<p>Math classes tend to give out more 'A's than those in almost any other field, and the math major is pretty loose in requirements as compared to, say, physics or any engineering major. I have also heard that math majors have the highest average GPAs. On the other hand, the people who tend to major in math here tend to be really good at math, so it's very difficult to compare. Without knowing anything about your background, it's impossible to know if getting 'A's will be relatively easy for you, or if you'll struggle just to pass your classes. </p>
<p>What kind of experience do you have with proofs and what math classes have you already taken? If you've just taken the more practical "for scientists and engineers" math classes in calculus, linear algebra, multivariable calc, and differential equations at another university you're going to have a hard time when all of the other math majors have taken all of these courses in an analytic, purely proof-based context. If you're transferring from a community college, you may not have even had the option to, say, take calculus and linear algebra at the level of Apostol. It's worth noting that if you find that you like applied mathematics more than pure mathematics, we do offer a major in that.</p>
<p>I'm not sure what classes you'll be able to skip here -- you might be able to keep the credit for some of the courses you've taken elsewhere, and you might have to take exams to show that you know the material at the level it's taught at here. You'll probably be entering at the sophomore level, depending on how advanced the courses you've taken are. Also of note: How many science classes have you taken? You will have to complete Caltech's core science requirements if you haven't taken the equivalents somewhere else.</p>
<p>A typical sophomore math major schedule will look like:
Physics 2 or 12 (Waves, Quantum Mechanics, Statistical Mechanics)
Math 2 (Differential equations, Probability and Statistics)
Math 5 (Abstract Algebra)
An elective like Ma/CS 6 (Discrete Mathematics)
Some humanities and social science classes (one a term on average)</p>
<p>If you don't have a lot of experience with proofs, Ma 5 will be tough, but Ma 2 will probably be fine. The math option also requires graduate-level classes such as Ma 108 (classical analysis) and Ma 109 (geometry and topology), which you will probably find difficult regardless of background. On the plus side, the median grades in these classes tend to be 'A-'s, which is pretty generous. If you're interested in applying to top PhD programs in pure mathematics, you are going to need at least an A- average. If you're interested in applying to grad schools in other related fields (perhaps CS or biophysics), your GPA can be lower, particularly if you have research. If you're planning on getting a job right out of undergrad (which will obviously not be in pure mathematics), your GPA will be less important.</p>
<p>As for research, it's pretty easy to get a SURF in any field. You do not need to have any research experience to get one. If you are interested in more applied or computational mathematics, there are usually a ton of SURF announcements of opportunities in fields combining math and CS, geophysics, chemistry, astrophysics, etc. If you want to do research in pure mathematics, it might be better for you to just contact professors whose research looks interesting, even if you haven't taken a class with them. They'll help you come up with a research topic that is appropriate to your background. As long as you get started on finding a SURF mentor early, do all of the appropriate background readings, and don't procrastinate on writing your proposal, it will be very easy for you to get a SURF.</p>
<p>Most professors here seem to like undergrads, and plenty strongly encourage you to go to their office hours. I can't think of a class that I've taken where the professor didn't have office hours (in math or any other field), so that's always a good way to approach them. I've had good TAs and bad TAs, though I have to say that most were pretty good. If you have a bad TA, you can always switch sections to one you prefer. Every TA I've ever had tried to be helpful, though a few are just bad at teaching. Like at most major universities, some of the TAs here don't speak English as a first language, but I've never been taught by a TA who was less than fluent. If you're not used to certain accents, you can always just switch sections. Your non-core classes will generally be small enough that you will only be taught by the professor for the class.</p>
<p>Collaboration on problem sets is very strongly encouraged and very widespread here. I'm pretty sure I've never done a problem set in math or physics where I didn't at the very least discuss how to do a problem with someone. The problem sets tend to be difficult enough where, for most students, you need to collaborate, and I think this is a good thing. For most of my sets, I just work with a group of people until everyone is done. There will be some problems that everyone can solve on their own, and there will be some problems that will take hours and hours for even one person to get a good idea of how to do. Often, even if no one can figure out a problem individually, sharing ideas on approaches can cause a group of people to solve it together. </p>
<p>Even as a transfer student, you're going to have to go through Rotation like all of the freshmen and be put in an undergraduate House (regardless of whether you actually live there or off-campus.) This means that by the end of the first week of school, you'll have 60-120 instant friends, not including the other people in your classes or that you meet during rotation. Some of these will be math majors, and if you're taking core classes, many of them will be in those. This is the easiest way to find people to collaborate with. In your smaller classes, you'll probably know the other students in the class well enough where you'll work with them. This is a great way to get to know people from other Houses.</p>
<p>I'm a physics major, so while I'm in the same division as math and am pretty familiar with all of the major undergraduate math courses, I can't tell you too much in detail about the math research going on or the graduate-level classes. There are several math majors that read this forum that can add more or correct me.</p>