<p>jerew,</p>
<p>Disclaimer: Take all of this for what it's worth (you decide) and what you paid for it (nothing.)</p>
<p>To begin with, I was not (nor am I now) a physics/math stud. I just like the subjects and work hard. Trite and a little corny, but true.</p>
<p>About me:
I went to high school (actually dropped out, but that's a different story) in a tiny town with no AP classes, but took Calc I at a community college the summer before starting school at a large public Tier 1/Research 1 Univ. My first year I took Calc 2 & 3 and Diff Eq. My 2nd year I took Linear Alg., Number Theory, Abstract Algebra, Adv. Calc. (this year SUCKED!! Straight A's, but I was so caught up in getting the farthest the fastest that I didn't really savor or retain what I was learning). My third year I took complex analysis and a required mathematical statistics class. My fourth year I took differential geometry.
As for the 4 majors, the math and physics have so much overlap that it's only like 1.5 degrees. I took all of my social science electives in economics and all humanities electives in Russian, so it wasn't really as hard as it sounds. Obviously the math and physics satisfied the science reqs for econ and Russian. The biggest thing was that I went to school year round. From that summer I took Calc I, I was enrolled for 12 consecutive semester of non-stop schooling inculding summers (I took 5 years). That took it's toll on my motivation and I would not recommend it.</p>
<p>My opinions about undergrad institutions: If you can get into any of the fine programs you mentioned, great - you should go. But if you 1) don't get in 2) get into only one or two that you aren't that excited about or 3) get in but have to take out massive loans, then don't rule out a solid public U. Having known many, many folks from "elite" programs for years, some things that people don't think about are:</p>
<ul>
<li><p>These schools are famous for their research and graduate programs. As an undergrad you will probably not (almost never) have too many opportunites to take advantage of these. There is a reason that many of the folks I know did REUs (Research Experience as an Undergraduate) during the summer at other universities (Texas, Michigan, Ohio State, Washington, Wisconsin are some of the best). You will almost certainly have more classes taught by graduate students than at a less prestigious school, as the elite faculty as busy doing their research that brings the school grant money. Side note: don't kid yourself, professional science is very much a business.</p></li>
<li><p>MIT and Chicago aside, the rest are (fairly or not) known for grade INFLATION! Look at what Princeton is going through now to regain some respectibility vis a vis grades. </p></li>
<li><p>Physics is probably the most standardized field left for undergrads. By that I mean that no matter where you go, you will likely take you first year of physics from Halliday & Resnick (or similar), mechanics from Marion & Thornton, E&M from Griffiths, Thermo from Reif or Kittel & Kroemer, QM from Griffiths or Shankar, math methods from Boas, etc. Master these and you're set for the academics of ANY grad program, no kidding.</p></li>
<li><p>Money. By staying in-state I not only had 100% of my education, room and board paid for, I actually made money. The total of scholarships I got exceeded the cost of my school and I got a fat check at the beginning of each semester. Coming from a very poor family, my quality of living actually went up in college! So I graduated with no debt hanging over me, actually saved (gasp!) a small nest egg, and still studied the exact same courses and texts as my contemporaries at MIT! Now we're at the same grad institutions I sometimes feel like "joke's on them" since I can buy a home as a grad student and a disturbing number of them have debt well over $100,000.</p></li>
<li><p>Prestige. Rather than be one of the rank and file at an elite institution, I was one of the standouts at my school. It was relatively easy to get into a good research group. The leader of my research group was a Princeton PhD whose thesis advisor was John Wheeler himself! That's some serious firepower for your recs. Now, I still had to work very, very hard and it's not like other students were slouches, but I imagine the competition was less intense than elsewhere for award and recognition (like nominations for the Rhodes and Marshall Scholarships.)</p></li>
</ul>
<p>If you live in California, Wisconsin, Illinois, Michigan, or maybe a few others, I would very seriously consider staying in-state and going to a public research univ.</p>
<p>Advice/Random thoughts:</p>
<p>-You are not behind in math at all. Truth be told, you can probably finish most undergrad physics progs. with no more than Diff Eq. (assuming you have no plans to go on).</p>
<p>-When you start college, talk to your advior about retaking the last math class you took in high school (sounds like you're at about multi-variable calc, no?). College is just different. As a longtime TA/instructor I've seen so many great students bite off too much their first semester, and suffer because of it. Remember it's not a race, or competition. It's about who UNDERSTANDS it the best.</p>
<p>-Calc 3 and Linear Algebra are the two most valuable classes you will ever take if you are interested in physics. Almost everything else builds on these classes.</p>
<p>-Actually read the textbook. There is so much valuable info that I missed just because I was able to absorb enough info from lectures to get straight A's. I was too concerned with grades and not concerned enough with knowledge.</p>
<p>-When you make the transition in math classes from calculation-based classes (Calc, Stat, Diff Eq, Lin. Alg., etc.) to proof-based classes (usually your first semester of Adv. Calce. aka Real Analysis), take a light load that semester. THIS is when you really start to see what it's all about. And it's a totally different way of doing things.</p>
<p>Regarding getting into a top 10 physics prog - it's a crapshoot (exact rankings really don't mean that much - think more in broad bands of 20 or so.) Figure each department takes an average of 40 students/year (and that's a high estimate) you can see why every single year there are 4.0 ivy league double-majors with good recs and research that don't crack the top 10. It's truly random - nobody can honestly say that any top 10 grad prog is a safety. Remember you are competing for slots with mostly international students now and Chinese and Indian students in particular are very, very well educated. </p>
<p>Anecdote: good friend of mine decided to go to Dartmouth for physics PhD (and going by rankings, Dartmouth really sucks). In his research area, though, there are 2 profs there that are extremely visible in their sub-discipline. He graduated in 5 years and got a faculty position right away (no post-doc!) at a top-10 school.</p>
<p>Best of luck - let me know if you have any specific qustions.</p>
<p>AT</p>