I am future math major who will be applying to universities in the coming academic year. I am certain that I want to be an academic mathematician, so I will be pursuing a PhD after undergrad.
Aside from the obvious choices of Princeton, Harvard, MIT etc. I am also looking at LACs such as Harvey Mudd and Williams. My one misgiving about these colleges is that by the time I enter as a freshman, I will have finished an equivalent of Calc III, Lin Alg, Differential Equations, and Analysis 1, which means I may be at the level of graduate classes by my junior year. Since these LACs don’t have grad schools, will I be missing out on the graduate level material I could be getting at a larger university? I have heard that small colleges offer one-on-one/small tutorials for advanced material, are these as good as graduate classes (both in terms of content and grad school prospects)? Or is the experience of getting through the material with other top students irreplaceable?
Many Mudders come in with a background similar to yours. You would be tested for placement (and quite a few students don’t pass out of every course they have taken in the past due to the rigor of Mudd’s expectations). Math majors can easily find professors to do research with (remember that there are no grad students standing between you and the profs at a LAC, so the profs have an strong interest in engaging undergrad students in research). I haven’t heard of a math major at Mudd being unhappy with the offerings or experience there. Mudders come out of undergrad well prepared for grad school in terms of coursework and research experience.
Look at the course catalogs for each college of interest. They are online. Are there enough courses to interest you- enough for one course in your major per semester? If the answer is yes, great. If not, then you have your answer.
Harvey Mudd is STEM specialized and among the best of its type. As noted above, their PhD outcomes are among the nation’s best.
Williams and Hamilton are liberal arts colleges (unspecialized, unlike Mudd) with particularly well-regarded math departments.
You won’t have any trouble getting into a top math grad program from Williams! Their students do so. But the question is if the undergraduate math offerings provide enough stimulation to sustain you through four years. Take a look at the course catalog, and maybe call and chat with the head of the department.
Also ask yourself: Which type of experience do you want? Liberal arts or technical/specialized?
One difference between HM and Williams is the HM is in a college consortium and reasonably close to a major city with more universities, and Williams is very isolated, so your options might be a lot more limited at Williams I imagine.
Looking through the course catalogs, there are probably not enough such courses. However, there are also independent study and senior thesis options; will they fill the gaps?
Additionally, is one course per semester in math all that I’ll be getting at a LAC?
Seems like a school with a good math PhD program would be much more favorable, since you could take the regularly offered graduate level courses (instead of hoping to fill in gaps with independent study), some of which also function as recruiting grounds for research opportunities. Additionally, if there is a large number of math faculty, the number of subareas offered in courses and research opportunities is likely to be greater.
Really, your situation of the highly-advanced math major is one of those where most LACs are unlikely to be academically fulfilling.
Do you have affordable safeties in your application list? Princeton, Harvard, MIT, Harvey Mudd, and Williams are reach for everyone.
A math major who has completed the lower level courses (calculus, multivariable calculus, linear algebra, differential equations, maybe discrete math) typically takes about two upper level math courses per semester (about half of the total courses during those semesters), but may take more depending on interest and schedule space.
@zazerbayev - if you’re certain you want a PhD in Math you should really be looking at what schools will give you better research opportunities. Some of the best Universities have fantastic opportunities but you’ll need to arm wrestle a lot of classmates to get at them. At a smaller school the opportunities may actually be better to get your name on published research before you apply to grad school - and that will be more meaningful for grad school admissions as well as more challenging personally than cramming your schedule full of courses.
Also - and I am trying to say this kindly - don’t assume your high school classes educated you to the level that an MIT or HM will require. Maybe they did but - ask those schools what percentage of the incoming freshman who took your same courseload in high school test out of those courses in college. The answer might surprise you.
@TheGreyKing Mudd IS a LAC. It only offers STEM majors, but students also have a secondary concentration in a humanities subject of some kind. And they have the depth and breadth of the whole 5C consortium to draw from for those classes, too. My kid took humanities electives beyond her secondary concentration, too.
OP, my kid took 8 math classes at Mudd, and she was not a math major. Some of them are half semester (and cover what most schools cover in a full semester). There are a lot of math courses she didn’t take. You’d take two or more pretty much every semester.
You can take more if you like. As an English major back in the day, I had to take nine English courses, which meant I took one per semester except for one semester when I took two. That was all I wanted to take, because I was enjoying the ability to learn a little bit about a whole lot of subjects. But each person is free to design your own course of study.
But if you do not see enough math classes of interest to you, even for the minimum I described, I think you may wonder if it is the best place for you.
@intparent , Yes, I do know that Mudd and MIT and CalTech and their ilk offer classes beyond math and science (art, history, language, etc.). But they specialize in STEM, and most people would go there to major in a STEM field. My sentence stated that Mudd specializes in STEM, whereas Williams and Hamilton do not have a specialization… which I think is a fair description, no? I guess I put the parenthetical part in a spot that made the meaning confusing.
The secondary concentration at Mudd sounds really cool, and it is great that they have the consortium!
The numbers of math majors at many of the top universities do not support this generalization.
General math majors (i.e. not applied math or stats) graduating in 2017
34 Williams
42 UCLA
39 Cornell
38 Columbia
33 Harvard
32 Princeton
31 Duke
28 Stanford & Yale
12 Brown
Liberal arts colleges fare well in PhD production when you use the overall enrollment figures. They fare much more poorly in fields like math when you calculate using the numbers of students in each discipline (an apples to apples comparison).
Mudd is really not the same “ilk” as Caltech and MIT in that respect. The Mudd mission statement says, “Harvey Mudd College seeks to educate engineers, scientists, and mathematicians well versed in all of these areas and in the humanities and social sciences so that they may assume leadership in their fields with a clear understanding of the impact of their work on society.” My kid actually picked Mudd because, as she said, it was her “best shot at becoming a polymath.” (Definition: A person of wide-ranging knowledge or learning.) And as a Mudd grad, she says she got exactly that.
I’m not dissing Williams at all, my nephew went there and I think it is a great school. But I think your understanding of Mudd is incomplete – it is not second rate when it comes to the overall LAC experience. I agree that non-STEM majors probably shouldn’t apply there – it is technically possible to major at one of the other colleges in something non-STEM (about 2% of a typical graduating class does so), but only done in rare circumstances when a Mudder realized partway through their course of study that STEM isn’t really where they want to focus after all. But Physics, Math, Chem, Bio – they ARE liberal arts, too, and 60% of Mudders major in one of those.
Since the OP knows they want to major in math, Mudd seems like a fine fit for them. And I don’t think they’d lose a step in terms of any non-math interests.
If you were to analyze strong LAC math departments in order to obtain an approximate course count, you might find the following:
About a dozen junior and senior level math courses other than real analysis that would be new, or mostly new, to you.
Sophomore level courses in topics such as counting and codes or linear optimization that might explore areas that you have not yet have covered and overlap with your interests.
Mathematically oriented courses from the physics department such as those in general relativity and mathematical physics that might appeal to you.
A selection of seminar-type courses that would, most commonly, be taken by seniors, but which you could request to take at an earlier time as well.
The option of a Budapest semester, which would expand the range of topics available for study.
In a best case scenario, then, you might find about 17 courses of potential interest to you that, with a semester abroad, you could choose from over a span of three and a half years at your home institution.
For a fair evaluation, consider the course offerings at colleges such as Harvey Mudd, Williams, Hamilton, Bowdoin, Haverford, Reed, Carleton and Grinnell. Should any of these programs seem sufficiently advanced for your level, you can then contact the respective department chairpersons for advice specific to your further concerns.
