<p>
Michigan’s is excellent. </p>
<p>
I wholeheartedly agree.</p>
<p>
</p>
<p>Okay, but please make sure John Doe is going to stay at Montana State and is not going to up and leave a year or two into the program. Having gone through a mild, toned-down version of “oh my god, my advisor is leaving!” I don’t wish that on anyone. You want to make sure there are a variety of professors you can work with at any given school, in case your primary advisor gets poached by another school or gets hit by a bus, etc.</p>
<p>If your son wants to work with junior faculty, have him check for their tenure review date. Additionally, you may want to ask the DGS in the department if the chances for tenure are good. And, eh, there’s really no good way to ask, “If you get a better offer from another prestigious institution, will you take it?” so you’ll have to really judge that for yourself.</p>
<p>I understand that Berkeley’s been bleeding professor for a while now (not sure if in math) due to the general financial state of California, but if I recall correctly, they’ve made an effort to match the offers from other schools, and their retention rate has been pretty good for the past couple years since the great meltdown.</p>
<p>
The weather in Palo Alto is better than the weather in Berkeley. ;)</p>
<p>I can’t give a generic answer to this question, but I could suggest how your son might answer it: Does he have a sub-field of mathematics that is of greatest interest to him, or perhaps 2 or 3 sub-fields? (For example, I am thinking of something at the level of “algebraic topology” as constituting a sub-field.) It would be a good idea for him to look at the faculty whose research interests match his, at each place. Then he can look at their recent publications, to see if any stand out as especially interesting to him. Then there is the personal factor: What are the people really like to work with? The best way to find out about this is to visit, and speak with the potential research advisers. Perhaps allow for a 2-3 day trip to each place, in order to speak with the faculty and see the area. </p>
<p>In terms of people leaving either school: If your son is working with a tenured professor, the faculty member is unlikely to leave either place. If he/she does, it will probably be to an institution of a similar rank. Many faculty will take their Ph.D students with them when they move, if the student has begun research already. The student may have the option to receive the Ph.D. from the former university or the new one (though occasionally, there might not be a practical option). In any event, this is not an issue that should shift the choice noticeably. It’s a bit different if a student is working with an untenured faculty member.</p>
<p>Picking a math program based on potential advisors is harder than doing so for science. In science, you choose your advisors in the first few months typically.</p>
<p>In math, I’ve heard you have 2-3 years of graduate-level math classes before starting research in earnest. In science, on the other hand, most people have a general idea of 2 or 3 profs they would want to work with before making the decision.</p>
<p>SOP14, my brother went to Georgia Tech for grad school, because he said he was NEVER spending another winter north of the Mason-Dixon line. He has been extremely happy with his choice.</p>
<p>My advice is admittedly a bit more slanted to the sciences, but I think it could still apply for a mathematician who has a general idea of the field of interest. For example, not counting the emeritus faculty, Berkeley has 6 faculty members in mathematical logic. I suspect that people are either strongly drawn to this field, or not drawn to it. Berkeley has 16 non-emeritus algebraists, but if the interests could be narrowed to algebraic geometry (just to take an example), then there are 8 faculty who list that as an interest. Only one of the people is interested in computational algebraic geometry. I was a little surprised by the number of people in analysis–10 non-emeritus faculty, with some overlap with the algebraists; similarly, 10 people list research interests in geometry. In a 3-day period, it would probably be possible to meet with 9 or so faculty members without too much trouble.</p>
<p>
</p>
<p>The big difference in that regard is that Berkeley is much more dependent on state funding than Michigan is. The state of Michigan went through its big economic downturn 30 years ago and essentially weaned the University of Michigan off state funding over the period since then, to the point that state appropriations now make up approximately 6% of the University’s budget. So when the state cuts its higher education budget by 10% (as it did during the recent recession), that amounts to 0.6% of the University’s budget. The University hasn’t spent the last 30 years crying over spilled milk. It went out and built up an approximately $8 billion endowment, something like 6th or 7th largest among U.S. colleges and universities. It built up its research capacity to over $1 billion annually, highest in the nation (except for Johns Hopkins which counts a huge off-campus government-funded lab in its total). And it diversified its undergraduate student body which is now close to 40% OOS, resulting in much higher tuition revenue. In short, it quasi-privatized. UC Berkeley is starting to take similar steps but it’s not nearly as far down that path, so when the California legislature takes the meat-axe to higher education funding, it cuts much more deeply into UC Berkeley’s annual operating revenues.</p>
<p>As for the OP’s question, Michigan and Berkeley both have outstanding and highly regarded math departments, strong in almost every aspect of the discipline. Berkeley edges out Michigan in the overall math rankings but it’s so close that the rankings are really irrelevant. I agree with those who say this is really a question of the Ph.D. candidate finding the particular faculty he wants to work with, in the specialty he plans to concentrate in. Unless there are big difference in funding or in teaching obligations, that’s really the only consideration that should matter.</p>
<p>I believe they do have ranking by subfields as well, so the OP’s son may want to take a look at that.</p>
<p>Obviously, he should also be consulting the professors at his undergrad school for their opinion.</p>
<p>When your son visits he should also make sure to talk to current grad students. And not just 1st year students, but2nd, 3rd & 4th year students as well. Best would be students working under the profs he is interested in studying under.</p>
<p>Important questions:
How much teaching do grad students have to do? Is it all grading exams, or is it leading discussion sections, or is it teaching your own course(s). </p>
<p>Case in point - S1 is a first year grad student in the math PhD program at a top 20 school (but not Berkeley or Michigan). A friend of his and college classmate is a first year grad student in the math PhD program at a top 30 school. S1 is a research assistant this semester, and his grad advisor says he is to do as much research as he wants, consistent with getting ready to pass his comps, which is is first priority. S1’s friend is already teaching a section of pre-calculus at his grad school. S1 is very happy to be where he is.</p>
<p>How is the funding for years past the first year? Will it come from the department for being a TA, his grad advisor as an RA, or is he expected to pursue and get outside fellowships?</p>
<p>Where have recent graduates (preferably graduates who studied under his intended grad advisor) gone? Post-docs or academic positions or industry? What kinds of places?</p>
<p>thanks to all of you for good insights and points to consider. I think he’s doing a lot of what you’ve suggested, tho only had about a day and a half at each place. He’s planning to talk in more depth with his professors back on school after Spring break…maybe after that he’ll flip a coin! 
No, seriously, he’s giving it alot of thought and points you’re making here will help us ask smart questions too. </p>
<p>Just FYI, his field is algebra and indeed, that’s how he ruled out other contenders–they didn’t have as many profs/potential advisors in that field.</p>
<p>Someone on another thread once mentioned this book, which might be of interest -</p>
<p>A Mathematician’s Survival Guide: Graduate School and Early Career Development By Steven G. Krantz</p>
<p>Good luck to him!</p>
<p>
</p>
<p>Where’s the LIKE button when you need it the most… :)</p>
<p>NY Times editorial: “Resurrecting California’s Public Universities”</p>
<p><a href=“The New York Times - Breaking News, US News, World News and Videos”>The New York Times - Breaking News, US News, World News and Videos;
<p>Okay, the bias is evident in my name (I have a doctorate from Berkeley), but I’m also a parent of a daughter who had to choose among top schools, and I’m also a professor (in a social science field).</p>
<ol>
<li><p>First, talk to your own professors. The OP’s son has probably done this. However, be aware that when the schools are well-matched, your professors may not be able to help you make the decision.</p></li>
<li><p>Visit both places. Can you see yourself living there for 5-6 years? It’s hard to complete a doctorate when you’re miserable.</p></li>
</ol>
<p>When my daughter graduated from MIT in physics, the department there encouraged her to go elsewhere for graduate study in HEP (that’s a long-standing policy at MIT – even Feynman had to leave). She was accepted to Cornell, Harvard, and Chicago. Her professors at MIT told her that in her field of interest, there was no appreciable difference between the programs and opportunities at these schools, so in the end, it came down to “Where do I want to live for six years?”</p>