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## Main Question or Discussion Point

Hey all! I've casually browsed this forum for a long time, but I finally registered today! I'd really like some advice regarding my math/science education.

I'm a freshman at a reasonably competitive university (not top-notch, but by no means mediocre/bad), and I absolutely love math. I decided to major in math towards the end of high school, when I finished linear algebra and DEs at the local community college my junior year before graduating a year early. Following that, I participated in the PROMYS summer number theory program for high school students, and then during my first year of college, took upper division linear algebra, abstract algebra, real analysis (all with stellar grades), and (currently) mathematical cryptography and recursive function theory. Up through this semester, I was also considering doing a double major in physics, since physics has always interested me. So even though I didn't need it for my math major, I signed up for the honors section of the lower division Electricity and Magnetism course.

This course is kicking my butt, and I can easily say that it's harder (for me) than any upper division math course I've ever taken, with the exception of PROMYS' number theory (but that's a given anyway). It probably doesn't help that I only did mechanics back in high school. Since it's an honors section, the course is curved so that average is about a B, which is about where I'm at. The homeworks are getting much, much harder though, and it doesn't help that it's a morning class so I have a tendency to sleep through/in lecture, so I'm afraid it could easily be a B-. I know it's kind of stupid, but I don't want physics to trash my GPA, and I'm considering just switching the grading option to P/NP. Of course, that would keep me from doubling in physics, but I feel that if I can only get a B in a lower division course, I just might not be cut out for a physics program anyway.

Ultimately, I'd like to go to grad school for math (probably pure, but applied is cool too), and I want to keep my options open so that I can study at the best schools (Harvard, MIT, Princeton, etc., depending on what I want to specialize in). To this end, I'm planning on taking graduate level classes as an undergrad, starting with analysis/topology next semester. I'm worried that having a P/NP in physics would look bad on my transcript, but then again I feel having a B- could also hurt my chances. I'm just worried because I know that math grad schools are very competitive. I really like the material I'm learning in E&M, but I'm just finding it quite difficult and would love some advice on what to do about it.

Also, can anyone give me advice about how much to specialize as an undergraduate? Should I almost exclusively focus on math as an undergrad and choose a focus within math by my junior/senior year? I finished almost all of my general education requirements back in high school, so I can do this if I want, but I want to take some other courses for personal enrichment, such as a Chinese language class next semester. While I love to do math, I personally feel it is important to do a broad range of things in order to most fully enjoy one's college experience, so I'd like to continue in clubs, choirs, competitive ballroom dance, etc., but I also don't want to be behind the curve when it comes to mathematical preparation for good grad schools. Along this vein of specializing but not being to specialized, can anyone suggest other possible double majors/minors that I can try out? Not to be blasphemous, but even something in the humanities would be cool as long as I can have fun with it.

Any and all advice is appreciated. Thanks so much!

I'm a freshman at a reasonably competitive university (not top-notch, but by no means mediocre/bad), and I absolutely love math. I decided to major in math towards the end of high school, when I finished linear algebra and DEs at the local community college my junior year before graduating a year early. Following that, I participated in the PROMYS summer number theory program for high school students, and then during my first year of college, took upper division linear algebra, abstract algebra, real analysis (all with stellar grades), and (currently) mathematical cryptography and recursive function theory. Up through this semester, I was also considering doing a double major in physics, since physics has always interested me. So even though I didn't need it for my math major, I signed up for the honors section of the lower division Electricity and Magnetism course.

This course is kicking my butt, and I can easily say that it's harder (for me) than any upper division math course I've ever taken, with the exception of PROMYS' number theory (but that's a given anyway). It probably doesn't help that I only did mechanics back in high school. Since it's an honors section, the course is curved so that average is about a B, which is about where I'm at. The homeworks are getting much, much harder though, and it doesn't help that it's a morning class so I have a tendency to sleep through/in lecture, so I'm afraid it could easily be a B-. I know it's kind of stupid, but I don't want physics to trash my GPA, and I'm considering just switching the grading option to P/NP. Of course, that would keep me from doubling in physics, but I feel that if I can only get a B in a lower division course, I just might not be cut out for a physics program anyway.

Ultimately, I'd like to go to grad school for math (probably pure, but applied is cool too), and I want to keep my options open so that I can study at the best schools (Harvard, MIT, Princeton, etc., depending on what I want to specialize in). To this end, I'm planning on taking graduate level classes as an undergrad, starting with analysis/topology next semester. I'm worried that having a P/NP in physics would look bad on my transcript, but then again I feel having a B- could also hurt my chances. I'm just worried because I know that math grad schools are very competitive. I really like the material I'm learning in E&M, but I'm just finding it quite difficult and would love some advice on what to do about it.

Also, can anyone give me advice about how much to specialize as an undergraduate? Should I almost exclusively focus on math as an undergrad and choose a focus within math by my junior/senior year? I finished almost all of my general education requirements back in high school, so I can do this if I want, but I want to take some other courses for personal enrichment, such as a Chinese language class next semester. While I love to do math, I personally feel it is important to do a broad range of things in order to most fully enjoy one's college experience, so I'd like to continue in clubs, choirs, competitive ballroom dance, etc., but I also don't want to be behind the curve when it comes to mathematical preparation for good grad schools. Along this vein of specializing but not being to specialized, can anyone suggest other possible double majors/minors that I can try out? Not to be blasphemous, but even something in the humanities would be cool as long as I can have fun with it.

Any and all advice is appreciated. Thanks so much!