Postby c3adv » Mon Dec 10, 2012 11:06 am
I appreciate your emphasis on feedback and a straightforward study strategy. I was under the impression that the 85th percentile was enough even for Berkeley, but I could be wrong. I think something I would like to eventually add would be a breakdown of sample study plans to give others an outline of how they could potentially budget their time. The REA book mentioned that studying for an hour a day for 12 weeks should be sufficient for preparing around anyone's busy schedule, but that can be shortened considerably for someone who knows the material well. For those who have gaps, it may be harder to extrapolate how much time is needed, but it seems that about 2 months is good enough. How often did you study? Every day or primarily on weekends? Roughly speaking, since you are not a math major/minor, did you study for 4 to 10 hours a day? Did you focus on specific topics? Can you mention a sample scenario concerning a concept you had previously never studied before?
Although it does not seem to be mentioned often, if at all, I would suggest looking into textbooks with hints or brief answers in the back. Mastering Rudin, Dummit and Foote, Lang, etc. is definitely better preparation for graduate courses overall, but for this test, some immediate feedback can help streamline study time while making the transition into the standard upper-level textbooks much smoother.
As such, I have a few study suggestions. First, review and memorize all the precalculus, algebra, and trigonometry theorems and any major geometry proofs from high school. For example, be able to recall double angle formulas and all the values from the unit circle. The very basics of vectors, partial fraction decomposition, and complex numbers (especially modulus, De Moivre's Theorem, and powers/roots of complex numbers) are taught in many standard high school textbooks, but it seems they are retaught, respectively, in calculus, introductory real and complex analysis, and linear algebra textbooks time after time. The same is true for set theory and the basic rules for functions, which get repeated too often (I hate it when a class spends even a single lecture going over this stuff when everyone in the class has seen it three times already, or more, only to rush through the more complicated topics later on).
The calculations needed for most problems on Stewart and other standard calculus textbooks are basic enough, so speed is the only thing that needs to be improved upon. The AP Calculus questions somewhat overlap with the ones on this test, so those can provide extra timed practice on standardized questions, and if I am not mistaken, they are also written by ETS. Some of the standard calculus/analysis proofs could be found in the solutions manuals. Student solutions manuals are not usually available, however, for higher-level courses. So, if you have not taken the classes before or if your professors skipped many key topics/problems, you are currently not enrolled in school, and/or you are all alone except for help on the forum and a few helpful textbooks, then it can seem daunting. Nonetheless, I have found problem books in analysis and linear algebra to be very useful in reviewing techniques I had forgotten or never fully mastered. The ones I have used so far are:
A Problem Book in Real Analysis by Aksov;
Problems in Mathematical Analysis 1, 2, and 3 by Kaczor;
Linear Algebra Problem Book by Halmos;
Problems in Real and Complex Analysis by Gelbaum;
and Problems and Solutions for Undergraduate Analysis by Shakarchi.
I am curious as to whether problem books exist for Abstract (Modern) Algebra and the other subjects; I have used and looked into the ones for functional analysis and algebraic number theory, but those aren't needed for the GRE subject test. I know Gallian and Pinter have some hints for introductory abstract algebra, and Ross is good for basic probability, but Grimmett's books on probability have some worked-out solutions if you are stuck or want to check your work. Boyce and DiPrima or Nagle cover basic ODE. Burton for Number Theory is easy enough for someone who has never taken a course in the subject before. For topology, I have not looked beyond Munkres as of yet. Definitely, look into Brown and Churchill or Wunsch for the basics of Complex Variables.
Can anyone expand on or provide corrections to what I have written so far?