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[lohai0]

Where I am now, they offer a MA-in-route to a PhD option.  Since there aren't a lot of students in that program, my intuition has reciprocal transfer agreements with a lot of the other grad programs in our field. Most of the schools are in the area, but one is part of a distance learning where the class is done mostly on-line, and our students sit in on lectures from a distant out of state school via satellite TV.  This might help get around the budget problems with offering more master's classes eventually.

[regular_joe]

See, I never understood the trend of getting a BS and going straight to a PhD program, but this seems to be the norm in math and science. When the trend was BS to MS (with a thesis required) to PhD, you got better (if fewer) students in PhD programs. Maybe it's time to push back against the current trend.

I myself have a B.A. (social science field) and a Ph.D. (humanities field) with no master's degree. (Didn't even get the master's on the way for passing quals as they do at some schools. Where I went to grad school, if you wanted a master's, you wrote a thesis.)

I am not sure whether this is a good thing or a bad thing. Some days I think "good;" other days, "bad."

[regular_joe]

Each UC has a different profile, and I am curious about which school is getting the students you write about and has the programs you describe. UCprof, do you mind saying whether you're from Santa Barbara, Davis, etc.?

[ucprof]

Actually it's not really relevant - the point is that we now have a very popular and highly ranked program that has been getting a steady stream of the top students.  Students that win NSF graduate fellowships are more the norm than the exception - or the ones that do not get them lose out because they do not apply rather than losing out because they are not competitive.  We are mainly competing with CalTech, MIT, some other top privates, and one other UC school for PhD students.  The students from SLACs that do not get into our program, I believe, are going to other good programs.

 I just visited such a program and talked to the students there about their experience.  They complained about being woefully unprepared and that their current phD program did not do enough to get them up to speed for PhD level work.  The faculty in that department may be dismissing the students too readily - I wonder if they spent an extra 6 months or a year working with them on the advanced undergraduate material, if they could get them closer to the level of student that they would like to have in their program.   The faculty there complain that they do not get such good students and they track them as such - training them more for teaching careers than for research careers. 

 I would say that in my field, out of the UC schools there are two that get the top students and the other UCs get a few top students and then the next level of students.  Also by "top" I mean this in an exclusive sense, i.e. both talented and prepared.  I definitely believe there are highly talented students who are not prepared and I have some ideas about addressing that issue.  Another reason that we have succeeded in attracting top students may be that we have excellent federal funding and can offer packages that compete with the top privates, and that we are located in a highly populated major metropolitan area (which narrows it down to a few campuses). 

[daniel_von_flanagan]

Incidentally, there is at least one SLAC which has produced more Nobel Prize winners total (not proportion) than UCLA, including the latter's graduate students. I wonder if their students would meet your course preparation standards. - DvF

[ucprof]

Yes there are some really good small colleges out there and we do recruit from them.  They do tend to be more the exception than the rule specifically on the issue of preparing students to jump into rigorous PhD level courses.
So my comments are not about selected SLACs but more the overall picture of our recruiting portfolio.

[pluto_ii]

as a recent graduate i agree with what you said, there are definitely a lot of very smart undergrads who are not prepared for grad math because they have been completely misinformed about the expectations.  the only ones that can handle phd math or pass the qualifiers within 2 semesters are ones that have been tailor made for grad school from very early on, meaning they are either extremely qualified or are extremely well informed, neither of which can be attributed to their undergrad institution sadly. 

Most undergrad programs(this goes for all schools ivies or not, only in the US however) is designed for someone to come in taking calc I in their fall freshmen and graduate with honors and typically involve a sequence way too easy for some of the more advanced students.  A lot of these smart but unprepared students you're talking about are typically the ones who were ahead in high school but get derailed in college by complacency through this lack of distinction on their universities' part.  For ex. many french and british unis require you to specify the major before you apply so the distribution is pretty even,  my cousin is doing his 2nd year at ecole normale and most smart motivated freshmen on the fast track have completed beginning analysis, topology, algebra and during their sophomore year do a sequence in commutative alg, lie groups, complex at the Lang level, and more analysis algebra topology at rudin,dummit,munkres, they begin one of alg geo or alg top or analytic/algebraic number theory or whatever else during their junior year and these are pretty much considered core.   

There's a lot that can be done by the undergraduate program coordinator as any math graduate call tell you in 20/20 hindsight. I'm still not entirely sure what it is they actually do since I experienced no help whatsoever except for a lot of confusion that almost caused me to not graduate this year because I didn't have some humanities credits, the program secretary and general staff however is superb but that's only the clerical end.  Add to this the general overestimation of ones' ability relative to what's actually needed to do a phd in math and that pretty much explains it. 

From my own experience and I think it's fairly accurate, a lot of students at prestigious universities are puzzled even chagrined at the thought of doing graduate studies at public schools like umd, minnesota, wiscosin, or even ucla, umich, uchicago (yes unbelievable), much less schools right outside of top 20 in math like rutgers, ucsd, uwash etc.  there seems to be too much emphasis on general pedigree and not enough on math pedigrees which is what matters, or lack of pedigree for that matter since math is one of those rare disciplines so old and intrinsic that you really only need a library card and raw technical ability to excel at.  The best thing for the department to do is to communicate to the students coming in what's expected for future studies in Phd, don't make it harder for someone to graduate with a BS since not everyone wants to go to grad school but give them the opportunities at least ie. a seminar on the different branches (there's no reason why you can't do this during first semester or during orientation even), what areas are hot, which schools are good in what areas, show them some profiles of students admitted to harvard princeton phd (lot of people are completely delusional and think they have a good shot and they might if they had known who they were up against, however this blow is slightly softened by the extra stringent requirements placed on the international applicants), or maybe even try to convey the general joy and prestige of finishing a Phd and making faculty in such a tough discipline (this last one might not be such a good idea since mathematicians have a sense of self entitlement to begin with) but I think quantitative finance for one/industry in general is pulling away a lot of talented but complacent students who never really peaked.  As dumb as this sounds, I see a ton of things that can be remedied almost immediately. 

[jackofallchem]

At my university, we have a few science majors that are not to prepare people for graduate school, but for BS level jobs.   We are upfront about it.  There is a declining number of high school students who are capable of handling the traditional science degrees without extensive remedial courses.  About half of our science majors now have to start out in Algebra instead of calculus.  The big stumbling block for them is the calc-based physics.  By allowing some majors to take trig-based physics, they can get through most of the traditional curriculum.  This doesn't prepare them for grad school, however, and I won't recommend someone with those degrees for grad school in chemistry.

Perhaps your school needs the opposite approach.  You need to have an beefed up major for those wishing to go on to grad school (or who want that option) and keep your current degree for people who want to be lab techs.

[bassoonchick]

Hi - this thread touches on exactly what I'm cruising the internet trying to figure out.   I'm a mom with two sons who want to major in math and go on to a PhD program.  One is a college freshman now and the other is a high school junior, so I really have two sets of questions.

1.  My older son is a freshman at Univ of Rochester.  He is in the honors sequence, which starts with Calc I (using Spivak) and has 4 semesters in sequence - even for students who had Calc in high school.  He's not sure if he should sign up for other high level classes until he's finished those 4 core classes (this sequence includes a Calculus series and Linear Algebra).  Students there have a general adviser until they officially declare a major at the end of sophomore year, so he is planning to seek out the advice of a math prof even though he doesn't have an adviser in the math department yet.  He's planning on a physics minor and taking a lot more math classes than required for the math degree.  Also, he plans to get the BA with honors which requires at least 2 grad level courses. 

Question 1 - do you have any experience with undergrads from University of Rochester, and do you have an opinion on whether it will prepare him well for a Phd program?

Question 2 - he would love to find a program to participate in for the summer and he's found a bunch online that even include stipends, but most require him to have completed sophomore year or Linear Alg, neither of which he will have done yet for summer of 2011.  Any suggestions on programs he should look into for a student the summer after freshman year who will have had proof based Calc I & II, Mathematical Logic (he loves Logic so far) and a Statistics class by the time summer rolls around?  He has a great GPA so far if that helps.



2.  My high school junior is starting to look for colleges.  We are in Indiana, so our state schools include Purdue and IU.  He says he's more interested in pure math than applied.  He'd love to go to a smaller school somewhere if it has a good program and he can afford it (which means getting aid).  This is a student who is really good at math and loves it.  We didn't become aware of extra things to do outside of school (AMC, other contests) until recently and he doesn't have a straight A GPA, so I think some of the top notch schools you've mentioned in this thread are probably not in the running for him.  He'll be taking the AMC 12 this year, but I have no idea how he'll do on it - he thinks he'll do well just having prepped at home.  Despite the lack of extra things that prove he's good at math, for the sake of this discussion, maybe you can make undergrad suggestions based on the assumption that he really is talented in math, has A-'s and B+'s in math classes only because he doesn't always  hand in homework but gets the top score on most tests given in the class. He scored 800 in math for SAT and SAT II.  He hasn't had much formal help in learning math beyond the classroom, but sits around looking at math books a local prof loaned him and getting excited about what he learns in them.  He's taking Calc BC now and Multivariable next year as a senior.

Question 1:  So - any suggestions for schools that will give him a great undergrad math education?  I'm assuming he won't get into Yale, Harvey Mudd, etc., but one of you mentioned this earlier - I know there must be great math programs out there that don't exactly have the name recognition of some of these other schools, and I don't know how to find them. 

Question 2:  Any ideas about what he can do to increase the chance of being accepted to a great math program between now (2nd semester Junior year) and next fall?  I've recently started looking at summer programs but he has a great summer job that he loves and is very good at, and he needs the money from it.  We would consider a summer program if it would really open up his world, but not JUST to pad a resume.

Thanks -

[daniel_von_flanagan]

Rochester has an excellent mathematics program, both undergraduate and graduate (though there was a notorious attempt a few years ago to kill their math graduate program), especially for someone with an applied bent.  One thing I suggest for any mathematics major: the core requirements for the first two years in an undergrad math program are usually minima that rarely include fun specialty subjects like combinatorics, number theory, logic, topology, etc.  Partly this is because these are considered hard for a less advanced student.  I suggest your son explore such courses (possibly with the aid of a faculty advisor).

W/r to your other son, both UI and Purdue have excellent pure mathematics programs, as does Notre Dame (as long as we're speaking of Indiana).  There is very little difference in the quality of the faculty at these institutions and those at more glamorous ones.  The bigger difference is in the quality of the students; for example, a one-semester course at CalTech or Harvey Mudd might become a 2-semester sequence at a state flagship to accommodate the ability of the average math major.  Your son should try to find the school where the students are generally at a comparable level of ability and interest. - DvF

[pluto_ii]

summer program like ROSS and PROMYS are good.  They don't give stipends and cost about 1.5 grand I think at least when I attended in 2002.  Mostly number theory and abstract algebra, ROSS has daily problem sets and does everything from quadradic reciprocity to fields and modules, also has a few short courses and some guest lecturers.  The problems can never be finished completely and it's a pretty tough but it'll give him a realistic look at what's out there and his own limitations.  PROMYS is more research oriented and has some group projects and presentations.  They both look really good for college applications and will allow you to jump into a beginning proof based sequence as a freshmen in college.  

IU is very nice and has probably the most beautiful campus I've seen and it's probably a better choice than even some of the top 10 in some areas.  Also IU graduates placed very well this year in some tier 1 schools.  The undergrad can be a problem for the exact reason the guy above me said but I think he's at that point where he's sufficiently exposed and can get some special attention from the department or a particular faculty member.  I don't think harvey mudd or yale is out of reach at all.  Other strong schools with easier general admission requirements but very good undergrad math depts. are umich, uchicago, ucla, nyu, umd and a ton of others.  I can't see any of them not taking him.  

Ideally I would go for a top 10 for undergrad and it's very doable; he has the scores and grades he needs to tie it altogether with the personal statement, the interview, reach out to some faculty members and convey some level of mathematical maturity and establish a fit with the overall direction of the dept.  The last part is basically the approach you take for graduate admissions and though it's largely untested I personally did this with my little cousin and he got in 7 of the 8 schools he applied for.  Granted this may seem contrived and premature for an undergrad but it really can't hurt.  You have to tread carefully and use the appropriate department liaisons, some adcoms particularly disapprove of this kind of initiation.  

[pluto_ii]

if you know what area in particular he's interested in you can pm me for a list of schools

also calc BC doesn't take a year or even a semester really, ask him if he's bored and see if he can switch to multivariate now.

[bassoonchick]

Thank you both for the replies.  I'm glad to hear IU offers a good undergraduate math degree, because it is one he can definitely get into with a scholarship.  He'd rather be at a smaller school (he's very interested in Harvey Mudd, but I don't share your optimism about being accepted!). 

pluto ii - I will ask him if he knows what area of math he is particularly interested in and PM you if he has an answer!

I've heard of ROSS but not PROMYS and will look into both. 

Yes, he does find Calc BC easy (he was tutoring Calc students last year while he was still in Pre-Calc), but he goes to a huge high school and flexibility is not part of the program!  He will continue Calc BC this year and multi next year.  Also, his math teacher suggested he sign up for an independent research/study project next year (senior year).  From what I can glean, they don't offer any help or guidance in getting that set up - he needs to find a college prof to mentor him and figure out what he wants to work on.  He's already found someone willing to mentor - a retired math prof from a nearby engineering school, but I'm a little worried about that because he disclosed to us that he has some serious health issues that may become debilitating in the coming year.  And neither my son or the prof know exactly what they should do, so any ideas there would be appreciated as well.  They discussed self studying a class of my son's choosing.

Thanks again for taking the time to offer some advice so far - more is always appreciated!

[pluto_ii]

I'm not sure but I think combinatorics, number theory, and geometry are good areas for good high schoolers.  Especially if he's prepping for the aime/imo he will see some of this already and he might get a small result out of it, by result I mean he can deterministically solve a specific case of a generally well known theorem or the same problem but with some added complications.  They are nevertheless original since no one has formally written up the solution but it does demonstrate your mastery of the material.  I had the same thing and did algebra as a senior with a local professor and got a result in coxeter groups.  In hindsight it was trivial but it helps us with your application a lot.

Also If he's sure he wants to do math don't bother with all the humanities during his last year so he can work with this professor.  They are meaningless for harvey mudd so just take the most standard ones offered.  If he likes humanities that's a different story.

[havesometea]

Sorry I did not see this topic earlier, but in case adviceseeker is still following it ...
My mathy son really enjoyed the  courses, books, and other resources offered on the following site:

http://www.artofproblemsolving.com/

I have to admit that I enjoy their materials also :-)
Your college student will most likely be too busy, but your high schooler may have fun with the site.