@mathmom Part of Gladwell’s talk is also about grad school and about how at each school only the top students publish much. Publishing is required to get a faculty job. So at Harvard, only the top students (who are exceedingly brilliant) publish and many others who are by normal brilliant, like your friend, decide ‘this isn’t my thing’. Those same students who have been the top students at other grad schools and there would have published and gone on to faculty/research jobs most likely. Although Harvard, Princeton, MIT, Stanford, UC Berkeley produce disproportionately more math faculty, most math faculty, if you look across all schools, do not come from those handful of schools. The career path of “pure math” tenure track faculty position at a major research university is followed/reached by very few. Most math faculty would be at an institution where they have heavy undergraduate teaching responsibilities. There likely a LAC undergrad is considered an advantage. In my PhD dept, biological science, those who had a LAC undergrad degree definitely had better luck getting interviews at LACs and other institutions focused on undergrad education (with small or masters only grad programs), however the students were also more interested in those positions.
I’m an applied mathematician, and while I do have a degree (not in math) from a HYPSM, I was the exception in my PhD program. Math undergrad degrees were fairly common in my department, biology is quite quantitative, but a math degree from a HYPSM would have been rare, or if they did, they would have double-majored in math plus something else like biology or chemistry, even those who worked in theoretical biology. In my department, I’d guess that the undergrad origins were 1/3 from Univ of XYZ or a few specific XYZ State schools, 1/3 came from LACs, and 1/3 from ‘name-brand’ private universities (meaning many in the states would recognize the name of the school).
Also my experience is that the path to a faculty position is circuitous for many who work in applied math. Last year, my standard dinner question was to ask applied math faculty while at different institutions where they’d gotten their undergrad degree (and in what) and how they ended up doing what they were doing. It was pretty eye-opening. I realize that the original comments had been about pure math and the poster stated clearly that her comments did not apply to applied math or statistics. I would guess that most research mathematicians are applied rather than pure. I’m mean applied mathematicians are doing research too…
I think it is important to note from @liska21 post, unless I am reading the results wrong, is that the author of the link is looking at pure numbers and not percentages. The NSF data looks at the percentage of students from a school who go on for a PhD. Berkeley pretty much wins in all categories of math and science for PhD grads according to the NSF by pure count alone, until you look at it as a percentage of total students. Then Berkeley drops down. So it makes a lot of sense that the large schools, with their large student body, and their large programs bring about a large number of professors, especially those from technical schools like CalTech and MIT…
A small percentage of the grads from a large school could be 100 math majors. The students will have associations with many different students, and not just math majors, at a large school. Think Venn diagrams…
Having watched DS run the gauntlet (currently in math PhD program), long term goals will make a difference in the answer to OP.
If the goal is to join Academia as a professor, then it is important to come from a top grad program. To get to that point, some of the things to consider at UG level are:
Advanced UG class availability. While the course catalog may look impressive, some courses may be offered every other year or sometimes cancelled when there is not enough students sign up. Helpful to actually look at the class schedule for a given semester to see what courses are actually available to take at any given point. I have been amazed at the difference between the course catalog and actual class schedule at times.
Graduate level class availability: quite important to have these for top programs to demonstrate ability. Grad schools invest large amount of money in the students and want to know the student can make it through the program. Top students often start grad classes by the junior UG year. Some U’s offer combined BA/MS in 4 years.
There is huge drop out rate in math PhD (completion rate well below 50%) and exposure to grad classes will let the student know if they can do math at that level and, just as importantly, whether they want to immerse themselves in it.
Grad school advising and prep help. Formal study groups for the Math GRE (different than usual GRE) as well as active advising would be quite helpful. Some schools have formal Putnam prep also but I’m not a fan of the Putnam myself.
Larger departments tend to have more active visiting lectures and symposiums. These can expose the student to some niche areas of potential interest that they may not otherwise see in their classes. This may influence their choice of grad school as different schools have strengths in different areas of math.
This is by no means to suggest that small schools/programs necessarily disadvantage a student. Simply listing some of the factors that I have seen play out as DS has gone through the process.
Caveat: Letter of Rec are huge in applications. If the student is reticent, an environment where it is easier to get to know profs (HMC for ex) would work better. If they are more of a go getter, can advocate for themselves and get good letters from a big shot prof at a large well known school, then that’s gold.
Also consider schools where a significant (e.g., 100-page), quality thesis is required of all undergrads, where it’s part of the curriculum and campus culture. It shows grad schools that you already know how to do research and write about it. You may plan to write one at any school, but the chances of finishing it are a bit higher when it’s a graduation requirement.
Math is different than literature, chemistry and other fields. Obviously lit students will be writing. Chemistry and other lab sciences will have research with a paper presenting results (100 pages- no way! being concise maters). Math is totally different- coming up with research yielding a worthwhile paper not as common. Therefore some schools may offer the option of taking grad level courses in lieu of doing a senior honors thesis. This is what UW-Madison does. Worth doing research for chemistry, better to take some grad courses (with undergrad tuition, mind you) for math.
ALL undergrads should not be subjected to a writing assignment as stated above. Churning out pages of discourse, often meaningless, is not the mark of a scholar. One size does not fit all. Math research is also much different than the lab sciences. The schools with good Honors programs know what works well for various students and have set their requirements appropriately. I would be leery of math in a school that focuses on humanities plus some social sciences. The math department is more likely to be a footnote even though it, too, is a liberal art.
Another comment based on the thread title. It can be more interesting to have many peers in your major who share your enthusiasm for your subject. The bigger math pond will have students who like different aspects of math. It also may have more students who are better than even the top student from a HS- the one who gets the 800 on the standardized tests. There is a reason the math GRE has a 900 top scale (and most good math students will have an 800 on the regular GRE). Choosing an all around excellent university will have plenty of top other liberal arts to indulge in. This would give the advantages of those along with the sciences.
“ALL undergrads should not be subjected to a writing assignment as stated above.”
Except that for those wanting to earn a PhD, it works; these are schools with a record of high future PhD production in many fields, science and humanities. There are just a few such schools; those who don’t like the writing idea can avoid them.
Very few colleges require a significant thesis of all undergraduates. Very many colleges offer all (or almost all) undergraduates the opportunity to write a significant thesis, as part of an honors program in their majors or otherwise. And I would guess that at 100% of colleges a motivated student could get credit and faculty sponsorship for producing a significant thesis regardless of whether it is part of a department’s formal program.
If a student wants to apply to PhD programs, he or she should probably write a thesis in the undergraduate major. But I don’t know that it’s all that important to go to a college that requires a thesis of everyone (e.g., Princeton), vs. one where it is effectively optional based on choice of major or tracks within a department (e.g., Yale, I think, or Chicago, or Swarthmore), but lots of people write theses; vs. one where relatively few (but among the best) students write theses (many/most public universities). Also, I think math is something of a special case, because as far as I have seen it’s pretty unusual for math departments to require bachelors theses. In math – and, for that matter in any field – I think the best advice is probably to find a good, plugged-in mentor, and follow his or her advice.
Some majors require theses at Harvard, or may require theses for Latin honors, but a thesis is not a requirement for all. Interestingly in math a five page “expository paper” is required of all math majors to be completed sophomore or junior year. As for a senior thesis this is what they say:
I know its been awhile since I posted, but S is now choosing between colleges that admitted him.
Thank you Thank you Thank you for such helpful and concrete advice! Also - what did you mean by HMC? (son does shy away from relentless lobby for attention and wants a smaller environment - but not to the extent it closes everything off)
@listener76 - HMC is Harvey Mudd College. It’s a very small school (about 800) but it is part of the Claremont Consortium (about 5,000 between the 5 schools). So it definite fits the bill (and has been mentioned earlier in the thread but you may not have made the connection to the initials HMC). Of course, the deadline for applying has passed so if your son hasn’t already applied, it’s a moot point.
Thanks again to everyone! S has applied to schools we never would have thought of without this list. St. Olaf, Oberlin, Kenyon, Amherst, Grinnell, Davidson, Furman, Vanderbilt, William and Mary and locally UK and UofL. He is attending math classes at UofL this spring (its nearby) and exploring the brave new world of college while still having the support of home. Your collective, specific guidance about math majors and music have been a godsend, because we were truly lost in how to approach this. (Thanks for the pointer in HMC - it seemed to far away for him, oh well).
The Nobel-Prize winning math PhD dissertation of John Nash was ~30 pages total from what I recalled from attempting to read it after seeing “A Beautiful Mind”.
STEM dissertations tend to be much more concise than their humanities/social science counterparts*.
One friend's PhD dissertation in Poli-Sci from an elite U was ~600 pages. Another friend's PhD dissertation in IR was ~300+...and that's around the norm for her field.
Great schools, but as a group, they seem to represent an offset complement (with exceptions) to those most frequently and credibly suggested on this thread.
Yes, these schools do represent the growth my son experienced as he explored the initial suggestions he got from this thread. It was ENORMOUSLY helpful to have some sort of educated guess list from which to begin a search. The most useful suggestion to him was St. Olaf, which lead him to realize more about what he was looking for - which lead to more colleges. Frankly, it was an enormous, “never ending” task for him, since he really had no clue what college was, and has never been one of these kids who seem to “know exactly where they are heading”. I assume others are benefitting from the excellent input from this group of writers, so I was hoping to offer them an idea about what one kid did with the information. He decided to take a couple of local college courses this year, to get a sense of what college really is - this helped him get much more comfortable with the whole process! He says the most helpful part of this whole thread has been the insight presented on what a math major (and grad school path) really looks like and what different college experiences (BSU vs LAC) might offer an individual who loves both math and music. Now to visit and make a choice. He is fortunate, no doubt. Thanks for your faithful help.
that post may not have been clear - as I review the initial picks, I noticed that he would take a suggestion, say “Williams” and read websites/student blogs and look at Fisk for “overlap schools” and look at them and then notice that Amherst was a better fit for him. This happened with all of the initial suggestions. For instance, he decided he did not want to go West, if there were “just as good” options in the midwest or east. In a similar vein, he was more comfortable with smaller schools than larger schools. Now that offers are dribbling in, he is about to visit and look at the numbers and make further compromises (helped by taking upper class math classes and realizing the posts who said that " BSU departments get small and more intimate at the junior level or above" are right on target. So as much as he liked an Amherst, or something small closer to home, he may well go to UK because the money’s right, the math’s good and there are music opportunities. I guess I am trying to say, thanks for giving him (through my post) the input that allowed him to frame a “gestalt” for making choices, rather than just let a school counselor tell him where to go (which is where he was a year ago).
(and for other parents reading this - our oldest child did not want to do this much work. Scholarships were critical for her as well as for her brother but her strategy was to focus on the PSAT, and then just go to the local BSU. It was easy and I look rather fondly at that college search.)
