Book Description

...This beautiful and eloquent text served to transform the graduate teaching of algebra, not only in Germany, but elsewhere in Europe and the United States. It formulated clearly and succinctly the conceptual and structural insights which Noether had expressed so forcefully. This was combined with the elegance and understanding with which Artin had lectured...Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach spaces to topological group theory...It is, in my view, the most influential text in algebra of the twentieth century.

Customer Reviews (6)

It ain't perfect!
OK, it's a classic. Still, I've got complaints.

Consider this:

A Euclidean ring is defined in van der Waerden's "Algebra" in such a way that the reals are a Euclidean ring. Just define g (the norm) as a constant. Since every number has an inverse, the division algorithm is satisfied since we can always have a remainder of zero. Fine. No problem.

Now, half a page under the definition of Euclidean ring, we have a discussion about "the" greatest common divisor of two elements, a, and b, of a Euclidean ring. The 'definition' of the term 'greatest common divisor' is given:

" ... d is also the 'greatest common divisor'; that is, all common divisors of a and b are divisors of d."

OK. Fine. Now, consider the reals which are a Euclidean ring by the definition given here (and I've seen similar elsewhere). Every non-zero real is a common divisor of every pair of reals. Furthermore, every non-zero real divides every one of these common divisors, so every common divisor is a greatest common divisor. That is, every non-zero real is a greatest common divisor of every pair of real numbers.

Well, this is not inconsistent, but the term 'greatest common divisor' in this case, is not descriptive to say the least. Furthermore, the description of a number fitting the definition of greatest common divisor as 'the' greatest common divisor is worse. It is, in this case, wrong.

So we have a mess. The difficulty would go away if we could not make fields fit the definition of Euclidean ring.

Here's another one:

"An ideal in D is called 'maximal' if it is not included in any other ideal in D except D itself, ...". OK, at this point, it sounds like D is a maximal ideal, but maybe not, depending on exactly what is meant by "... other ... except..." (although, that D's exclusion is implied by these words is far from clear and one wonders why, if it is intended that D be excluded, it is not made explicit).

However, the definition continues with an alternate wording, "... or in other words, if it has no proper divisors except the unit ideal D." OK, so this recasting excludes D itself if it is taken to mean that it is required that D be an exceptional proper divisor, but again, this is far from clear. But then the implication that the term 'maximal ideal' includes the ring D itself is strengthened in the statement of the theorem which follows immediately: "Any maximal ideal p in D, different from D itself, ...".

Well if D is not supposed to be maximal, why put in the unnecessary words "different from D itself"?

We are given a very ambiguous idea of 'maximal ideal' here. In definitions given by others, 'maximal ideal' unambiguously excludes the ring D, itself, which is better.

These are not the only problems of this sort.

Still, the book is very interesting. As an early translation, these kind of problems are forgiveable. I would hope a modern text on the settled, well understood material covered in van der Waerden's text would not have such problems. Unfortunately, I find that most texts covering well understood, settled material do have such problems, and it is a rare gem that does not.

It takes a lot more time to read a book with difficulties like those described above, time that could be devoted to learning something else.

I wonder whether the original German text had these problems.

A classic of abstract algebra
I think there are few words to say about this book. This is a classic of Abstract Algebra very well known around the world among algebrists. This is a book that everybody interested about Algebra must read.

Classic Book in Algebra
Great Quality. A book that will be in the bibliography of all algebra textbooks. Worth collection.

a classic, for better and for worse
mathematically, this book is first rate. I turn to it when stuck on a passage in hungerford. However, this book shows its age in certain respects - e.g. category theory is completely snubbed - hence the index doesn't square well with a lot of the current standard terminology.

Still, the fact that this book is in its seventh english printing says something about its value. It's like reading Dirac's principles of QM: sure, Griffiths is much easier, and exactly covers the standard undergrad subject matter -- but Dirac does it all in a third of the space, and with such brilliant clarity...

Bottom line: don't buy this as your first algebra book, because it's old-fashioned. The point of reading a textbook is to get you far enough out there that you can read the current literature and be done with textbooks. But, if you already own Dummit and Foote (for undergrad material, lots of hand-holding in tough parts) and Lang or Hungerford (or even Herstein) for the standard first-year grad course perspective, this will round out your algebra library nicely.

this is the classical book
if you want to learn algebra, you need this book at first, necessary thing, and you will feel that is true even after you read the first pages only, that is very nice book, also this can give you imagine about modern algebra, the book constructs whole algebra by strict way, finally, one word about this, if you reference this book in your scientific work or student work, this can be proof of that your job is more strong, and in more higher level, ok, ... Read more

Customer Reviews (1)

A gem of Group Theory! Please reprint it, Springer!
Van der Waerden wrote this book in 1932, about the same epoch of Hermann Weyl's book on group theory, in German. After a staggering gap of 42 (!) years, he prepared this second edition, this time in English. It's probably the cleanest and most rigorous exposition of group theory ever made "for physicists". The quotes were needed because van der Waerden's slant is mainly towards math, as far as mathematical rigour is concerned. But what a clarity! And what a great choice of topics! After a review of basic quantum mechanics in a rather mathematically rigorous and clean style, itstarts with group theory itself. It manages to proof the basic theorems about groups with or without operators, discuss representation theory in the context of observables and symmetries, expose thoroughly Lie groups (translations, rotations and the Lorentz group), spinors and the Dirac equation, and permutations, and introduce briefly molecule spectra, all that in about 200 pages!! No time-wasting like most other books, which seem to "over-wrap" the main core of the subject, making it hard to peel.There is a rather large amount of references to heavy Lie group theory and functionalanalysis' theorems, but here I have to agree with the author that inserting also theirproofs wouldn't add anything profitable, because they would be beyond the book's scope and totally out of context. Even in these exclusions we notice the author's wisdom.

I deeply regret that this masterpiece is out-of-print. I DO insist that Springer should reprint it as soon as possible! ... Read more

Customer Reviews (1)

price out of this world
This is one of the finest books on the history of early astronomy I have ever read.It is highly recommended.Oxford University Press published it years ago in hardcover (the edition I read).I wanted to reacquire it but when I saw the price my jaw dropped !
It covers early egyptian astromony (what little there is of it)and does a masterful job on babylonia .
The price however, prohibits me recommending it to anyone, as it is possible to cover the subject as a much lower cost. ASTRONOMY BEFORE THE TELESCOPE , FROM THE OMENS OF BABYLON and ANCIENT ASTRONOMY AND CELESTIAL DIVINATION are three other books that come to mind, the latter two dealing exclusively with Babylonia.For Egypt there is Lockyer's DAWN OF ASTRONOMY.The list goes on.
Still, it is a first rate study of the subject. ... Read more

Book Description
Der Autor wurde am 2.2.1903 in Amsterdam geboren. Im Jahre 1924 ging er als Student nach Gttingen und wurde dort mit Emmy Noether und der abstrakten Algebra bekannt. Sein Hauptinteresse galt damals vor allem der Begrndung der algebraischen Geometrie mit Hilfe der neuen algebraischen Methoden. Als er im Jahre 1926 als junger Doktor mit einem Rockefeller-Stipendium nach Hamburg kam, hatte er Gelegenheit, eine didaktisch hervorragende Algebra-Vorlesung von Emil Artin zu hren. Die Ausarbeitung, die er von dieser Vorlesung machte, wurde zum Kern des vorliegenden Werkes. Es erschien zuerst 1930 bis 1931 unter dem Titel "Moderne Algebra" in der Sammlung "Grundlehren der mathematischen Wissenschaften". In der Folge wurde das Werk in die englische, russische und chinesische Sprache bersetzt. Im Jahre 1928 wurde der Autor Professor an der Universitt Groningen. Seit 1951 lebte und arbeitete er bis zu seiner Emeritierung in Zrich als Professor an der dortigen Universitt. Heute lebt er in Zrich. ... Read more

Customer Reviews (1)

Make no mistake, this is a math book -
A comparable book might be an Introduction to Algebra book.Complete with descriptions and examples of usage (and of course history).Ifyou're interested in knowing more about Babylonian sexagesimal notation, Egyptian fractions, poetic numbers, Pythagoras, Plato or Hellenistic science interest you then this is a good source for the material and thankfully it has been translated into English.While I believe the translation was accurate, this can be a sleeper if you're not fond of numbers or their manipulation. ... Read more