Is it bad to keep aside Lang's Algebra in graduate school?

Solution 1:

You have to read whatever you are comfortable reading. There is no reason to torture yourself.

At the same time, there is also no reasonable reason for you to put yourself in a position where you eliminate one of the possible sources of information about what you want to know! (Lang's book is not only known for being difficult: it is also known for being an amazingly good source of information.)

As you go along, you will find yourself in the situation where you want to know something and you have to know it, and yet the only source available is quite not what you would have hoped it to be —this will happen with papers, for example. What are you going to do? Quit the subject because you do not like the source? Wait for somone to provide another source (as this may well never happen, this may have the same consequence as quitting the subject!)? You will have to make do with what you have. Yes: that takes some training... and you might take the opportunity of this course to train yourself also in that respect.

Solution 2:

I really disliked Lang's book, at first. His depth is comprehensive, but he jumps into most topics at the maximum level of complication and detail, which is extremely jarring for someone just learning the material. On top of that, the topics are sometimes somewhat out of order, with examples from one chapter coming from material from a later chapter (though this can be said of Dummit and Foote as well). It can be very frustrating trying to learn anything from this book if you've never seen it before.

With this said, when trying to study the same topics for my course from other books, I found myself eventually coming back to Lang. Other sources proved to be good introductions to a subject, but few approached the depth that Lang eventually got to. I eventually came to really appreciate the vast array of examples Lang included, even though some of them were above my head at first. You could do what I did, too: read other books when first learning a topic, get a basic grasp of it, then transition to Lang to finish. However, it can be hard to keep terminology straight during these transitions, so the best approach may be to just work through Lang slowly, realizing that you won't be able to understand right away and that that's okay.

Anyway, if you do choose to replace Lang with something else, it shouldn't be Dummit and Foote. Dummit and Foote is a great book, and you'd do well to read it concurrently, but it's a level below Lang. Many of the topics you listed will only be touched upon briefly, and some not at all. A common alternative is Hungeford, which achieves a comparable level of detail. Personally, I am partial to Isaacs. (Admittedly this probably stems from already being a big fan of his finite group theory book; still, I dig his writing style.) There are a couple topics (such as Hilbert's Theorem 90) which are not treated quite as thoroughly in Isaacs as they are in Lang, but for the most part, it is on the same level, and I find Isaacs exposition to be very clear and well-motivated.

Solution 3:

First of all, congratulations on entering the PhD program. The particular choice of book really doesn't matter that much; there certainly isn't a single, canonical source for any of the items on the syllabus you posted. Figure out the way you learn best, including what kinds of textbooks you like, and go from there.