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Is this a good study plan for grad school?

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By Anonymous Hero
Posted Mon May 29, 2006 at 06:24:26 PM PDT

I am independently studying for grad school while at college. The following list outlines my study plan for the next several years (the books are listed in the order they will be studied in.) It would help me a good deal if anyone could tell me, for example, whether or not I should study the books in the order I have laid out, whether I should add/delete certain books, etc.- up until now I have had to rely on information gathered from amazon.com:

Algebra (Lang)
Introduction to Lie Algebras and Representation Theory (Humphreys)
Commutative Algebra (Eisenbud)
Algebraic Geometry (Hartshorne)
Topology (Munkres)
Algebraic Topology (Spanier)
Principles of Mathematical Analysis (Rudin)
Real and Complex Analysis (Rudin)
Complex Analysis (Ahlfors)
Functional Analysis (Lax)
A Course in the Theory of Groups (Robinson)
Ring Theory (Rowen)
A Course in Arithmetic (Serre)
Algebraic Number Theory (Neukirch)
P-adic Numbers, p-adic Analysis, and Zeta-Functions (Koblitz)
A First Course in Modular Forms (Diamond)
Basic Number Theory (Weil)
Class Field Theory (Gras)

*Note: I have already studied Lang's "Undergraduate Algebra" and Lax's "Linear Algebra".

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Is this a good study plan for grad school? | 2 comments (2 topical, 0 hidden)

[new] suggestions (none / 0) (#1)
by Emil Volcheck on Mon May 29, 2006 at 07:32:09 PM PDT

Weil's Basic Number Theory is not "basic" in the sense of elementary, and I wouldn't recommend starting there. Since you're doing independent study, you might want a more gentle introduction. Stewart and Tall have a nice introduction to algebraic number theory. Ireland and Rosen's Classical Introduction to Modern Number Theory is also worth looking at. For a readable problem-based introduction to algebraic number theory, look at Marcus's Number Fields.

Hartshorne is a standard introduction, but I prefer the three-volume series by Ueno, published by the AMS in their Translations of Mathematical Monographs series.

[new] progress? (none / 0) (#2)
by Vanes63 on Mon Jul 31, 2006 at 08:27:06 AM PDT

Just wanted to see if maybe you could post something about the progress you are making at your list. I also didn't see anything in your post about how long you had to be able to do this, or how long you were taking to do this. Are you in your 2nd year of undergrad? 1st year? Just wondering.

Personally, I have not been keeping up with my readings :( for what I have recommended for myself. A lot of life-changes have prevented me from doing that, but I intend to focus more on reading in the near future.

I am already in an MS program, but want to get into a Ph.D. program after I finish, so I want to keep up with things myself lol. I have found that if something in a book is too difficult to understand, which may come up when reading these books, or maybe not, but you should also consider using MathWorld as a reference and if there is a subject you'd like a brief intro to the Dover books are a pretty good quick read.

I like their style and brevity and they move very quickly. You could probably use it as a quick reference, or not. Some people don't like them, some do. It's a personal preference thing.

Just some thoughts and questions.

Is this a good study plan for grad school? | 2 comments (2 topical, 0 hidden)

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