Assuming that there are no restrictions on where one could go, what colleges would be the best choices to specialize and learn more about math? Please explain why these colleges would be good.
There are always restrictions.
Not only that but fit matters. A great math school for someone who took the honors math track at an ordinary high school is different from a great math school for someone with a drawer full of international math competition medals, for example.
Depends very much on what you’d want to do with your math major after college.
These highly selective colleges appear in a Princeton Review sampling, “Great Schools for Mathematics Majors”:
Harvey Mudd
MIT
UChicago
Caltech
Harvard
Bowdoin
Hamilton
Haverford
Reed
Rice
Carleton
Grinnell
Macalester
Students commonly face restrictions like:
- Where can you get admitted?
- Where can you afford the net price after financial aid and scholarships?
Also, as suggested above, what level of math will you have completed by high school graduation?
Mathematics departments are very different in terms of their emphasis. There is theoretical mathematics, statistics, math applied to engineering, and so on. I would look at their classes and degree requirements and see which you are comfortable with.
HarveyMudd, Northwestern, Caltech, HYPSM, Williams, Uchicago…
The fit would be VERY different though
@SlateGate
The pure math powerhouses, i.e. the elite of the elite have traditionally been Harvard, MIT, Princeton, Caltech.
Stanford, UChicago, are close seconds.
Here you can find which colleges perform best at the Putnam competition throughout the years. https://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition
The level of maths I will graduate highschool with will be the first year or so or of general college math, specifically up to Calc III and Differential Equations taken online at my local community college. To answer some other questions, I would want to research pure mathematics after undergrad, so I would want to go on to graduate school, preferably at the same school I go to for undergrad.
Cost constraints and state of residency?
I am in Iowa and I am hoping for cost to be minimal.
Is your family low income / wealth so that you may get enough financial aid at those colleges that do give good financial aid? Or high income / wealth so that you need to seek merit scholarships?
Try the net price calculator on the various colleges’ web sites to get an idea of what net price you may see at each one.
By my own calculations from IPEDS and WebCASPAR data, colleges with the highest math PhD production rates (per 1000 math majors) include the following 25:
Amherst College
Bowdoin College
California Institute of Technology
Cornell University
Duke University
Georgia Institute of Technology-Main Campus
Grinnell College
Harvard University
Harvey Mudd College
Lafayette College
Massachusetts Institute of Technology
Oberlin College
Princeton University
Rice University
Smith College
St Olaf College
Stanford University
Swarthmore College
University of Chicago
University of Notre Dame
University of Pennsylvania
University of Puget Sound
Whitman College
Williams College
Yale University
Each of the listed LACs generated at least 10 math/stat PhDs between 2011-2015 (per WebCASPAR);
each of the listed RUs generated at least 20 math/stat PhDs between 2011-2015 (per WebCASPAR).
Each of the listed schools appears to have generated at least 100 math/stat PhDs per 1000 math majors, as represented (imperfectly) by the number of math majors graduating between 2010-2014 (per IPEDS).
This is not necessarily an exhaustive list. I may be omitting, for example, some colleges with high rates but relatively low absolute numbers (< 10 for LACs, < 20 for RUs). Very large universities may suffer scaling effects that disadvantage them in these comparisons.
Program yield ratios (math/stat PhDs per 1000 math/stat majors) for these colleges appear to range from 10%-42%. Compare that to the ~7.6%-34.9% STEM institutional yield ratios for T25 schools reported in Fiegener & Proudfoot 2013, Table 4 (https://www.nsf.gov/statistics/infbrief/nsf13323/).
^ Haverford should be on that list.
These well-funded colleges provide excellent need-based financial aid, should that apply to your circumstances: