Could you say just which book this is? (I can't recall if I've asked before...or if someone else asked before.) Could you give a list of the books you remember and your ratings of them? I'm fairly sure now, that even if I don't make it career, I'm going to be going through the same stuff you are now.
Fraleigh's Introduction to Abstract Algebra (7th edition), or whatever it's called. I can't actually remember. In any case, it's the Fraleigh book.
Algebra (Bourbaki) - This is a really hard collection. I haven't used it much, but I've heard some complaints about "Bourbakification," which is the tendency to prove things by citing a bunch of lemmas. Easier to use if you set out to prove every statement yourself, and then look at the lemmas it references only if you've hit a brick wall. In any case, it's nice about noting places where the student might trip up and providing all sorts of rare types of algebraic objects. It's neat, to say the least. Only use for a second book.
Algebra (Lang) - extremely slick. Unless you already have serious proof skills, it will be impossible to even read. Notorious for its dryness and terse exposition, but I like it quite a bit. It's clever and has really good typesetting. If you have never heard the phrase "proof by abstract nonsense," this is the place to fix that. Only use for a second book. I used it as one of my first serious approaches, having only attempted the first couple of chapters of undergrad Lang, and had no idea why towers/any of the other things he was obsessing over were so important.
Undergraduate Algebra (Lang) - Pretty good. Not great, though. If you're going to use a Lang book, I'd go with big Lang rather than little Lang. On the other hand, it's good to at least take a look in here for some of the less-covered topics. Takes a straight-up group theory approach, rather than the symmetry approach. Many redundant exercises.
Algebra (Artin) - Okay. I have a desperate hatred of linear algebra, and in my opinion Artin introduces it far too early (first section). It's a cute text, but the exercises are way too easy and will just waste your time, rather than teaching you anything. Might be good for a very first introduction to mathematics, but in general it isn't going to enthrall you.
Survey/Introduction to Algebra (Birkhoff and MacLane) - A classical exposition. Initial emphasis is on construction of various sets of numbers from axioms--i.e., the first 6 chapters are on that. I don't recommend using it alone for this reason, especially as it starts with rings rather than groups. Though rings may be more common in everyday life, I find groups a lot easier to understand. Symmetry covered only briefly. I don't recommend this one.
Algebra (Birkhoff and MacLane) - The better version of the above book. Starts with grounding the reader solidly in functions and morphisms before moving on to the aforementioned constructions, and then quickly into other topics. Written by the inventor of category theory and therefore a very, very solid introduction. Excellent exercises for the intermediate student, though the advanced undergrad will be mostly bored. Can't recommend this book highly enough. Over and over again, I was shocked by its elegance and clarity.
Category Theory for the Working Mathematician (MacLane) - Used this only briefly. You need more mathematical background than I had to really profit from it, but it will give you some useful vocabulary and a new perspective to fit things into.
A Course in Arithmetic (Serre) - Haven't used this. Very, very advanced, and I recommend the author highly--though he's even more terse than Lang, so watch out!
Linear Representations of Finite Groups (Serre) - Used this only briefly. Only attempt after you've worked through a couple of other books. Solid algebraic background absolutely necessary. It's beautiful, though.
Presentations of Groups (Johnson) - Another book I used only briefly. It needed a lot more category theory than I had, so I'd recommend working through one of MacLane's things first. Development of free groups, which I personally find interesting... but again, I didn't have the necessary category theory or background to put this into perspective.
Contemporary Abstract Algebra (Gallian) - Out of print. Unfortunately, I both own a copy and hate my copy. Good for someone who needs a lot of examples and trivial exercises. I am not this person.
Algebra (Dummit and Foote) - I only briefly looked into this, but it seems like the best elementary text I've found thus far. Good exposition, nice depth, no settling on the author's favorite lens for page after page and leaving a disinterested reader far behind. Very clear and I think I remember reasonable exercises.
Survey of Modern Algebra (Herstein) - Haven't used it, but it's a classic. I'd probably recommend a combo of MacLane and Lang over this one.
Notes on Algebra (Wodzicki) - this is where I learned most of my basic algebra from. Unfortunately, I don't think it even covers cyclic groups or a number of other important subjects. If you can find this online (it was produced by a professor who periodically takes his things down), it's one of the best sources I've ever seen on which questions one should ask. Good mathematical taste, but needs a lot of other supporting works for it to make sense. You should also know that the professor in question believes in sketching an introduction to topics which he doesn't go back later to explain, simply to pique interest. Really, really good source, but do not attempt without some other things to fill in the holes (you definitely won't be getting the complete picture that most other undergraduates have in their courses). Also, I know a number of students who hate this guy's work like no other, so be forewarned. The exercises are completely trivial once you've achieved a certain level of cleverness, but before that you'll have a lot of trouble with them. They all require different approaches. Once you can do them, though, you'll probably be at an entry graduate level of problem-solving--and they're the fastest thing I've ever seen to get you there.
Some of the titles may be wrong, but the authors are not. Or at least they're pretty much right, even if I spelled them wrong. If you want the full list of textbooks I've ever used, you're going to have to wait a while. It's a really long list.
Fraleigh's book has so many errors that the (substitute) professor had us find three major theoretical gaps in the preface.
In other news, I was called a troll for the first time today and seem to have some sort of illness. Caught it from my roommate, who spent yesterday sick. This gives me time to rest, though, which I really needed. It was also good to get more sleep than I usually do, even if I'm very tired.
And, it turns out that turning sick was what gave me moodswings, so now I feel settled out again and pretty good.
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Topic: Things that made you sad today thread. (Read 9790845 times)