<p>Just wondering about how intense the graduate courses are, specifically in mathematics... (I'm personally broadly interested in number theory, foundations, analysis, topology if there are any Cal math people out there who can say something about study in these fields at the school.) </p>

<p>On a side note, and I know this is probably harder to answer, how do Cal's undergrad and grad math programs match up to other top programs (Princeton, Harvard, MIT, etc) in terms of the intensity? </p>

<p>The “real” graduate courses are intense but they aren’t too stressful. Sometimes the grade is based completely on the homework and other times you get an open-book take home exam. But courses like 202a and 250a (analysis and algebra respectively) that are easily accessible to advanced undergraduates are more like ‘normal’ classes (your standard upper division analysis and algebra courses). </p>

<p>Cal’s math program is pretty darn good at the graduate level. But, I feel that the undergraduate program at Cal is a bit weaker than those at other schools. </p>

<p>For one, we don’t have those rigorous lower division classes like math 55 @ harvard or the honors 50s series at Stanford. Even the upper division honors classes at Cal can barely keep up with the lower division honors courses at other schools. For example, look at Math 53H at Stanford:</p>

<p>Lie algebras, Picard’s Theorem, etc in a 1st year lower division class.</p>

<p>Picard’s Theorem is covered in Math 205 at Cal (graduate class) and Lie Algebras are covered in Math 261a-b. Obviously, the lower division class (53H) can’t cover both of these topics in great depth.</p>

<p>Also, the prelims at Berkeley are EXTREMELY easy. I can already complete the majority of the problems, as a 2nd year undergrad, with little problem. The prelims at Stanford and Harvard are a lot more difficult (probably the same hard difficulty for other top-tier grad schools).</p>

<p>Math 55a-55b at Harvard is not exactly just an honors lower division math course; it covers material from two upper division math courses as well (Math 113 and 122 at Harvard). The target students are those who would ordinarily just go straight to upper division math courses as freshmen at a school that did not have such a course.</p>