Abstract Books

I must admit, my progress through this book can be measured in lines. It's not that it's confusing, but that it's pretty dense. The proofs are structured in such a way as to leave teasing amount of details to the reader, and the text measures understanding as much as the exercises. It is that which makes reading this book worthwhile.

From an academic point of view, the material in this book is very standard. The content of the first four chapters is closely paralleled by an introductory graduate level course in Lie Algebra and Representation Theory at MIT (although the instructor did not explicitly declare this as class text.) In many ways, this book is my ticket out of attending lectures, and it has done a great job so far.

I must admit that it can be frustrating at times to work out the statements of the proofs, but it only makes the understanding just that much more pleasant and adds the perfect amount of emotion to an otherwise black/white text.

Humphreys' book on Lie algebras is rightly considered the standard text. Very thorough, covering the essential classical algebras, basic results on nilpotent and solvable Lie algebras, classification, etc. up to and including representations. Don't let the relatively small number of pages fool you; the book is quite dense, and so even covering the first 30 pages is a nice accomplishment for a student. Small caveat, the notation might be a bit confusing until you get used to it, but this is a common problem due to having both a Lie and a matrix product floating around, and is not a fault of the text. There is also a nice selection of exercises, between 5 and 10 per section.

Highly recommended; every mathematician should know the basics of Lie algebras.

This book is a pretty good introduction to the theory of Lie algebras and their representations, and its importance cannot be overstated, due to the myriads of applications of Lie algebras to physics, engineering, and computer graphics. The subject can be abstract, and may at first seem to have minimal applicability to beginners, but after one gets accustomed to thinking in terms of the representations of Lie algebras, the resulting matrix operations seem perfectly natural (and this is usually the approach taken by physicists). The book is aimed at an audience of mathematicians, and there is a lot of material covered, in spite of the size of the book. Readers who desire an historical approach should probably supplement their reading with other sources. Readers are expected to have a strong background in linear and abstract algebra, and the book as a textbook is geared toward graduate students in mathematics. Only semisimple Lie algebras over algebraically closed fields are considered, so readers interested in Lie algebras over prime characteristic or infinite-dimensional Lie algebras (such as arise in high energy physics), will have to look elsewhere. Physicists can profit from the reading of this book but close attention to detail will be required.

The first chapter covers the basic definitions of Lie algebras and the algebraic properties of Lie algebras. No historical motivation is given, such as the connection of the theory with Lie groups, and Lie algebras are defined as vector spaces over fields, and not in the general setting of modules over a commutative ring. The four classical Lie algebras are defined, namely the special linear, symplectic, and orthogonal algebras. The physicist reader should pay attention to the (short) discussion on Lie algebras of derivations, given its connection to the adjoint representation and its importance in applications. The important notions of solvability and nilpotency are covered in fairly good detail. Engel's theorem, which essentially says that if all elements of a Lie algebra are nilpotent under the 'bracket", then the Lie algebra itself is nilpotent, is proven.

The second chapter gives more into the structure of semisimple Lie algebras with the first result being the solution of the "eigenvalue" problem for solvable subalgebras of gl(V), where V is finite-dimensional. Cartan's criterion, giving conditions for the solvability of a Lie algebra, is proven, along with the criterion of semisimplicity using the Killing form. The representation theory of Lie algebras is begun in this chapter, with proof of Weyl's theorem. This theorem is essentially a generalization to Lie algebras of a similar result from elementary linear algebra, namely the Jordan decomposition of matrices. Again, physicist readers should pay close attention to the details of the discussion on root space decompositions.

This is followed in chapter 3 by an in-depth treatment of root systems, wherein a positive-definite symmetric bilinear form is chosen on a fixed Euclidean space. These root systems enable a more transparent approach to the representation theory of Lie algebras. The theory of weights along with the Weyl group, allow a description of the representation theory that depends only on the root system. In addition, one can prove that two semisimple Lie algebras with the same root system are isomorphic, as is done in the next chapter. More precisely, it is shown that a semisimple Lie algebra and a maximal toral subalgebra is determined up to isomorphism by its root system. These maximal toral subalgebras are conjugate under the automorphisms of the Lie algebra. The author further shows that for an arbitary Lie algebra that is true, if one replaces the maximal toral subalgebra by a Cartan subalgebra. The proofs given do not use algebraic geometry, and so they are more accessible to beginning students.

In chapter 5, the author introduces the universal enveloping algebra, and proves the Poincare-Birkhoff-Witt theorem. The goal of the author is to find a presentation of a semisimple Lie algebra over a field of characteristic 0 by generators and relations which depend only on the root system. This will show that a semisimple Lie algebra is completely determined by its root system (even if it is infinite dimensional).

Chapter 6 is very demanding, and will require a lot of time to get through for the newcomer to the representation theory of Lie algebras. Weight spaces and maximal vectors are introduced in the context of modules over semisimple Lie algebras L. Finite dimensional irreducible L-modules are studied by first considering L-modules generated by a maximal vector. It is shown that if two standard cyclic modules of highest weight are irreducible, then they are isomorphic. The existence of a finite dimensional irreducible standard cyclic module is shown. Freudenthal's formula, which gives a formula for the multiplicity of an element of an irreducible L-module of heighest weight, is proven. A consideration of characters on infinite-dimensional modules leads to a proof of Weyl's formulas on characters of finite dimensional modules.

The last chapter of the book considers Chevelley algebras and groups. Their introduction is done in the context of constructing irreducible integral representations of semisimple Lie algebras.

This is a typical mathematical monograph
which means it is densely written with
almost no examples. It's too bad since
that makes decoding the text much more
time consuming.

I am just beginning to explore pollacks work - book is well laid out

This may have been one of the better Pollack books when it came out in 1972, but now I think its main use is for die hards who want every detail. And the details are exhausting: galleries, museums, who what where - too much for me. What I was looking for was more process/personal/mindset stuff, and there is some but you have to go through a lot to get to the little of it there is. I recommend "Jackson Pollack" by Ellen G. Landau. Great reproductions and good text.

This book is a thorough review of Jackson Pollock's work and his professional life; however I would have enjoyed it more if there had been more indepth reporting of his personal life. HIs relationship with his wife, parents and brothers would have made for a more insightful view of the artist as a man.

I was wowed reading this energetic, straightforward book, mainly by the many connections made--how Pollocks studies with the great Mexican muralist Orosco who used used/taught a dripping splashing underpainting technique can logically link to how Pollock got splashing and painting on large scale canvases---to the influence of other artists, such as Picasso, on the early works of Jackson Pollock, to the revelation of Pollock's love of and use of found natural forms...

Just once, I'd like to pick up a math text that delivers the basics up-to and including the point of the book. This "undergraduate" book requires prior knowledge and didn't work for me as a self-teach, even with my 5-semesters of calculus. Very disappointed.

The Laplace Transform: Theory and Applications (Undergraduate Texts in Mathematics)

Joel Schiff has demonstrated on a number of occasions that he is a master expositor of Mathematics and the current volume has to be among Dr Schiff's finest. 'The Laplace Transform' is an excellent starting point for those who want to master the application of transform techniques to boundary value problems and thus provides a backdrop to Davies' Integral Transforms and Duffy's Transform Methods.

Dr Schiff is to be particularly commended for his treatment of the inverse Laplace transform, which often receives scant attention in engineering texts.

Dr Schiff's book can be read at several levels; readers less interested in mastering the proofs may be interested to note that most of the standard transforms one meets in practice are covered either in the text or in exercises.

In sum, 'The Laplace Transform' is for those who want to get beyond the 'operational technique' status of the method, and is strongly recommended to readers who have covered a first course in complex variables. It should appeal to Mathematicians and Engineers alike.

This book is written in a very clear style, suitable for self-study. The exercises have been well chosen and correctly placed. It might be most effective if read concurrently or immediately after an elementary course on Differential Equations at the level of Zill's book. Teachers should take a look at this book, it shows how to deal with the subject rigorously without being boring. No measure theory is required.

I thought this book was really well written and presented. It has really helped with my understanding of Laplace Transforms. I would highly recommend this book to engineers who want a deeper understanding of transforms. It is worth while reading up on Residue Theory and Cauchys Theorem before reading this book. I am sure that I will constantly reference back to this book for my work.

I am a big fan of Klaus Mai's first book, KM7, so I had big expectations for this follow up book. Suffice to say I was very disappointed. The work in this book is very tame and boring compared to the first book. The text pages are printed in black on a very dark brown background making them impossible to read. I reccomend buying the first KM7 book and not bothering with this one.

I can't not give Klaus Mai's 2nd book the highest rating, since he is by far my favourite designer, but I wish it was a strong as "License to Design"! i remember seeing "License" at Borders for the first time and it was the most inspiring book on design that I had ever seen- beautiful, tight and meaningful design, with both strong typography and excellent use of images- quality of work that no other firm could even come close to! "see" is a great book, but does not have the magic of the first one

This book gives a very, very good example of today's design trends. It has design examples from NIKE, MTV, AUDI and much more. The book features the big brands with today's designs. This is absolutely the newest trend what design is concerned. Klaus Mai and his design firm use a lot of vector graphics to enhance the accompanying pixel images. Which totaly a new and cool design approach.

I agree with my fellow countryman that the reviews are not very readable (some black text over a dark brown background) but the designs are the thing that matter and they speak for themselves. It is a very cool book. If you should make a choice between Klaus' 2 books, buy them both. You will see Klaus' growth from the first book to the second, design wise....

It is to bad that evil art bases his opinion on the review (text pages. Which is not what the book is about. There aren't even that many text pages in the book. I'd say ± 90% of the book is design. And cool design it is.

One of my favorite design books! The design work is more mature and beautiful than "License to Design." The first book had far to many Rave invitations. It's true that the text is difficult to read but great design does not have to be explained.

I just picked up all 5 volumes and have been going (slowly) through them. You can really see how the authors art and storytelling ability evolved over time. In book 1 the characters looked a little rough and the writing was fairly cliche and one dimensional.

By the time you reach book 5 everything is polished.

Book 5 reprints issues of the comic 61 - 76 and the Molly & Poo stories from 46, 49 and 73.

On the Strangers In Paradise website they just announced that #90 will be the final issue in the series so it looks like there will be just one more Pocket Book and the entire run is complete.

I can't say I'd consider myself a hardcore SIP fan since I don't buy every color issue that comes out, but I do own all 5 pocket books. I usually finish them in a couple hours because they're just that good.

To those who have never read SIP, I highly recommend it. It's not a child's comic book. There are some real and deep situations in these novels and it's probably best for kids not to read them.

These novels deal with (un)conditional love, where the line between the love that two people share as friends and the love that two people share as lovers is blurred.

You'll find that the images are drawn to perfection, conveying emotions so well you'll swear the characters were alive.

Please give this a read, you won't regret it!

I enjoyed it but not as much as I enjoyed the previous books. The exploration of the characters and relationships is still great but there wasn't as much flow to the drama and action, i'm starting to wonder if Terry Moore is getting a bit burnt out on the characters.

Still, it is better than a lot of other stuff out there and adds a hell of a lot of respectability to the comic medium.

The neverending love triangle of our three main characters (Katchoo, Francine and David) extends itself in this latest volume from Terry Moore. Initially I was happy to receive it as a gift and read through it in two days, but afterwards was left feeling emotionally empty and was beginning to question whether or not I should continue on with this series.

I mean, the reason I started reading SiP was because of the dynamic relationships involved, but in real life relationships either get better or worse, not stand still as they have in this case for the past several years. Case in point is where Katchoo is reunited with David. The two get drunk and married in Vegas. They are about to go through with it, when Katchoo's undying love for Francine kicks in, not to mention the fact that she loves women more than men. Surprised? I don't think so. It's the same thing that's been happening between them ever since they met.

There are also other dramatic events that take place which could have added a lot to the story, but fails to do so because things are resolved far too easily. For example, while in Vegas we encounter a lethal stalker who is after Rusty - a friend of Casey Femur. The guy threatens them at gun point and all Katchoo has to do is break his nose and it's over. Just like that. Rusty is then written out of the plot and Casey moves back to Houston where she belongs. So in other words, the crew goes back to square one. In another dramatic scene Sara Bryan and detective Walsh interrogate Katchoo, determined to throw her in jail for crimes she didn't commit. But a simple phone call to Tambi solves all that. I also find that Casey's character seems to have grown a bit inconsistent. Last I recall she was in love with this guy named Joe and proved to be smarter than she looked. Now she's madly in love with David and has evolved into a ditz.

So, my verdict: Entertaining, Yes. Progress, No. These characters aren't strangers anymore and I'd like to see a long awaited resolution to cycle of make-up and break-up that has plagued these characters for so many years. The formula still proves entertaining but is losing its effectiveness fast.

I agree with the reviewer who said most the content categories run a little thin. Each page is dedicated to one site with two screen captures from that site on the page. The largest section in this book by far is "design and illustration" which seems to focus on portfolio sites and comes in at 200 pages of examples. No other section has more than 40 pages and most have under 20. There are a ton of international sites in this book and not a single "major" web site. Which is good because that means the majority of the content in this book should be new to most readers. There is also very little text; there is no discussion of the designs, just large colorful screen captures and then credits at the bottom for the designer/agency and a url.

If you need inspiration for edgy or artistic sites, then this is a good resource. If you're looking for more corporate site design, you won't find much of that in here. Personally all my design falls in the later, but I do think this will be a good resource for when I decide to revamp my portfolio site or if I want to experiment with more non-standard design. Since all my work is corporate, I find the more whimsical and creative side of my brain has shut down a bit. And it did have a good selection of sites with a black/dark color scheme which is nice; that style tends to be a challenge for me so having this many examples is handy.

I gave this 3 stars instead of 4 because I would have liked to see a more balanced representation of web design styles.

I found this book in my local bookstore, cased in shrinkwrap, and debated whether to risk buying it without seeing the contents first. In the end, I took a chance and am glad that I did. As a beginning designer, I found several designs that gave me some ideas for my own site. Ironically, the biggest section in this book is devoted to graphic designers.

Web Design Index by Content 3 covers a wide spectrum of industries. However, I felt that the majority of the industry sections ran a little on the thin side. That said, the publisher of this book (Pepin Press) accepts submissions and recommendations at [...].

As a professional within the area, this is a terrific book, since it provides an insight to what is currently being done, all over the globe. The author doesn't just focus in one particular country, the focus is worldwide and strongly reflects what is done in web design these days. Highly recommended.

This is my second Web Index Book from this publisher and they have been great books for inspiration in my freelance work. Filled with great websites and large images to really see the detail and craftsmanship of each website. One cool thing was when I ordered this book and chose 3-5 day shipping I actually got it within 2 days which was a nice surprise. If you only need to get inspired this book is for you.

Page 174 volume 2 the author did not follow completely the proof of Nagell theroem as in Algebraic Number Theory by Stewart & Tall Instead He introduced the matrix [1 1, -2 0], We may name it here for short S, The author claims that S**42k = [-1 -1, -1 -1] mod 3 which is wrong S**42k = +-[1 0, 1 0] 4|k or 2|k respectively and = +-S 4|k-1 or 2|k-1 respectively in both cases the first entery in the total matrix as S**(42k +13) * [0 1] would be -1 and destroy the logic of the author in his argument However it deos not violate the theory for -1 in a field of chratersistic 3 need not be -1 in the integral domain Z[sqrt(-7)] I do here thank Amazon.com for the chance to report that for neithe the author nor the editorial at the publisher has an address to communicate with. Abdu Shokr 35-17 Ditmars blvd suite 202 NY NY 11105 August 3 2000

This two volume set is by far the most complete text on abstract algebra available. Rich in detail, a wealth of examples and clear yet concise explanations provide the reader an accesible source to deepen his understanding of abstract algebra. Spindler conveys his love of algebra and a desire to reveal its riches to the average student. If you've relied on Hungerford's / Lang's Algebra or Warner's Modern Algebra, this text is the last text you will need.

This is the premier handbook for Southern Baptist Theological views. In this book, Boyce conveys the Biblical support for the modern conservative movement in Southern Baptist life. It offers several Biblical references to support any theory that is offered. It is an excellent resouce for Bible students.

This systematic theology by the first president of the Southern Baptist Theological Seminary, now in Louisville, KY, puts the lie to the theory that Baptists are not adept in the finer points of theology. Well-written and easy to follow, this work is great for those who love solid, Reformed (Calvinistic) theology but may have trouble following Calvin or Turretin. Boyce readily admits that he learned his trade at Old Princeton and indeed the spirit of Jonathan Edwards, A. A. Archibald and Charles Hodge are immediately seen. This is, however, far from being a derivative work. Along with Dagg's "Manual of Theology," it constitutes one of the two great works by Southern Baptist theologians in the Nineteenth Century. Today's Southern Baptists who often have a weak, decisionalistic, Arminian theology would do well to heed the learned wisdom of their founders. This is an eminently Biblical and sound volume answering almost any query a Sunday School teacher, deacon or even pastor might have. I have given it four, as opposed to five, stars merely because there is no discussion of the sacraments or ordinances as Baptists are prone to refer to them. This may reflect the lesser importance of these facets of the Christian Faith to Baptists or it may be that there was a desire to avoid bringing divisive confessional differences into his masterwork. Whatever the reason, it is only a mild distraction and the rest of the work is so beneficial that owning it becomes a great joy and privilege to any Christian, whether Southern Baptist or not.

it is so sensual - makes me want to lick the pages. i sit with my daughter (21 months old) and we both just sink into it. life is beautiful. and sad.

I am mad about Gerhard Richter. Especially when it comes to his masked and stripped oil paintings. Therefore it makes sense that I would have to acquire this little book full of detail panels of Richter's painting. That's it. That's why you would buy this thing. It's straightforward and there's really no other use for it once you are done staring. It gets filed under "reference" in my library. When someone wants to see what it is about this German painter that get me so juiced, and we don't want to run out to the Saint Louis Art Museum and I don't have Sonic Youth's Daydream Nation lying around (or even if I do) then I let them flip through this little art book.

I used this book as a reference resource for an advanced algebra course. At times, wording of key concepts was a little long. This book is a good complementary reference to Joseph Gallian's Contemporary Algebra book.

This is the book version of a series of lecture notes on abstract algebra written by the author and still available on his web page. However, given the price (it's a Dover book...) it's worth buying just to avoid that thick pile of sheets lying around. The best thing about this book is that it avoids formalism whenever it can without sacrificing rigor. Many theorems are "proved" by means of an example of a general case. In this way, the reader gets the intuition behind the result without having to deal with the abstract and sometimes artificial constructs of a rigorous proof. In any case, supplying that rigorous proof can be seen as an extra exercise (or you can look it up elsewhere!). In other words, it's a great book to learn the ideas behind the theorems dealing with groups, rings, modules and fields.

The second part of the book deals with commutative algebra, algebraic number theory, algebraic geometry and homological algebra - areas where it's very hard to find intuitive explanations in the literature, since books on those subjects tend to assume (quite reasonably) the reader has a solid background in abstract algebra. Unfortunately, that means that examples and intuitive explanations are drastically reduced, sometimes to none at all. That makes this book even more attractive.

In any event, after you get the intuition, it will be much easier to to tackle the more rigorous approaches of Dummit & Foote or Hungerford (I don't know Lang's book but I'm told it's much dryer than these two).
Or you can start your study of algebra with any of these more traditional books and use Ash's as a supplement. If a theorem or its proof proof seems opaque, look it up on Ash. Chances are his explanation will clarify things.