## When non-mathematicians judge the math major

I was going to blog about some serious stuff this morning but then someone (specifically, my cousin Anne Hall) sent me this socialist and feminist redo of 50 Shades, which made me forget everything else. Favorite line:

“You need to go away and sit and think about commodity fetishism and the compensation of emotional labour. Also your obvious issues with women. By the way, how did you get this number?”

Oh wait, I guess I still have 18 minutes to say something.

So yesterday my Facebook page lit up with mathematicians discussing this USA Today list of top 10 colleges for math majors:

- HARVEY MUDD COLLEGE: CLAREMONT, CALIF.
- COLORADO SCHOOL OF MINES: GOLDEN, COLO.
- MASSACHUSETTS INSTITUTE OF TECHNOLOGY: CAMBRIDGE, MASS.
- UNIVERSITY OF CALIFORNIA – LOS ANGELES
- CARNEGIE MELLON UNIVERSITY: PITTSBURGH, PA.
- UNIVERSITY OF CHICAGO: CHICAGO
- CORNELL UNIVERSITY: ITHACA, N.Y.
- WASHINGTON UNIVERSITY IN ST. LOUIS: SAINT LOUIS, MO.
- UNIVERSITY OF PENNSYLVANIA: PHILADELPHIA
- CALIFORNIA INSTITUTE OF TECHNOLOGY: PASADENA, CALIF.

These are some fine schools, but not at all the typical list one would consider. That makes you wonder, how *does* one decide where the best place is for a math major? Scanning this list, I have no idea, and it certainly doesn’t correspond to the places that produce the most research mathematicians. But maybe that’s not what USA Today cares about.

In fact, it isn’t. The methodology is outlined here, and the “full methodology,” which doesn’t actually explain much, is here. But as for figuring out what is actually valued, we get some glimpse:

Factor |
Weighting |
Description |

Graduate Earnings |
||

Early-Career Salary | High | Average salary of bachelors degree graduates from the college in that major with 0-5 years of experience. |

Mid-Career Salary | Med | Average salary of bachelors degree graduates from the college in that major with 10+ years of experience. |

Major Focus |
||

Major Focus % | Med | Percentage of students at the college studying that major. |

Bachelors Degree Market Share | Med | Percentage of all U.S. bachelors degree graduates in that major represented at that college. |

Masters Degree Market Share | Low | Percentage of all U.S. masters degree graduates in that major represented at that college. |

Doctoral Degree Market Share | Low | Percentage of all U.S. doctoral degree graduates in that major represented at that college. |

Related Major Concentration |
||

Related Major Focus (mPower Index) | Med | Measure of how much all the other majors at the college are related to the major. |

Related Major Breadth | Low | Number of closely related majors offered at the college. |

Accreditation |
||

Relevant Program Specific Accreditation | Med | Whether or not the major is accredited by a relevant accrediting body (ie. ABET for engineering). If no obvious accrediting body for a major, this factor is ignored for that major’s rankings. |

Overall College Quality |
||

Best Colleges Ranking | High | The College Factual Best Colleges ranking, a measure of overall college quality. |

So here’s the thing. We mathematicians think that money doesn’t buy happiness, and we don’t care so much about early career salaries. That’s the first thing that sticks out.

But also, and I’d say just as importantly, we do care about the extent to which the average undergraduate math major is exposed to research mathematics, which is why we care much more deeply about the “doctoral degree market share” than this ranking does. I mean, I guess to the non-expert, it makes sense to care way more about the undergraduate focus of a college for judging the quality of an undergrad math major, but it all depends on what you want to have happen next.

I’m enjoying how different this list is from the typical inside baseball list. I don’t even know who it’s for, if anyone, but as a thought experiment it’s interesting to imagine what would happen if suddenly all the math departments everywhere suddenly tried to game this particular system, like colleges do with the *US News* ranking.

So, for example, we’d throw out pure math majors altogether in order to focus our attention on applied math majors that will make loads of money out of college. We’d also compete for students against other majors, something very few math departments actually do. It would be interesting, but I’m not holding my breath.

I wouldn’t care about “market share” at all. “Market share” here just seems to be a measure of how many students there are in the department. A small department can be the best.

What might be more helpful is if they have two lists: one for students who want to continue in academia, and one for students who want to go into industry. The first list could consider percentage of students accepted to the best graduate programs (as judged by yet another stupid list 🙂 ), while starting salary would be more relevant for the second list.

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One possible lesson: define your benchmarks and evaluation models or someone else will define them for you.

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I studied and majored in math so I could teach math, with no consideration for salary. The 16 math courses I took for my B.A. from UMass-Boston were taught by outstanding profs from UMB, MIT, and Harvard. Not a bad deal for $100 per semester! (I graduated in 1975)

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Wow, you just made everyone very jealous.

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I think Mudd deserves its #1 spot! It does a really good job of exposing students to research problems

andproblems in industry. (It also produces a ton of research mathematicians for its size.)The AMS has an award for exemplary programs, which is another measure of quality. The AMS awards often go to programs which have attracted students to the math major who

didn’tplan one as freshmen. That’s a measure of quality somewhat orthogonal to the ones you propose.LikeLike

I second this. Like most elite undergrad-only colleges, Mudd sends a solid proportion of ts students on to grad school, where we do very well. Having excellent research unfortunately often doesn’t translate into providing an excellent undergraduate education. Mudd is full of professors for whom teaching and education are priorities, and that matters – for example, Mudd’s new intro CS curriculum has helped us maintain a gender ratio 2-3 times better than the national average. Determining how to evaluate undergrad math programs is a complicated problem, but it is definitely a very different problem from evaluatimg graduate math programs or simply the research strength or size of the school.

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The good thing about this ranking is that at least they tell you how *they* are weighting the various factors. It would be way cooler if you could change the weightings to get rankings that suited your personal tastes.

I will also point out another not-bad thing about this list: it does demonstrate that there are a wide variety of schools where one can have a meaningful mathematical experience.

I think you’re right that few Math Depts compete for students from other departments. There are a number of Departments that make it easy for students who have to take a lot of math for their major to complete a double major (or math minor, at least). I think that’s a good thing, so I would including that (percentage of majors who are double majors) in my ranking (though it probably runs counter to a factor like “percentage of students who go on to graduate school”).

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In some schools a math major is a fallback option for students who don’t succeed in the major they really wanted; when the desired major had some math requirements, it is then not so hard to complete the math major requirements to get a degree. So if you want to count students who switched to a math major, you have to somehow distinguish between students who did so because the math major is awesome, and students who did so because they had little other choice. (One can usually get some idea by looking at the student’s transcript.)

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I wonder if the CBMS data on undergraduate mathematics (http://www.ams.org/profession/data/cbms-survey/cbms) contain enough information to do an interactive ranking like this (but better — with the ability to re-weight various factors). Would it be valuable for the Mathematics Community and/or for the World to have such an instrument??

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Yes it would. For all kinds of rankings.

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If you get the funding for this I can help with the project management. It would need to be entirely open source and easy to use.

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“We mathematicians think that money doesn’t buy happiness, and we don’t care so much about early career salaries.”

For someone who cares about precision and analytical rigor as much as you do, that’s an AWFULLY broad statement to make. Not even “most”, or “many” as a qualifier? Do they care about it less than English Lit majors? Than Religious Studies degree candidates? Do good mathematicians care about it less than average mathematicians? Pretty sweeping stuff, Cathy.

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I’m basing that on the fact that most of them aren’t paid very well but don’t quit their jobs. They care about stuff like freedom to think about things that interest them and travel. I don’t think it’s too crazy a theory.

On Tue, Feb 17, 2015 at 4:13 PM, mathbabe wrote:

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