Also, this is funny: the author in a preface-type thing says that she wrote the book for laymen. BuGreat.
Things get very, very depressing at the end.
Also, this is funny: the author in a preface-type thing says that she wrote the book for laymen. But the publisher, Springer-Verlag, promoted the book only to its existing audience, and that as a result it was only read by mathematicians and scientists. She expressed the hope that mathematicians will continue to read Hilbert, but "that it will also come at last into the hands of the mathematically interested laymen for whom I originally wrote it."
Well, the back cover of this edition says that it "makes this book available to new generations of mathematicians who know the name Hilbert."
This book was assigned summer reading when I was in high school. I was in the IB program, and we were going to discuss this book extensively in my socThis book was assigned summer reading when I was in high school. I was in the IB program, and we were going to discuss this book extensively in my social studies class. I hated it. It seemed so tedious and just packed through with boring facts. This is what happened to work of art A; this is what happened to work of art B; this is what happened to work of art C... On and on. So I didn't read much of it. I sort of skimmed. Really it probably couldn't even be called skimming. I was really afraid I was going to have a serious problem in class.
I was relieved to find when school started that NONE of the other students had read it either. The teacher mentioned the book a couple of times, but we never really discussed it and after the first week he never brought it up again. I don't know if he realized that no one had read it and gave up or what.
I wonder if I would have a different opinion now, a little more mature and knowing/caring a little more about both art and history. We will probably never know because I am still too traumatized from my earlier experience to give it another shot. ...more
In the preface to my edition, Hofstadter complains that people have frequently misinterpreted the point of his book, and he outlines what he was gettiIn the preface to my edition, Hofstadter complains that people have frequently misinterpreted the point of his book, and he outlines what he was getting at.
Well, halfway through the book, I can see why people were confused. It just rambles and goes on and on about different topics and makes little effort to tell the reader where it's headed. The Bach stuff, Escher, the dialogs... to me it has little connection to what seem to be the main points. It's just tedious.
So I quit. I don't abandon books very often. But I'm abandoning this one.
The good thing about this book, I suppose, is that it has gotten some people without any real mathematics background (although probably not people with a strong aversion to mathematics) interested in some real math. ...more
Another Goodreads reviewer, Choupette, has posted a quote from this book. The portion "Now that you've been warned, you needn't panic at the sight ofAnother Goodreads reviewer, Choupette, has posted a quote from this book. The portion "Now that you've been warned, you needn't panic at the sight of the mathematical notation that will be introduced." is the most relevant to me. Why would people who panic at new math notation ever be taking a class out of this book? It's just so condescending and ridiculous.
And it's SO VERBOSE. No textbook needs to be 1200 pages.
This book is very clearly written and I like Kaplansky's style.
On the other hand, it provides no motivation at all and no connection to geometric ideaThis book is very clearly written and I like Kaplansky's style.
On the other hand, it provides no motivation at all and no connection to geometric ideas. It also gives hardly a single example. This is a perspective that is still very strange to me: why would someone write a book about rings without actually mentioning any rings? Surely one will fairly often need to give a counterexample to an obvious conjecture, or want to illustrate the application of a theorem in a concrete case, or what have you... but not here. ...more
I don't recommend this. The problems just aren't closely aligned with the actual test. Some of them are way too difficult or time consuming. Some of tI don't recommend this. The problems just aren't closely aligned with the actual test. Some of them are way too difficult or time consuming. Some of them are just not relevant, on topics that would never appear on the actual test, like game theory. ...more
Eh. It's OK. Several ridiculous errors in equations and whatnot that have apparently been known about but not corrected since the first edition. The pEh. It's OK. Several ridiculous errors in equations and whatnot that have apparently been known about but not corrected since the first edition. The problems aren't completely like those of the actual tests, but they are OK. ...more
I liked the clarity of this translation; other translations I looked at for some reason use archaic language and assorted silliness.
It seems there arI liked the clarity of this translation; other translations I looked at for some reason use archaic language and assorted silliness.
It seems there are some textual/historical issues that could be very interesting, because you've got the text itself, which is sometimes obscure, and then a significant tradition about the text, giving context and meaning.
I found the thing pretty repetitive, to the point of really boring me at times. How many times do we have to discuss the rewards of the believers and the punishment of the unbelievers? But, I guess, as the translator says, the Qur'an is not normally read straight through like a novel, so perhaps in other situations it's not so painful. ...more
I'm a math major in school. I'll be applying to graduate school for math in a few months. I'm taking the General GRE in a couple weeks and the Math SuI'm a math major in school. I'll be applying to graduate school for math in a few months. I'm taking the General GRE in a couple weeks and the Math Subject GRE not long after. So, to help me prepare I bought a few books on... arithmetic?
Yes. See, I have a problem. I screw up arithmetic constantly. I have actually written the following on a Calculus test: "6 + 3 = 8." Usually I'm not quite that bad, but when adding/multiplying large numbers, chances are extremely high I will make a mistake.
So I thought maybe there were other algorithms out there that could improve my accuracy here, and I ordered some books. Unfortunately, I don't believe this system is helpful. It mostly consists of reworkings of the standard multiplication/division algorithms. They are described in such a way that it may not be immediately apparent that that's what they are. For instance, instead of memorizing, say, the times table for 6, you memorize a rule for how to multiply a digit by 6. This really doesn't buy you anything.
The methods usually involve less writing down intermediate steps, but all the same calculations are there.
One very good thing mentioned in this book is the error checking method "casting out nines," here called the "digit sum method." However, this is not original to the system; it has been around for hundreds of years (as the book admits). Plus, unfortunately, the book does not make clear that it is possible for a calculation to pass this error check and still be incorrect; that is, when the check says you're wrong, you're wrong, but when it says you're right, you're only *probably* right. In fact, the book strongly implies the contrary.
The foreword claims that students using this system faced off in a test of arithmetic against "mechanical brains" (did people really call computers that??) and the students won. Hmm. Well, the mechanical brain sitting on my desk right now can do millions of arithmetic operations per second. This kind of statement may have *almost* made sense in 1960, but today...
Lastly, I have to complain about one more thing. This book strongly encourages a misconception that some people have about mathematics. I'm referring to the idea that arithmetic IS mathematics, and that being good at mathematics means being good at arithmetic. Arithmetic is to mathematics as spelling is to poetry. ...more
This is fine, for a terse and unmotivated exposition of Galois Theory. But then, what's the point? If you like your Galois Theory terse and unmotivateThis is fine, for a terse and unmotivated exposition of Galois Theory. But then, what's the point? If you like your Galois Theory terse and unmotivated, buy Grove's Algebra for half the price of this book, and have at Chapter 3, plus get a complete graduate course in algebra with the deal. I think the only thing you will be missing would be the cubic and quartic formulas. Just grab those online somewhere; you can actually find some really cool derivations of them. ...more
This book is OK as far as presenting abstract algebra in the usual way to undergrads. Competent explanations of the basics of groups, rings, and fieldThis book is OK as far as presenting abstract algebra in the usual way to undergrads. Competent explanations of the basics of groups, rings, and fields. Numerous easy exercises, which is fine, although it might be nice if there were more challenging ones too.
There are two problems.
The first problem is, I don't believe in the purely abstract approach to teaching a first course in algebra which this book uses. This book doesn't give you any real idea what the heck algebra is good for and doesn't provide any real connections to anything else. The attempts to liven things up with silly quotes and bios give the book a condescending middle school type feel. I would rather the author attract readers' interest by showing them the power of the algebraic structures discussed. Groups and rings are extremely powerful concepts, but to read this book you would think they are just a game where you write down some axioms and see what random statements you can prove. (None of this is unique to this book. It seems students are simply not expected to see algebra put to any use until grad school, if at all.)
The second problem is, this book sells for $170. There is no excuse for this. It is simply disgusting. No one should buy this book or require it for a course at such an exorbitant price. It doesn't do your laundry or cook you breakfast. A $12 Dover book would do fine. ...more
See my critical review of Gallian's algebra book. It all pretty much applies here too, but possibly even more so.
My impression (possibly wrong) is thSee my critical review of Gallian's algebra book. It all pretty much applies here too, but possibly even more so.
My impression (possibly wrong) is that this book is intended to present abstract algebra to weaker students, or to students at an earlier stage than would normally see this material. Fine. But if, as seems to be the case, the students never see how the material can be applied to an interesting problem, what was the point?
In any case, no one should pay the $187 this book sells for. ...more