How's the Math Department? Any Math Majors?

[phuriku]

<p>

I will mention that many students at Caltech and MIT take more graduate math classes as undergrads (I took 28–in retrospect many of them were so over my head I didn’t get anything out of them…as in didn’t understand a single word) than are OFFERED at Chicago (this is of course not reflected in any rankings since grad students don’t choose departments based on course offerings). OTOH Chicago makes up for it with the directed reading program which allows students to study any subject in math they want with grad student mentors, and is probably as good approximation as any to what grad school is really like.

</p>

<p>I guess I would like to put in a word in defense of the Chicago system. Yes, it is true that most students don’t take graduate courses until their 4th year (although each year, about 5-10 3rd years do take graduate courses), but I have to give my opinion that from what I’ve seen, Chicago’s honors undergraduate courses seem to be about equivalent to the graduate courses at peer institutions.</p>

<p>For instance, many (by which I mean ~5-10 or so) MIT first-year math majors opt to take 18.125: Measure Theory and Integration ([MIT</a> OpenCourseWare | Mathematics | 18.125 Measure and Integration, Fall 2003 | Home](<a href=“http://ocw.mit.edu/OcwWeb/Mathematics/18-125Fall2003/CourseHome/index.htm]MIT”>http://ocw.mit.edu/OcwWeb/Mathematics/18-125Fall2003/CourseHome/index.htm)), which is a graduate course. Although it is technically a graduate course, the course content resembles very closely that of Honors Analysis at Chicago, which is an undergraduate course taken by about 5-7 first-years and 10-12 second years each year. 18.125 covers the first 3 chapters of Rudin in the first semester, and in Honors Analysis, the first quarter covers Chapters 1-6 of Royden. The former is slightly more abstract (using abstract measure theory instead of just Lebesgue measure theory, although the presented proofs don’t differ by much), but the latter covers more material (for instance, a more rigorous theory of differentiation and the (abstract) fundamental theorem of calculus). I have compared problem sets from both classes, and I see no tangible distinction.</p>

<p>Chicago’s Graduate Analysis class, on the other hand, is significantly more advanced and covers about 5x more material than 18.125. It covers the first 9 chapters of Rudin, along with the professor’s (rather long, I might add) notes on rigorous probability theory. So although yes, Chicago’s undergrads take fewer graduate courses, it seems that the undergraduate honors courses are just as rigorous, and that Chicago’s ‘beginning’ graduate courses are about equivalent to other schools’ more advanced graduate courses (which most incoming graduate students probably start out from anyway).</p>

<p>It is true that Chicago’s DRP program is rather popular, although I’m not sure if it would have too much of an effect if Chicago’s undergrads didn’t take classes as equally challenging as the graduate courses presented elsewhere. More of the esoteric topics of mathematics require a sophisticated understanding of abstract concepts, and so I don’t think the DRP program would be as effective without the strong undergrad program in place.</p>