Prep for GRE Math Subject Test: Best Books to Use?

[epsilon>0]

What's the best book to use to prep for the GRE subject test?

For Topology, I was going to use the first few chapters of Munkres, and algebra first two chapters of Dummit and Foote. Are these good selections.

I planned on working my way through Rudin for Grad school prep, but that seems like overkill for GRE prep. I thought maybe I should use Spivak or Apostol for Calculus...I've heard that apostol exercises will often appear on the exam. However, the apostol book is expensive, so if Spivak is good, I would rather use that book. I would assume that apostol and spivak would also help me review for gre style analysis.

What about Number Theory?

Finally, how about linear algebra. I've heard that there aren't any good books on linear algebra. If I spent the $300 dollars on apostol...I know that covers some linear, but I don't like the idea of spending that kind of money on a textbook.


Anyway, I'd appreciate it if you guys and girls could give me insight on the best books to work through for Gre prep.

 

[Bourbaki1123]

I'm using a combination of the Princeton Review "Cracking the Mathematics Subject Test" and "Putnam and Beyond" (mostly because I'm determined to solve a couple of questions on this year's putnam exam, but the subjects line up nicely with the gre so it can't hurt).

I'm mostly using the Princeton review to refresh on some stuff in multivariable calc. On top of that, I'm picking through Griffith's Electrodynamics (for more interesting multivariable stuff) and Gilbert Strang's linear algebra book. I've been thinking about skimming M. Artin's book on abstract algebra (titled "Algebra", which some have found to be misleading).

ETA: I would recommend Artin's text over Dummit and Foote; Artin's pedagogy is great and the material is more solidly presented IMO.

 

[snipez90]

Yo you should probably review some calculus since it makes up half of the exam I think? It would be pretty stupid if you knew what the quotient topology was but couldn't solve a first-order linear ODE or a maxima/minima problem.

Also note that the first few chapters of Munkres is a lot of material. Chapters 2 and 3 pretty much cover a basic undergrad course in topology. I highly suspect you won't need much more than that.

Rudin and Spivak have similar exercises, so it's probably more efficient to do the problems in Rudin (since he covers all the material in Spivak in 7 chapters).

For linear algebra, why not just use wikipedia (which you should be doing so already unless you're one of those people who is afraid of the rather minimal chance that there is actually something factually incorrect in the superb math articles) and some undergraduate course webpages with solutions?

 

[epsilon>0]

Do you think Spivak is a good calculus review for gre?

I was going to use Rudin as grad school prep...I've been out of school a couple years, so I figured Rudin would get the math brain cells firing again.

 

[snipez90]

Not particularly, since by 50% calculus, it seems they really do mean the mechanical or computational aspects. Spivak is for all intents and purposes an undergraduate basic real analysis text, and the GRE attempts to categorize this under real analysis I guess. Certainly reading over the chapter full of integrals (19 I think?) may be useful.

Focus on the computational aspects of calculus that you may need to brush up on (e.g. for me this would be Taylor series if I hadn't used Lang for complex analysis). You probably haven't forgotten how to take a derivative of an elementary function, but you may be given a PDE and asked which of the 5 answer choices is a solution. Actually finding the solution will cost you time, so you need to be able to take derivatives quickly, and preferably in your head.

What I really meant was look over multivariable calc and ODE, which rightfully fall under calculus. Multivariable calc is by nature a computational subject, so make sure you know the techniques for finding maxima/minima (one particular significant application), Taylor's theorem, vector calc, etc.

Also basic complex analysis is on there. Review contour integration, e.g. the residue theorem, Cauchy's formula. You probably won't need to shift contours to compute improper integrals, but certainly basic manipulations with integrals over closed circles and the like are fair game.

 

[R.P.F.]

I'm using a combination of the Princeton Review "Cracking the Mathematics Subject Test" and "Putnam and Beyond" (mostly because I'm determined to solve a couple of questions on this year's putnam exam, but the subjects line up nicely with the gre so it can't hurt).

I'm mostly using the Princeton review to refresh on some stuff in multivariable calc. On top of that, I'm picking through Griffith's Electrodynamics (for more interesting multivariable stuff) and Gilbert Strang's linear algebra book. I've been thinking about skimming M. Artin's book on abstract algebra (titled "Algebra", which some have found to be misleading).

ETA: I would recommend Artin's text over Dummit and Foote; Artin's pedagogy is great and the material is more solidly presented IMO.

Hey! We have exactly the same taste in books. Artin, Strang, Griffiths and 'Putnam and Beyond'! Woo-hoo!