardy and Wright...it is "more objective" and almost 100% elementary...a good high school reader could do well with it. The chapter of diophantine equations has some divine proofs, very clever and very beautiful. And there is an easy proof of the irracionality of Pi. The only negative point is the existence of some points where the authors could be less concise and a bit clearer, stating the theorems before giving the demonstrations, instead of saying at the end of the paragraph "we then have proved the theorem of..." Its a good book for self-study. It has many exercises.

I've found a marvellous proof...
It's a excellent book. Guide you through the simplest proofs until the great ones. If you can follow the book since start until end you'll be prepared for beginning research in this incredible world. ... Read more

Book Description

A complete, highly accessible introduction to one of today's most exciting areas of applied mathematics

One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms. Because of its success in solving difficult problems in areas from telecommunications to VLSI, from product distribution to airline crew scheduling, the field has seen a ground swell of activity over the past decade.

Combinatorial Optimization is an ideal introduction to this mathematical discipline for advanced undergraduates and graduate students of discrete mathematics, computer science, and operations research. Written by a team of recognized experts, the text offers a thorough, highly accessible treatment of both classical concepts and recent results. The topics include:
* Network flow problems
* Optimal matching
* Integrality of polyhedra
* Matroids
* NP-completeness

Featuring logical and consistent exposition, clear explanations of basic and advanced concepts, many real-world examples, and helpful, skill-building exercises, Combinatorial Optimization is certain to become the standard text in the field for many years to come. ... Read more

Reviews (3)

A Classic in Combinatorial Optimization
Combinaorial Optimization is one of those rare books that is an instant classic. The authors weave a readable fabric of intuition and theory that is unmatched in this exciting discipline. The choice of topics covered begins with two fundamental optimization problems, namely, the minimum spanning tree and shortest path problems. Next, maximum flow and minimum cost flow problems are discussed, followed by matching problems, polyhedral issues arising in combinatorial optimization, and the famous traveling salesman problem. The text concludes with chapters on matroids and NP-Completeness. The exposition on these topics is very well written and the proofs are rigorous. There is a terrific blend of theory, algorithms and applications without overwhelming the reader with computational details. The authors also do a good job of developing an accurate historical perspective of the material, most of which evolved during the time period 1955 to 1995. The book is suitable for an upper-level undergraduate, or a graduate course. The exercises are very well thought out and are at an appropriate level. I have taught undergraduate courses in combinatorial optimization for over 10 years and have always struggled to find an appropriate text. My problem has now been solved.

Elegant one, but not a lot of details.
This book was thoroughly written by great-minded Masters. It is well-organized in their topics and presentation. However, the book details is unbalnced, some chapters are overwhelm the data, and some others are insufficient. By the way, I graded this book a Very Good one. Worth Reading !!

A superb introduction to Combinatorial Optimisation
A good introduction to Combinatorial optimisation and integer programming.

Especially recommended are the chapters on minimum weight matching and the TSP. ... Read more

Book Description

Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography. The Handbook of Applied Cryptography provides a treatment that is multifunctional: ... Read more

Reviews (16)

Excellent reference indeed
If you're going to work in the area of Cryptography, you can't afford
to neglect this book.

We used this in a course, and even though it's a handbook, it doubles up
pretty well as a textbook, since it has all the underlying mathematical
theory, presented in a clear and concise manner.

For sheer breadth and depth of coverage, this book is unmatched in the
field. It may not have enough on some topics to satisfy everyone, but
then i suspect most such topics were not so prominent in 1996, which
is when the book was written.

Starting with number theory, it goes on cover pseudorandom bits and
sequences, stream and block ciphers, hash functions, and digital signatures,
establishment protocols, implementation, patents and standards - you name
it, you got it.

On the one hand, there's enough theory to make you wonder whether it
should be called 'applied', but then it indeed qualifies as implementations
are discussed as well.

And of course, there's an exhaustive bibliography, with more pointers to
the literature than one could possibly follow up.

One word of caution, though : it requires hard work. If you want a more
'relaxed' coverage of comparable breadth (but not depth), you can do
worse than look up Bruce Schneier's 'Applied Crypography', which is a
delightful read, but nowhere as rigorous (read academic) as this one.

All in all, this is an indispensable reference for those in the field -
rigorous and exhaustive, yet eminently readable.

If you still haven't made your mind up, here's one final piece of advice :
visit the authors'(rather the book's) website, where you'll get the
implementations of all the algorithms in the book, and a (presumably)
pleasant surprise :-)

An excellent reference for anyone in computer science
A thorough coverage of topics in cryptography is only one of many features which make this book invaluable to computer scientists. While not intended to be a textbook, this handbook includes enough background information to be of use to those with minimal theoretical computer science knowledge. The chapter organization is logical and very modular so that after reading the introductory chapters, one can skip ahead to the chapters of interest with little difficulty.
The second chapter provides a concise review of probability theory, information theory, complexity theory, and number theory. This chapter would be helpful to anyone in computer science who already has some discrete math background. For readers with no discrete math background I would recommend first reading "Discrete Mathematics and Its Applications" by Kenneth Rosen, the editor of the series this book belongs to.
The coverage of number-theoretic problems in chapter 3 is very easy to follow and provides a handy reference to the average case performance of the best known algorithms for each.
The next few chapters are very math-intensive and outline the most common encryption algorithms and standards with examples. The chapter on block ciphers includes a section on classical ciphers and cryptanalysis which, as a sidenote, might be of interest to students of linguistics.
The later chapters present protocols for authentication, digital signing, and key management which build on the algorithms of the previous chapters, but can be understood independently.
One of the final chapters presents methods of effecient computation which again would be useful to anyone in computer science, not just those who are interested in cryptography.
Overall, the development of the topics in the book is complete (although by no means rigorous) and concise, including examples only where necessary. I highly recommend this book to students who want to learn more about cryptography, anyone whose job requires some knowledge of standards for authentication, digital signing, etc., such as internet security, and any computer scientist who has an academic interest in algorithms and their applications.

Advanced Crypto for the college mind.
This very detailed work is not for the light hearted. It's an in depth look at the mathmatics behind cryptography. If you're looking for a book to help you program then look for Applied Cryptography by Bruce the crypto king instead. If you're looking for something to help you learn cryptoanalysis and how to break codes then this is the first step.

Fantastic traditional reference
The Chapter 14 - Efficient Implementation - shows several multiple precision algorithms. They are very easy to understand and implement under any microprocessor. It is a very good complement to the book set written by Donald Knuth (The Art of Computer Programming, Volumes 1-3 Boxed Set), another fantastic traditional reference.

A very detailed book, but not for everyone.
This is a fairly strong book on crypto, with heavy detail on the math involved. The upside is that the second chapter is devoted to most of the important mathematical theory you'll need to understand for the rest of the book. The downside? That chapter tries to cover just about the same breadth of information as a semester long course in Number Theory.

If you don't have a ton of mathematical background and are scared of having to take a crash course in number theory, or are looking for a higher level view of things, I'd suggest something more along the lines of Bruce Schneier's 'Applied Cryptography' (ASIN 0471117099). If you have some mathematical background, but want to get into things in detail, this is probably for you.

If you're not sure whether you'll like the book, you should definitely take a look at it. While Amazon currently doesn't have sample pages, if you do a Web Search on "Handbook of Applied Cryptography", you can find Sample Chapters hosted online to give you a good feel for the book's style. ... Read more

Book Description

This book offers guided access to a collection of algorithms for the digital manipulation and analysis of images. Written in classic "cookbook" style, it reflects the authors' long experience as users and developers of image analysis algorithms and software.For each task, they present a description and implementation of the most suitable procedure in easy-to-use form.The algorithms range from the simplest steps to advanced functions not commonly available for Windows users. Each self-contained section treats a single operation (histogram evaluation, low-pass filtering, and edge detection, among others).The coverage includes typical situations requiring that operation and then discusses the algorithm and implementation.Sections start with a header illustrating the nature of the procedure through a "before" and "after" pictorial example and a ready-reference that lists typical applications, keywords, and related procedures.Annotated references can be found at the end of each section. An accompanying CD-ROM contains a collection of C programs for carrying out the book's procedures. ... Read more

Reviews (4)

It's just great
The book is just great! I used the source code from the CD-ROM for various image processing projects. The algorithms are also very practical if you have to deal with images. The code is neat and ready to compile and run.

Also this book is good on the description of image process and image analysis algorithms. I read the whole book and use it as a reference during my programming. It sits in my bookshelf and I use it almost everyday.

I recommend anybody who wishes to do serious image programming to have this book. It's just great!

Luis J Gutierrez
Excelente libro. hace un tiempo que he estado estudiando y desarrollando estrategias para la implementación de sistemas de vision computarizada. Este libro es de una gran claridad práctica sin abandonar la necesaria base teorica. Muy buenos ejemplo, información adicional, ejemplos y aplicaciones. Para cualquier investigador en el área debe ser considerado como un recurso indispensable. (if you want my comments in english please send me an e-mail to innovacl@vtr.net)

Practical is the Word
The title says it all. This book was meant to be used. It is organized around a series of transformations that are performed on an image in going from the raw, captured form to usable result. Each step is well identified so you can go directly to the part you need. The methods and routines used are the author's choices, but they give enough information so you can dig deeper if you suspect you may have special needs.

I particularly liked the illustrations. They aren't fancy coffee table illustrations but they are very clear and pointed to what is being discussed. There are many illustrations that show the effect of the procedures on actual images from a variety of fields.

There is a CD-ROM of the executable programs.

A comprehensive book, with good examples
The authors use clear easy-to-understand algorithms to explain difficult concepts. Carefully selected examples make it very a comprehensive and insightful book. It is a good cookbook for beginning as well as advanced machine vision people. The text is supported by an abundance of figures and graphics. The full C source companion software on CD ROM enables the reader to quickly apply the theory. Altogether indispensable for the researcher and innovator, who will return to this remarkable book again and again. ... Read more

Book Description

This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics.It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective. ... Read more

Reviews (14)

General Problem Solving Strategies.
Perfect match for all math problem solvers.
Wonderful Book with around 660 problems.
Level National Math competition, IMO, Putnam.
If I have to pick the best two problem solving books so far publish in the English Language
Problem-Solving Strategies (Problem Books in Mathematics) by Arthur Engel and this Book by Paul Zeitz are the clear winners.

This particular book has very clear explanations of the main problem solving strategies illustrated with carefully sample problems. Reading this book brings to my memory the works of Polya. One of the only things I think the book is lacking is on strategies to solve Geometry problems in particular or to use the same strategies in the book to solve more Geometrically flavor problems. Nevertheless is a Joy to read.
Please Paul keep writing this beautiful problem solving books.

One of the best
This book is indeed one of the best problem-solving textbook so far. As a frequent lecturer of Taiwan IMO team, I have many many MO books. Most of the books available are well-written by professionals and excellent mathematicians. However, since IMO does really prevail in recent years, these authors could not be the participants themselves (^^). Furthermore, usually these books (except those are merely problems collections) contains a good proportion of "harder" and beautiful problems, and the easier and basic training problems are relatively few. It often get the beginners frustrate.

Now this maybe is the first book written by a member of former MO team, and now a training lecturer. (The author himself won the USAMO and IMO in 1974, and helped train several USA IMO teams, including the 1994 "perfect score team"). So here is the precious experience! Besides, the ratio between the harder problems and the easier problems is really good. In my opinion this is an excellent textbook for ambitious beginners (both teachers and students), for self-studys and problem-solving fans. Highly recommended.

Essential for budding (and experienced) problem-solvers
I join the ranks of previous reviewers here who honestly feel that having read this book in high school would have almost certainly changed my life. I, too, did very well in high school math competitions, but the maturity I am gleaning from this gem may have vaulted me into a different league.

It contains hundreds of problems from various levels of competition, from AIME problems all the way through some of the toughest Putnam problems (which, if you know anything about the Putnam, are about as hard as competition problems come). But the biggest help are the vital insights and exciting ways of looking at these problems. Don't take my word for it-- many past IMO contestants have suggested this book too.

You don't have to be a math competition buff to gain from this book, however. If you're simply interested in mathematical puzzles and problems, and looking to expand your repertoire, this book will help you. Anyone with a good dose of intelligence and motivation will benefit.

For an additional problem book, check out Mathematical Olympiad Challenges by Andreescu and Gelca. For purely Putnam treatment, there are several volumes written by Kedlaya. And if you're a CS student, looking for honing those CS math skills to be razor sharp, you should definitely look into Concrete Mathematics by Graham, Knuth, and Patashnik.

Happy solving.

The Book I wish I had in High School
When I was in high school, I placed second in the Alabama State Mathematics Contest and won many others. However, I might could have been competitive with the IMO style problems had I had this book and would be much better off today had I seen this book earlier.

This book is for the exceptionally brilliant and the mentally tough. It is absolutely necessary to approach this book in a different way from a standard math textbook. You MUST attempt the examples BEFORE looking at the example solutions, NO MATTER HOW DIFFICULT OR FRUSTRATING. You may be bamboozled by the problems, but even trying to understand the problems before looking at the solutions and thinking about how a solution might proceed will pay huge dividends in the long run.

For example, in the first chapter Zeitz presents an example asking the reader to prove that the product of four consecutive integers cannot be a perfect square. The solution involves some clever algebraic trickery not visible to the inexperienced, but persistence and getting your hands dirty is key.

If you persist in spite of the considerable difficulty, you will find that you get better very, very quickly. You will also notice that it isn't just contest problems it helps you solve. I have found that I have solved my homework sets in the Berkeley graduate engineering program much more easily since working these problems. You will start to see creative and clever solutions where they exist in everything problem oriented.

PATIENCE PATIENCE PATIENCE!

Brilliant
As a high school student that is essentially bored with the regular, ho-hum classes that my school offers, this book is perfect. It gives a problem-solving foundation for math enthusiasts desiring to compete nationally in contests like the AMC, AIME, and USAMO. The problems are excellent and cover a wide range of difficulty (past ASHMEs, USAMOs, and, finally, IMOs); and the solutions are well-written, logical, and intelligible. In short, if you are looking to "get better" at problem solving, this is the book for you.

Note: I also bought Problem-Solving Strategies by Arthur Engle. Those, perhaps more advanced, problem-solvers that want even more of a challenge should purchase this book as well (as both books give very challenging problems, but Engel's is undoubtedly more advanced). ... Read more

Book Description

This text, written by best-selling developmental mathematics author Pat McKeague, features a more streamlined review of elementary algebra, allowing for earlier coverage of intermediate topics. An early introduction to graphing presents the foundation for a wide variety of graphing problems throughout the text. Early coverage of functions helps students feel comfortable with the many examples and graphs of functions that occur in later chapters. The first ten chapters of this book cove the topics usually found in a college-level algebra course. The last three chapters cover the essential topics from trigonometry. Optional technology sections and integrated throughout text as a way for students to better understand the material being discussed. ... Read more

Reviews (2)

Excellent
An excellent book such as this one deserves praise. I read it, I got it, and I can teach it.

This book was not very helpful.
This book was the text for a class I took. Everyone, including the teacher, found it almost impossible to learn from the book. We used it for exercises and examples, but that was about it. ... Read more

Book Description

The Fourth Edition of College Algebra helps students see the dynamic link between concepts and applications. The authors' hallmark approach, the Aufmann Interactive Method, encourages students to interact with math by presenting an annotated example, then guiding students with a Try Exercise, and finally presenting a worked-out solution for immediate reinforcement of the concept.

• An Instructor's Annotated Edition, unlike any other offered for this course, features reduced student text pages with special instructor resources in the margins: teaching tips, extra examples, ideas for reinforcing concepts, discussion suggestions, highlighted vocabulary and symbols, challenge problems, quizzes, suggested assignments, and references to transparencies that may be found both in the Instructor's Resource Manual and on the web site.
• Side-by-Side Solutions to examples pair an algebraic solution and a graphical representation to accommodate different learning styles.
• Integrated web resources include selected Take Note boxes (identified by a special web icon) which direct students to an interactive example or a downloadable file on the web site.
• Exploring Concepts with Technology, a special end-of-chapter feature, expands on ideas introduced in the text by using technology to investigate extended mathematical applications or topics.
• Projects at the end of each exercise set are designed to encourage students (or groups of students) to research and write about mathematics and its applications. Additional Projects are included in the Instructor's Resource Manual and on the book's web site.
• Take Note and Math Matters (formerly called Point of Interest) margin notes alert students about interesting aspects of math history, applications, and points that require special attention.

Reviews (4)

".....you're going to need a different book!!
I've just finished using this book and, while I normally keep my textbooks as reference materials, I found this book to be so bad that I'm selling it back! This book falls short when it comes to providing solid examples; clear, concise text; and valid exercises. Specifically, the pages are so crammed full of text and colors that it is often difficult to quickly find specific information. Much of the text and many of the examples fail to adequately prepare the student for the exercise sets. Additionally, the accompanying solution manual, which helped me immensely, has numerous typos and is missing several pages of solutions. I wish I were alone in my opinion, but the overwhelming majority of my class felt about the same. Even our professor was less than impressed. If this is the textbook you must have for class, get some additional references, i.e. Schaums, or something similar, perhaps even another 5 star rated book from Amazon.

College Algebra by Aufmann
This book is written for the average college student. The
material is illustrated well and there are many examples
depicting the mathematical concepts. More advanced students
are sufficiently challenged, average students will work hard
and below-average students may have problems. It is important
for the instructor to assign frequent homeworks and review
the homeworks before continuing with new material. A small
minority of students enter college having had NO ALGEBRA in
high school. I wish that some of these students would return
to high school to complete the work they never finished.
Overall, I'm satisfied that the text represents a fair
concensus of the problems encountered in College Algebra.
There are sufficient word problems which require students
to translate verbiage into mathematical formulas. In addition,
classic areas; such as, "complete the square" are covered
thoroughly.

Drop the class if this is the text-book.
To date, this is the worst textbook I have encountered in my math classes. In fact the instructor uses this book for homework assignments only as the text itself is useless.

To start with, I found the explanations to be badly written, wordy, and confusing. Seems as though this book was designed for a refreshment course rather than for people who are going over the material for the first time.

Then, the examples: there are not enough of them, and the examples do not support the exercises at the end of the section, so if you work out the exercises at the end of the section and encounter a problem, you just don't have an example to help you out.

It continues with the student solution manual on line: due to the lack of examples the student's solution manual is the next tool to try to figure things out. However, the manual appears to be put together almost as an after thought. It is very unorganized, uses shortcuts to the solutions that are sometimes difficult to figure out.

In summery, this book makes it difficult to learn on your own. It does not help deepen and re-enforce your understanding of the material covered in class. From my experience so far, there are much better books that make the time learning more efficient, productive, and fun.

Best text I've ever seen in 10 years of teaching!
Aufmann's text is excellent. The problems are clearly organized and worked in detail. Aufmann really makes a serious effort to help the students understand the material. His applied problems are very interesting and the illustrations and helpful and numerous. I learned algebra from an old text by Dolciani, and I think Aufmann's book is much better. If I were learning algebra for the first time today, I would hope that my instructors would choose Aufmann's book rather than any of the other sorry excuses for algebra textbooks that are available today. Trust me when I say: ALL ALGEBRA TEXTBOOKS ARE NOT CREATED EQUAL. AUFMANN RULES! and if you give the text half a chance, you will be able to learn algebra from it. ... Read more

Reviews (1)

interesting applications
If you are majoring in the life sciences, then the authors have striven to teach calculus in a manner that will interest and motivate you. Here, life sciences encompasses both the biological sciences and various social sciences like finance and economics.

The authors customise the course via numerous examples and problems in each chapter. To be sure, in the text, outside the examples, it is a straightforward explanation of the important ideas in caculus, like finding derivates and solving differential equations. Which is as it should be. The maths is independent of the applications, after all. But much of the value of the book to you is in those examples and problems.

There is a fascinating plethora of problems. I will only cite a few: Modelling a foot and mouth disease epidemic. Alcohol concentration in a person's blood as a function of time. Rate of pollution entering a lake. The Gini coefficient of income inequality in a country.

The book shows that the uses of calculus in the life sciences are myriad and worthy of your understanding and appreciation. ... Read more

Book Description

This tried-and-true book of differential equations expands upon the authors' Differential Equations: Computing and Modeling, 2nd Edition. It covers the core concepts and techniques of elementary linear algebra—matrices and linear systems, vector spaces, eigensystems, and matrix exponentials—that are needed for a careful introduction to linear equations. Complimenting this solid foundation, the book emphasizes mathematical modeling of real-world phenomena, and offers a fresh new computational flavor evident in figures, examples, problems, and projects throughout.Chapter topics include: first order differential equations, mathematical models and numerical methods, linear systems and matrices, vector spaces, linear equations of higher order, eigenvalues and eigenvectors, linear systems of differential equations, matrix exponential methods, and nonlinear systems and phenomena.A geometric visualization for those interested in science and engineering. ... Read more

Book Description

Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide­­--more than 104,000 copies were bought of the prior edition--­­includes problems and examples using graphing calculators.

Reviews (8)

Good for review but errors abound
A good overview of calculus, though--admittedly--I am using it to review the subject rather than learn it for the first time. Very practical, and offers enough examples to get the hang of it in most cases.

However, the egregious number of serious errors in the book (in a 4th edition?!) can often be frustrating if not misleading. Some errors are misstatements of theorems or errors in the worked problems! Others include mislabeled graphs, incorrect PROBLEMS (yes!), incorrect answers etc. Believe, me, I've spent hours checking my work, assuming I had made the mistake (but have verified using mathematica, graphing calculators etc.) For someone working nearly every problem, this leads to a lot of confusion and a huge waste of time. I estimate that I have found 20-30 major errors already, and I've only finished the chapters covering calculus of a single variable. :(

If they had errata published, it might be a little better, but haven't been able to find any.

Unfortunately, haven't tried other review texts...probably better just to get a real calculus book. I've forgotten the one I used in high school and subsequently sold. :(

I wish it had more....
This book was a bummer, man. I LOVED the Schaum's Outline for PreCalculus and it was awesome. This book however, left me wanting more. It needs more SOLVED exercises. In each section you get about 3-5 solved problems and then 10-15 problems with answers without solutions. I bought this book hoping it would be a supplement to my text book, but it just didn't have enough step-by-step solutions which is what I need when I'm learning new material.

Schaum's Calculus
I've worked with several versions of the Schaum's Calculus
over the years. This work has excellent coverage of derivatives,
integrals, curvilinear motion, polar coordinates, indeterminate
forms, indefinite integrals, centroids, arc length, tests for
divergence/convergence, partial derivatives, volumes, triple
integrals and a host of exotic areas. There are many multi-
dimensional diagrams to aid in your understanding of this
fairly complex subject. I did well in Intermediate Calculus

garnering an "A". In addition, the Fundamentals of Engineering
Licensure Exam covered quite a bit of basic and intermediate
calculus. This is an excellent supplementary work to complement
the course textbook and class notes.

An excellent companion to Calculus
I found this book to be a very good supplement to anyone taking a calculus course. The main highlights (and some, but few) lowlights are as follows:

The Good:
1. LOTS and LOTS of topics covered ranging from limit concepts to l'Hopital's rule to integral tests to multiple integrals, this book covers A LOT (and even a brief intro to differential equations.)

2. Enough practice problems to ensure that the reader will comprehend the material (as is the case with most Schaum Outline books).

3. Lots of graphs for visual learners.

4. A fraction of the price of most calculus books.

The Bad:
1. The only bad thing I could possibly think of in this book is that it explains vector concepts and differentiation and integration of vector functions and gradient, divergence, and curl, but leaves out Green's and Stokes' theorems (must be covered in the vector analysis Schaum book).

For more detail, check out the list of chapter topics on the back cover of the book (it's a pretty thick paragraph)

Indispensible if you want the "A"...
My instructor had a nervous breakdown about 1 month into an integral calculus class. He spent the rest of the semester discussing his personal problems during class, instead of teaching. He stopped giving tests and cancelled his office hours. We had a midterm, which I failed (with a 28/100), along with the rest of the class. My entire grade hinged on the final exam. I bought this book and spent the last half of the year using this book to teach me integral calculus. Two weeks before the final, the instructuor told the class that he was throwing out the midterm, and that our grade for the class would be based solely on our performance on the final exam.

I got a 96/100 on the final, and an "A" for the course. This book saved me. (This sounds ridiculous, I know...but it is absolutely true.) ... Read more