Advice for an undergraduate math major about graduate school?

Hey, I am a freshman math major. I was wondering if you guys had any ideas for getting into a strong math graduate school, such as MIT or Princeton. I understand that a genuine passion in math, along with strong recommendations, grades, and GRE scores are not enough nowadays. Any ideas would be appreciated, thank you.Advice for an undergraduate math major about graduate school?
Get involved in undergraduate research. In addition to possibly doing something with the faculty where you're in school, there are lots of summer programs called REUs (research experiences for undergrads) around the country that pay you to do new math with other students for six to nine weeks of the summer. The MAA, the AMS, and the NSF list these things (just Google ';reu math'; and web pages from those organizations should be near the top.) Some of these have prerequisites you may not have taken yet, but it's worth looking.





There are also special study abroad programs for math majors that help a lot by both providing classes not usually available to undergrads and networking with other good students. The best known is the Budapest Semester in Math. Penn State has something similar (although less exotic) called MASS (math advanced study semesters).





Another way to distinguish yourself would be through taking the Putnam Exam offered each year and doing more than one of the eight problems (they're really hard). Some colleges have Putnam study programs, but if yours doesn't, ask around and see if somewhere nearby does.Advice for an undergraduate math major about graduate school?
Get involved with any research projects that you can. Depending on your university, there are usually professors open to bringing in motivated undergrads to help with some sort of research. Often this will involve doing some grunt work for graduate students, but if you can get your name on a paper or two before applying to grad school, I'd expect your chances to grow quite a bit.





Also, find out what sort of research the professors are into at the grad schools in which you are interested. Granted, specific things may change in the next few years before you go to grad school, but you can get an idea of the areas of research of the professors. If you can somehow connect with a specific professor before the application process (without bothering them--a tricky task) you may increase your odds. Don't email/contact any of them unless you have some understanding of their work, though.





Getting into a top program in any field is very difficult. Kind of like becoming a pro athlete--so few spots with lots of high quality applicants. It is good you are considering how to improve your chances at such an early stage. Good luck.
I went and got my PhD in physics. But I always wished that I had opted for applied math. Later I learned how important that is. At the time when I went to school, there were covered wagons, we had no computers save the IBM 360 and we had to use cards. Now there is so much more that you can do with a PC. So my advice is applied math. Good luck