i want to go for a PhD in applied/interdisciplinary mathematics. i have a bachelors in math and a masters in math education. i wish to be a professor so that i may both teach and research math.

i have applied to 11 programs for fall of 2009. so far i've got 3 rejections, and some waitlists, and a few more no-responses that i'm waiting on. but overall, its just not looking too good at this point. a couple more of those are almost certainly rejections, and the state of the economy has: 1) decreased the available funding to programs and hence decreased the number of spots available, and 2) it has increased the number of applicants because of so many people wishing to ride out the economic crisis in grad school. 1 + 2 = harder to get into a good program for everybody except for the absolute top candidates.

i took the subject test once in november. i did very poorly. my score was below 40%. (a very small consolation is the fact i did get an 800 on the Q part of the general GRE.) i had studied for a solid 2 months. and i used the "cracking the gre math test" as well as my old calculus and linear algebra textbooks from my undergrad. i spent about half my time studying calculus and the other half studying a mix of linear algebra, a little bit of number theory and a little bit of abstract algebra.

truthfully, only 4 of the programs i applied to required the subject test. still, i get the feeling i may have to re-apply all over again next year. and i think i should retake the test.

a couple of problems that i had with the GRE subject test:

1. i didnt have NEARLY enough time. i answered only about 2/3rds of the questions.

2. i did not study my abstract algebra enough. in fact, i barely studied it and i didnt realize how much of the test would be about this topic. i also didnt even have a good text on this subject to study from.

3. so much uncertainy. it felt like so many of the questions were "trick" questions that required the memorization of one little odd fact that would cut the time necessary to do the problem substantially.

i really like my calculus book from college and it feels like such a great book, but it seemed like there were a number of 'trick' calculus questions on the GRE that i don't feel are really emphasized in my calculus textbook.

could someone recommend some actual textbooks (not study guides) to study from that cover the kind of questions that the GRE asks? (particularly abstract algebra)

and what are the best approaches to studying and preparing for this exam?

whatever i did the first time didn't seem to work, and i believe i have the capability to do so much better than what i did. (and hell, i already did one masters degree, so i know i'm not as stupid as the test results made me feel)