Review: Abstract Algebra, 2nd Edition

Like most Adequacy readers, I am very good at higher mathematics. In high school, I placed near the top of my Algebra II class, and aced the Math portion of the SAT with a 590. As my children are currently working their way through middle school, I felt obligated to renew my skills in order to help them with their homework. But after slogging through Dummit and Foote's turgid tome, I can only say that it is the worst mathematics text I have ever had the misfortune to encounter.

The first flaw a reader will note is the incredible rate at which the material is presented. Section 0.1 breezes through difficult concepts like functions, sets, and complex numbers. By Chapter 1, my head was spinning after reading statements like, "For n in Z+, Z/nZ is an abelian group under the operation + of addition of residue classes as described in Chapter 0," and, "A subset S of elements of a group G with the property that every element of G can be written as a (finite) product of elements of S and their inverses is called a set of generators of G."

As we see from these excerpts from the text, Dummit and Foote are disciples of "new math," a doctrine discredited in the 70's. Too often, strange symbols and jargon take the place of clear English prose. Extraneous concepts like "sets"--much less "finite nilpotent groups" or "invariant factor decompositions" or "symmetric multilinear maps"--are merely obstacles to a student's understanding of algebra. Sadly, the authors, holed up in their ivory towers, have not yet learned these vital educational lessons.

Yet for all the apparent erudition of the authors, the text is full of obvious errors. For example, on page 44, the authors assert that z*a = z + a, an obvious error. On page 97, we find the ludicrous assertion that a^p = a, clearly flase unless p = 1. And on page 329, the text asserts that r(x + N) = rx + N, an obvious typo.

That the authors could publish such a sloppy text and remain employed at the University of Vermont speaks volumes about the evils of tenure.

I can only recommend this text to those already secure in their knowledge of Algebra who might derive amusement from the frequent missteps of the authors. And even then, with a $100 price tag, it can hardly be considered worth the expense.

I fear for the education of the next generation when prominent publishers push "new math" on hapless educators. Using this text to teach learn Algebra from this text will alienate students from math and science, driving America further behind the rest of the world in education. I can only hope that our school boards will reject this attempt to corrupt high school curricula and get back to teaching the basics.

Rating: 0 of 5 stars

	Oooh... that's pretty good (5.00 / 1) (#1)
	by Anonymous Reader on Sun Oct 14th, 2001 at 05:11:55 PM PST

	Have you tried posting it to sci.math?

	Perhaps you are right (5.00 / 1) (#7)
	by moriveth on Sun Oct 14th, 2001 at 07:18:51 PM PST

	I am sure that sci.math would be interested in my perspective. Perhaps misc.education.home-school.christian would appreciate a crossposted warning on this horrible text.

	Alt.syntax.tactical (0.00 / 1) (#8)
	by egg troll on Sun Oct 14th, 2001 at 08:02:27 PM PST

	Anyone know if this group is still active? Posting for the love of the baby Jesus....

	They were snuh-ing the dickens out of (none / 0) (#17)
	by Adam Rightmann on Mon Oct 15th, 2001 at 05:47:11 AM PST

	rec.music.gdead a few months ago. A. Rightmann

	My thanks! (none / 0) (#22)
	by moriveth on Mon Oct 15th, 2001 at 07:03:15 PM PST

	Anonymous Reader, you did not steer me wrong. Thanks to your astute guidance, sci.math is now infinitely better informed about proper Algebra education. I can tell that, apart from the incomprehensible rantings of a few intellectual elitists, my review was greatly appreciated.

	Don't mention it. (none / 0) (#26)
	by Anonymous Reader on Mon Oct 15th, 2001 at 10:18:13 PM PST

	And to top it off, you've done a great step in bringing the mathematical elitists and home-schoolers closer together. I find it highly entertaining that some of the sci.math people are actually trying to convince home-schooling parents to use Lang instead of Saxon. I'd love to hear how that turns out...

	very funny. (5.00 / 1) (#2)
	by osm on Sun Oct 14th, 2001 at 05:27:38 PM PST

	Warren (5.00 / 1) (#30)
	by Craig McPherson on Tue Oct 16th, 2001 at 02:05:42 AM PST

	Hey man, Your e-mail address in your profile is backwards. Just thought I'd let you know. Craig -- If you want to know why Lunix is so screwed up, just take a look at the people who use it. Idiocy.

	Upon reading this review, (5.00 / 5) (#3)
	by RobotSlave on Sun Oct 14th, 2001 at 05:40:05 PM PST

	I went to my shelf to take down a tome by the same title (though by a different author). A quick review of the contents revealed a tangled mass of erroneous nonsense much like that which you found in the Dummit & Foote volume. But that is not what I am here to write about today. Upon opening the book, an envelope postmarked 10 October of many years ago fell out, bearing the return address of perhaps the most promising potential spouse I have ever encountered. Inside was a single sheet of stationery, bearing a single word. Neither the fact that this former potential spouse is now married to another person, and beset with offspring, nor the fact that a glacial shift has transformed the former Potential Spouse into a Dear Old Friend, has done anything to mitigate the burbling wash of wistful melancholia that flows now over my dessicated heart. © 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

	Huh? (4.00 / 2) (#4)
	by Anonymous Reader on Sun Oct 14th, 2001 at 06:16:31 PM PST

	What was the word?

	Come here, lad, and sit on Uncle Robot's knee, (5.00 / 4) (#6)
	by RobotSlave on Sun Oct 14th, 2001 at 07:04:07 PM PST

	and we will have a little lesson on the very common literary or poetic technique known as "deliberate omission." Now then. The first part of this common effect is to leave a significant detail out of an account or description, and to simultaneously draw attention to its absence. You seem to have picked up on that part. The second part requires either imagination or analytical effort on the part of the reader. The idea, you see, is either to have the reader imagine something of sufficient magnitude to fill the gap (and the author may or may not provide hints as to the nature of the omission), or to cause the reader to realize and ponder the insignificance of the omitted detail relative to its effect on the salient character or characters. I think that's the part that you're having trouble with. This stuff is actually quite easy to pick up, once you've been pointed in the right direction. Your local librarian can probably be quite helpful. Just ask him or her for "some literature or poetry, please." That ought to get you started. © 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

	I believe I understand completely now. (5.00 / 2) (#9)
	by Anonymous Reader on Sun Oct 14th, 2001 at 09:08:25 PM PST

	Thanks for enlightening me. It makes a lot of sense now. There's just one thing I still don't get. WHAT WAS THE WORD??

	Okay, okay, I get it. (4.66 / 3) (#13)
	by Anonymous Reader on Sun Oct 14th, 2001 at 11:42:55 PM PST

	I think I understand now. But, just for the heck of it, please fill in the blank in the following statement: "The word is: ___________." Please fill in the blank. Thank you.

	Perhaps it was 'Sussudio' (nt) (5.00 / 1) (#14)
	by elenchos on Mon Oct 15th, 2001 at 01:09:20 AM PST

	I do, I do, I do --Bikini Kill

	I am not going to tell you. (5.00 / 3) (#10)
	by RobotSlave on Sun Oct 14th, 2001 at 09:26:14 PM PST

	Maybe you shouldn't go to the library, after all. The high level of ambiguity in there could trigger any number of nervous disorders in persons of a particularly rigid mindset. © 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

	No, no, no. (5.00 / 3) (#15)
	by RobotSlave on Mon Oct 15th, 2001 at 02:28:33 AM PST

	See, when one attempts this technique of "deliberate omission," it is very, very important to get the "omission" part right. If one simply withholds a bit of information, but then reveals it later, then what we have is, at best, "forshadowing." No omission involved at all, at the end of the day. See? See? Perhaps what you are really looking for here is more along the lines of "not saying something, and then holding out amidst loud protest, like a cock tease, but then eventually giving up the goods, as if the situation were no more than a satisfactorily formulaic porno vid." Believe me, I understand the appeal of that approach, but it just isn't what's happening here. I am terribly sorry for any confusion that this might have caused-- in the future, I will try to affix a footnote, when appropriate, to alert the reader to the deployment of any stylistic conceit that might not be appropriate to viewers of substandard literary exposure. Again, you have my sincere apologies. © 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

	I know what game you're trying to play. (5.00 / 4) (#16)
	by Anonymous Reader on Mon Oct 15th, 2001 at 03:44:53 AM PST

	I figured out what the word was several hours ago, through an intensive process of research and deduction. I know what the word. I'm thinking it's you who doesn't know what the word is, and is trying to trick me into telling you the word. I'm too clever for it. You don't know what the word is, but you knew I'd have the deductive power to find out, and now you're trying to trick me into telling you the word, by claiming that you know the word and I don't, when in fact I know the word and you don't. It's classic reverse psychology, propped up by senseless erudition about fabricated "literary devices." Now, this attack on your character may be unfounded. You may know the word after all, which would mean that both of us know it. But how can I believe that? You've already violated my trust once, so you're going to have to prove to me that you know the word by telling me the word. Seeing as I know the word already, I'll know straight-away if you're right. For several posts now, you've been using clever reverse psychology to try to trick me into telling you the word, but it's not going to happen. You're going to have to step up and prove that you know the word.

	Sorry, I'm too smart to fall for it. (5.00 / 1) (#20)
	by Anonymous Reader on Mon Oct 15th, 2001 at 05:00:38 PM PST

	You've been trying to trick me into telling you by claiming that YOU know the word, when in fact, you don't. Unless, of course, you DO know the word -- in which case, PROVE IT, so I won't have to think less of you.

	Huh? (5.00 / 1) (#21)
	by RobotSlave on Mon Oct 15th, 2001 at 05:29:31 PM PST

	What was the word? © 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

	No, no, no. (5.00 / 1) (#23)
	by Anonymous Reader on Mon Oct 15th, 2001 at 07:46:26 PM PST

	I'm NOT going to tell you. Because you USED me and you VIOLATED me. My FEELINGS are HURT and VIOLATED. I am both ALARMED and SHOCKED.

	Let us end this farce (apologies to RobotSlave) (5.00 / 1) (#24)
	by moriveth on Mon Oct 15th, 2001 at 08:01:29 PM PST

	The word was obviously "homomorphism." A sad tale indeed.

	Heh-heh, heh-heh. (5.00 / 1) (#25)
	by Anonymous Reader on Mon Oct 15th, 2001 at 10:10:45 PM PST

	You said "homomorphism". Heh-heh. Heh-heh. Homomorphism. Heh-heh. I have a bunghole. Heh-heh.

	Please help me. (none / 0) (#28)
	by RobotSlave on Tue Oct 16th, 2001 at 12:31:36 AM PST

	I would like to rate your comment, but I do not know if I ought to give it a high rating for clever maths humour, or to give it a low rating for math humor. © 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

	My advice (none / 0) (#29)
	by moriveth on Tue Oct 16th, 2001 at 12:49:02 AM PST

	Better stick with the low rating, lest I be tempted to continue in a similar vein. I also know dozens of viola jokes.

	Oooh! (none / 0) (#32)
	by RobotSlave on Tue Oct 16th, 2001 at 09:14:35 AM PST

	Viola jokes! Viola jokes! Tell me some viola jokes! Please! © 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

	Viola jokes...comin' right up (none / 0) (#33)
	by moriveth on Tue Oct 16th, 2001 at 10:04:16 AM PST

	Enjoy! Why do Violists make effective rapists? It's hard to fight back when you've got your hands over your ears. Why do Violists get antsy when they see the Kama Sutra? They can't handle any subject reference to "more than one position". What is the longest Viola joke? Harold in Italy What's the difference between a Viola lying in the road and a used Tampax lying in the road? Eventually someone will pick up the Tampax. What's the difference between a dead Viola player lying in the road and a dead snake lying in the road? Skid marks in front of the snake. What's the definition of a minor 2nd? Two Viola players playing in unison.

	More! More! (none / 0) (#35)
	by RobotSlave on Tue Oct 16th, 2001 at 11:37:30 AM PST

	I almost didn't get the Harold in Italy joke, because I left my collection of Berlioz under the passenger seat of an El Camino ten years ago, and never bothered to replace most of it. Keep it coming. I like doing stuff like this until I black out. © 2002, RobotSlave. You may not reproduce this material, in whole or in part, without written permission of the owner.

	I bet it was 'rosebud'! (nt) (5.00 / 5) (#11)
	by elenchos on Sun Oct 14th, 2001 at 10:16:34 PM PST

	I do, I do, I do --Bikini Kill

	Good review (5.00 / 2) (#5)
	by Logical Analysis on Sun Oct 14th, 2001 at 06:41:52 PM PST

	Personally I have extreme distrust of any book with a "Chapter 0." Any time you see that you know it is written by someone completely out of touch with reality. You know, like a geek, but not just an ordinary geek, but a geek who watches stuff like Japanese Cartoon Porn and Xena Warrior Princess. Of the few books I own which do have a Chapter 0, they are all of inferior quality and content. I suggest avoiding "zeroism" at all costs. As for the University of Vermont, it is an unfortunate truth that the fair state of Vermont has become infested with leftist agitators of the worst sort. The muddled thinking which you described in this book can only be the result of socialist influence. It is good to see that debunking of obscure left-wing concepts like "new math" is alive and well here on Adequacy.

	You're wrong (3.00 / 2) (#12)
	by Anonymous Reader on Sun Oct 14th, 2001 at 10:53:40 PM PST

	because every claim you made about errors (typographical or otherwise) in this review were in fact NOT typographical. This is a text on ABSTRACT ALGEBRA, considered an extremely difficult subject by most professors of mathematics. The pioneers in the field are heavy-hitters like Lagrange, Abel, Galois and Hilbert, and mathematics students are usually introduced to the topic after taking a few middle level courses on modern algebra. 1. The claim that the authors are followers of 'New Math' is fallacious. The terms the authors used are actually over 100 years old, and are quite necessary to teach abstract algebra. Indeed, without a decent understanding of set theory, you are unlikely to get very far in abstract algebra. 2. The errors you claim to be typographical are not. a)Firstly, a + p = a*p is quite possible, depending on the context in abstract algebra. b) a^p=a is true for any value p that is equal to the order of the cyclic group that contains the element a. c) r(x+N)=rx + N is perfectly valid, since any multiple of an ideal N is equal to N. Do you REALLY want me to explain what an ideal is? Abstract algebra is nothing at all like the classical algebra we are all taught in high school. The text you reviewed may be just fine for a typical third or fourth year mathematics student who is already quite familiar with set theory, functions and complext numbers (which are dead easy). In order to help your children with algebra, I suggest asking their math teacher about what sort of text you should be studying. Abstract algebra is NOT taught at the high school level!

	Heavy Hitters?? (none / 0) (#27)
	by Craig McPherson on Mon Oct 15th, 2001 at 11:37:57 PM PST

	"The pioneers in the field are heavy-hitters like Lagrange, Abel, Galois and Hilbert." Oh, really? If they're such "heavy-hitters," then why haven't I heard of ANY of them. Never heard of Lagrange. Never heard of Abel. Never heard of Galois. Never heard of Hilbert. Now, this could mean one of two things. Either I know nothing about the history of mathematics, or YOU MADE THEM ALL UP. I imagine you thought, "Haw haw, these people sound gullbile, so I'm going to pretend to be a math expert and make up some names of fake mathematicians and BS like that, and see if they fall for it." Sorry, that's called "trolling." Making something up and then acting as a "false authority" in order to convince gullible people of your dubious facts is one of the lowest passtimes I could imagine. What kind of person would intentionally write something containing lies and intentional, gross factual errors? A sad, lonely person crying out for help. I think you should grow up. -- If you want to know why Lunix is so screwed up, just take a look at the people who use it. Idiocy.

	Heavy Hitters (none / 0) (#31)
	by Anonymous Reader on Tue Oct 16th, 2001 at 08:58:02 AM PST

	Joseph Louis Lagrange: 1736-1813 Frederik the Great of Prussia considered him the greatest mathematician of Europe. Niels Henrik Abel: 1802-1829: Considered Norway's greatest (probably only famous) mathematician. If you do algebra, abelian groups are named after him. Evarist Galois: 1811-1832. Died in a pistol duel. Galois theory is advanced group theory. David Hilbert: 1862-1943. Considered the most important pure mathematician in the 20th Century. Oh BooHoo. Looks like you know nothing about the history of mathematics. I suggest never opening your mouth again, due to your propensity to spew excrement when you speak. thank you, A sad lonely person crying out for help, who studies the history of mathematics. ps. Actually I have found that most people here are gullible and uninformed. But then, what else is new?

	We may be gullible, (5.00 / 1) (#34)
	by Hammurabi on Tue Oct 16th, 2001 at 11:12:03 AM PST

	But you are the one who is uninformed. For you to be so deluded as to believe that the sort of man who engages in pistol duels would have anything to offer intellectuals is sad indeed. And Lagrange?? You base your judgements of mathematicians on those of Frederick the Great, a war-obssessed monarch whose name you can't spell?? Amazing. And I won't even take up the issue of the mental capabilities of Norwegians. I fail to believe that these men you mention could possibly have had any useful impact on mathematics. In the extensive amount of mathematical knowledge I acquired for my degree in finance, I have never heard of an 'Abelian Group'. Undoubtedly it is another part of 'Pure Mathematics', That useless branch of study that many academics turn to when they find they are ill-prepared to survive in real world subjects, and must pick something which allows them to spend their time poring over obscure symbols that have no bearing on reality whatsoever. Too weak to deal with the uncertainty that is real life, they must study a field with clearly defined axioms so that they can feel 'secure' in their 'knowledge'. Such pursuits are vain and self-masturbatory, and I find it repulsive that you would consider any of it's practitioners to be a 'heavy-hitter' in mathematics. Only the most dangerous and hardened of criminals attempts to blame the law when he is the one who broke it.

	Dummyfoot (none / 0) (#19)
	by slaytanic killer on Mon Oct 15th, 2001 at 11:59:59 AM PST

	Funny. That's a book I really want to grab, but it's a real pain to get where I am. Well, I'm sure you can find even more enjoyable errata here. You can even set up a "mirror" site, so you can get rid of all that pesky context. Dummit and Foote are disciples of "new math," a doctrine discredited in the 70's. Too often, strange symbols and jargon take the place of clear English prose. I know! I was just leafing through a copy of "Perl by Example," and the whole damn book was riddled with code! WTF?!