I'm currently working on a B.S. in Mathematics at a southern, liberal arts university in the US. I feel as if I've missed out on several classes that any undergraduate who wishes to go onto a much more prestigous university should have (MIT, Stanford, etc.). In this particular area, the only university that offers graduate-level courses is roughly about an hour and a half away, and I'm not financially-stable enough to make the commute. I chose to attend this particular university, because it was all that was available to me at the time -- I earned a high-school diploma about the time I turned 15, and had a lot of difficulty getting into an undergrad program for some reason, so I got into what I could. I'm currently a junior and feel as if I have missed out on several, vital courses. By the time that I graudate, I'll have taken every Mathematics course the university offers. Here's a run-down of the courses: [completed] Basic Calculus I, II, and III sequence (using Larson's text, which is a basic, plug-and-chug text with very little rigorous treatment -- better than Stewart, IMO. Had very incompetent instructor -- more on this later.) [completed] Introduction to Abstract Mathematics ('Transition to Advanced Mathematics' by Smith, Eggen, and St. Andre. Typical proofs course taught by a reasonably competent instructor, but I feel that we could've done more if it weren't for the class -- half of which were re-taking it for a second time, because they failed the previous one. I was the only student that completed the course with an A. The next grade was 20 points away). [completed] Linear Algebra ('Linear Algebra and its Applications' by Lay. Typical one-semester introduction course. Again, taught by a relatively competent instructor, but we could've done much more in the course if the same group of students who keep failing weren't in there) [completed] Probability and Statistics ('Probably and Statistical Inference' by Hogg and Tanis. A Calculus-based statistical course, taught by the same incompetent instructor that taught the Calculus sequence. I basically came out of the course hating statistics, and having very little understanding. Emphasis was placed on plug-and-chug, while this text was more theoratical. Bad combination, IMO.) [completed] Ordinary Differential Equations ('Introduction to Ordinary Differential Equations' by Saperstone. Taught by the infamous, incompetent instructor. Emphasis was placed on plug-and-chug, but I think most one-semester ODE courses would suffer from this, as well.) [completed] Numerical Methods ('Numerical Methods' by Kincaid and Cheney. Same situation as the previous courses -- taught by the same incompetent instructor with a classroom full of students that were struggling to graduate) [taking Fall of '06] Abstract Algebra (not sure what the text is, yet, but the same failing group is re-taking course, because they failed it the previous year it was offered. Taught by the competent instructor) [taking Spring of '07] Advanced Calculus (unsure of what text we're using, but the competent instructor I've mentioned previously has said I'll be only person in the course, and that she'll try to 'enhance' the curriculum a bit for me) In addition to the listed courses, there is also a Special Topics course, where the subject of the course fluctuates from year to year. Sometimes the subject is decent (last year we had 'Complex Variables), but this year it was dedicated to "Problem Solving" (seemed like a way to improve the exit exam scores, IMO). We also have a 'Directed Individual Study' type of course, that I plan on taking with hopefully the competent instructor. It may give me a chance to do some research before I enter graduate school. This incompetent instructor I've mentioned several times has the policy of "the homework is the test." Exercises that are encountered on the homework are used as a 'problem pool' on exams and homework. This policy may be acceptable in some courses where the homework problems are extremely complicated or lenghty, but that's not the case here -- basic plug-and-chug. I think I'm missing serveral courses that more 'focused', undergraduate programs offer. Namely, Complex Variables, Real Analysis (two semesters would be nice), and possibly some graduate courses. Unfortunately, my university had no graduate school, so graduate courses aren't available to me, unless I go elsewhere. I'm currently a junior, so I'll be graduating Fall of 07', and I'm just wondering what I should do by then if I want to get into a top graduate school (if I have to go into a Tier-II school, this would be acceptable, but I'd absolutely love to get into Stanford or some equivalent). Basically, I'd like to open up a dialogue in this thread with several people that may have been or seen people in the situation I'm presently in. It's really discouraging looking at several of my peers at other universities, and seeing what they're taking. On a slightly more positive note, Spivak should be arriving within the next day or so via priority mail.