Algebra Texts - Hungerford vs. Lang

[sparkster]

Springer is having their annual Yellow Book sale and I was going to pick up an algebra text to supplement Dummitt and Foote. I'm not really satisfied with D&F--to me, the tone is too conversational and I have trouble finding the information I want from their long paragraphs of discussion.

I've had people recommend Lang and Hungerford, but I've never given them more than a cursory glance. Does anyone here prefer one over the other?

Also, in the catalog there's a book by Lorentz that I've never heard of. Anyone know anything about it?

 

[DeadWolfe]

Hungerford, by miles.

 

[sparkster]

Hungerford, by miles.

Any particular reason?

 

[mathwonk]

well hungerford is on a much lower level than lang so they are not really comparable.

hungerford is easier to understand but lang has many more advanced and deeper topics. so i have both. also lang is a much more famous and accomplished researcher, to the best of my knowledge, which always means something to me.

hungerfords book was written to provide a basic source that the average grad student could read. langs was written to provide future researchers with a reference for most of the topics they would eventually need to know about.

i myself found in my beginning research career that even lang did not have everything i needed, only just the bare minimum beginnings of what i needed.

so hungerford is more of a textbook for basic stuff and lang more of a baby research reference. one tries to address the beginning grad student on his level, and the other tries to raise that level to nearer what it needs to be.

hungerford has more standard type problems. problems in lang, which tend to be made fun of, like "take any book on homologiccal algebra and prove all the theorems in that book without looking the proofs given in that book", are actually excellent advice..

i.e. the emphasis in not on actually succeeding in doing this, but at least on trying. that is actually a very good exercise. homological algebra is a subject in which the proofs are more or less all of certain predictable type. practice in that kind of computation is useful exercise.besides, trying to give the proofs of any theorem without reading the proof first, is a habit every student should acquire, in every book, and even every paper. that's how you learn to be a mathematician as opposed to remaining a student.

so lang is teaching you as if you want to become a mathematician, and hungerford is teaching you as if you are a beginning student.

there is a huge difference.

so if you are a struggling student you will probably appreciate hungerfords careful, if pedestrian, proofs. if you want to become amathematician, at some point you need to acquire langs point of view.

I considered lang indispensable myself even as a young student. does this help?

 

[mathwonk]

by the way i also find DF rather annoying and wordy. I chose it for my grad class and am somewhat frustrated by that now.

I would put DF noticeably below Hungerford in sophistication and depth.

I.e. what used to be considered a basic book for average grad students, namely hungerford, has now become considered a more difficult book, replaced for average students by DF.

Lang on the other hand is almost never considered as a text anymore, as if it were some otherworldly and unrealistic book.

I think, recalling using them both now, that one needs both lang and hungerford. lang has the right point of view, and the right topics, and hungerford has the examples that flesh out the basic topics.

I thought DF looked appealing at first review, but now actually using it, I find it so verbose as to obscure the topics rather than illmuminate them.

 

[sparkster]

Thanks for the advice, it really is helpful. I think Lang is more of what I'm looking for, although I would probably benefit from another beginning treatment of Galois theory. I still don't feel comfortable with it.

So I'll probably buy Lang and see if the library has Hungerford for that section.

 

[mathwonk]

if you look on my webpage you will find a free set of notes that do galois theory in detail, math 843-844-845.

i had always wanted to elarn it, so made sure i did it first that year, and worked out everything in full.

i also ahd alight load tht eyar, just the one grd cousre so i wrote up everything after class and then rewrote it as students gave feedback, i.e. "huh? meant rewrite.

 

[mathwonk]

now i am covering groups in ym clas and I find the sections on groups in DF quite good. I conjectured they were group theorists aND LOOKED up the webpage for vermont.

indeed foote is a group theorist. so most everyone haS HIS SPECIALTY.

in my book you will probably notice more uniformity as I am nota specialist in anything. so it should be uniformly naive.