My daughter graduated last year and received several job offers. She is now happily working as a systems engineer at a highly regarded company. Everything worked out for her, but I think that a lot of the math heartache could have been avoided if 1) she knew ahead of time what she was getting into and 2) bailed out of math once it started to cause her extreme stress. We are proud of her for sticking with it because she came out of it stronger; however, I’m still not sure whether all the angst was worth it.
I should add to @prospect1 's comments, that 300 hours is most likely nowhere near enough studying per exam. You will typically be studying 500 or more hours per exam, and still failing often. And remember, these people were the smartest kids in school, never close to failing anything, now routinely getting kicked in the gut by the Society of Actuaries. It’s very upsetting and humbling. I say this from experience, being married to the record holder for most exams failed before completing them all.
To add to Post #57 from @comeonpeeps :
Due to the way that high school math is taught in the US, there is no way to predict which excellent high school math student (male or female) is going to be able to reasonably get through the Theorem/Proofs courses, which make up the core of the undergrad math major. I was one of those great high school math students who slogged my way through proofs etc. as an undergrad, and slogged my way through math grad school. This was over 25 years ago, and the field has gotten much more competitive since then.
Math departments at the elite privates and public u’s are going to attract the types of students that will have relatively little trouble with those courses because
a) they have been trained in the “out of the box” way of thinking about math since middle school, primarily via AMC type contests/activities -or -
b) they can pick it up very quickly
The Art of Problem Solving web site has already been mentioned in this thread many times, and I would suggest that any future math major check it out.
This is really not about LAC vs large university - it’s the nature of the “math beast” if a student wants to pursue it beyond the undergraduate level. A supportive LAC environment for math majors would be attractive to many students. And a well rounded education from a good LAC can be great background for a career with a quantitative emphasis. However, they are going to face the competitive math students in any good, respectable grad program. Plus, those grad programs also attract formidable math talent from Europe and Asia (both male and female).
Pure math at a higher level (grad school and beyond) is performance based in a way that is more similar to music than to other fields. Applied math is less so. And stats has enough variety that one can choose among various paths.
Math is a field that can be frustratingly self-serve in terms of outcomes after graduation because the career paths are somewhat poorly defined. I’d broadly characterize the different paths as academic, education, financial, and engineering. In terms of academic rigor I’d say generally education < finance <= engineering < academic. In terms of money I’d say academic < education < finance < engineering. It was an observation of mine (as a graduate with a double major in math and engineering) that despite the fact that math was as difficult a major as engineering, engineers tended to make more money because of supply and demand (similar story for engineers vs doctors for what it’s worth). Also, for math your outcomes depend very strongly on how you structured your own learning - it isn’t standardized the way engineering is.
On proofs: they exist, they might be hard if you’re not used to them or not good with logic. Honestly I wouldn’t worry about it - if you have a strong natural understanding of math and mathematical principles from calculus, then mathematical logic is pretty intuitive. Most people who struggle with proofs either memorized their way through calculus or weren’t good at it in the first place. To be honest I think you should know by calculus if math in general is for you.
On the different disciplines:
Academic is the kind of math that leads to graduate school and a doctorate program, then a job in math research. You probably want to do mathematics research for this path, focusing on the more theoretical side of math. You also want to learn all or at least most of the traditional mathematical fields, the kind that are associated with the qualifying exams. A decent list of them is given by UCLA: http://www.math.ucla.edu/grad/handbook/quals
These topics are very tough if you want to learn them in any depth, and to put it very simply, I will say that if the academic path seems like it might not appeal to you, then you probably won’t change your mind. Adjusting for intelligence, it’s one of the lowest paying careers there is because your only employer is academia.
Education is a path to grade school and community college teaching. Academically it’s probably the simplest - you won’t be teaching past calculus, or DiffEq/LinAlg if you’re particularly ambitious. You will probably need to take a standard math sequence up to analysis, including geometry, and some courses on teaching. Generally it doesn’t pay that great, but offers good job security and good benefits. If you’re smart enough to do a PhD in math at a top school then you could probably find one of the few high-paying teaching jobs as well.
Finance is the Wall Street/actuary path. The actuarial exams as previously mentioned are strongly rooted in probability, statistics, and economics. Also very useful is a working knowledge of programming (computer science classes and computation classes) and classes for dealing with data (linear algebra and numerical linear algebra). It pays pretty well, though it’s not particularly easy. Financial institutions and insurance companies are the standard employers here.
Engineering is generally focused on mathematical solutions to engineering problems. It can involve programming and computation (computer science and classes like numerical analysis and scientific computing), solutions to physics problems within engineering (differential equations and numerical analysis), and advanced quantitative/computational skills in general (linear algebra for data, probability and statistics, lots of different software skills, some engineering experience). If you play it right then you can manage an engineering job with the math degree, which pays as well as an engineering job does. Usually it’s an “applied math” job of some sort in an engineering capacity. Closely related is applied math work in a more academic “science” capacity, which would fall somewhere between “academic” and “engineering” in both rigor and financial considerations.
To put it simply, a math degree is what you make of it, and if you get one without a goal in mind then you will probably get nowhere. You should figure out what you want to do with it and pursue that goal (choosing schools and classes accordingly) to pursue one (or more) of the paths as above.
Thank you @NeoDymium. This summary was most helpful.
To parents who want a “nurturing” environment for their D’s. I guess I’m used to very independent women who do not need that. I and likeminded women friends were better nurtured at a large U where we were able to get intellectual/academic nurturing through excellent courses rather than mothering.
Another comment on being good in math in HS. Most of us were not in the same league as the math majors- our math skills were good for sciences requiring the ability to use math, not pursue it in depth for itself. Wisconsin has more than one calculus sequence- Honors has a theory based while the regular is problem based- different approaches for different wishes/needs. I question a school where “one size fits all” for STEM courses, unless it is a purely STEM school. But, I am a science person who rounded her education with the other fields, not someone who accepted limited choices in the sciences.
LACs, at least the one I’m most familiar with, offer different paths as well. I know there’s more than one beginning Calculus, Chemistry, Stats, based on previous experience and desired direction (not counting those who might skip an intro, which is somewhat rare but doable). I’m thinking of Stats - one intro is based on modeling, one isn’t, and there’s a long explanation on the dept web site as to who should take which one (to take the modeling version you should have had Calc, maybe AP Stats). Similar guidelines for the others.
They do converge at some point though, and everyone has the same required courses for the major after the first semester or two.
@NeoDymium Nice summary. There are also many math majors in my field, resource management. These people typically got an undergrad degree in math and then went on to graduate school in Biology, Zoology, Oceanography or Fisheries. Fisheries is very quantitative so full of people with b.s and m.s. degrees in math. PhD in (applied) math is much less common though some of the top ‘thinkers’ in these fields come from that background. Training in modeling and statistics (esp. Bayesian) and informatics is especially important in these fields. Ability to communicate and work well in interdiscipliniary teams is really important if you go in this direction with a math background. Also you’ll have a hard getting a job (undergrad or post-undergrad internship) without classes in the whatever field you are aiming for (Wildlife, biology, oceanography, fisheries, earth sciences…). Then there is the whole academic theoretical biology side—job prospects there are limited to academia however.
Though I describe myself as a applied mathematician (research in time-series analysis), my own path went through Mechanical Engineering + Biology --> Zoology PhD (theoretical biology). The Mech Eng training was very useful because it was all about taking real world problems and figuring out reasonable solutions, which in Mech Eng involved math & models.
H’s path, also an applied mathematician, was Math B.S. --> Stats M.S. --> Operations Research PhD which led to a career in computer science, not writing code but working on algorithms related to image processing and compression.
Wow, this thread has been a real source of information. I think I’m going to print it out and keep it in our college folder for future reference. Thank you so much to all the mathematicians out there giving free advice, opinions and providing resources. When D decided to major in Math, I don’t think either of us knew how broad the subject/career range could be. Of course, she will need to fine-tune it but there are so many avenues it’ll take some time to figure it all out.
This thread is a most excellent thread! Thank you everyone!
Thanks @comeonpeeps. If she takes after me, she won’t be breezing through. I had the interest in theorem/proof Math, but lacked the discipline to put in the required time. Hopefully she’ll be different.
@clowncar, I would third the suggestion by @ordinarylives and @ucbalumnus of applying to, and starting out in Engineering if she thinks she might want it. Maybe it’s possible to apply as a double major - Engineering and Math - to avoid the problem of transferring. I’m not sure if you can get accepted to two majors out of high school , but I’m sure someone here knows.
If she starts in Electrical Engineering and switches to Computer Science, the first few EE courses will not be a waste of time at all. They’ll actually give her a much better foundation, in my opinion, even if she ends up in software.
I really like the idea of a consortium as a way to get the best of both worlds. Does anyone have any first hand accounts of students having success cross registering for upper division Math or CS electives at one of the bigger schools in a consortium? You hear about a lot of kids at LACs not getting the classes they want. I’m wondering if the same thing is happening these days at universities, due to budget cuts.
Math, as a major, isn’t easy for anyone, even the brilliant ones, and I can attest to that from experience (mine and that of the other top tier math students I studied with). Though they might always end up getting the grade and acing the exams, it is always borne of a long, painful process of learning the material, with plenty of frustration, and plenty of failure along the way. It only looks like a breeze from the outside; rest assured that the brilliant ones struggle as well.
@NeoDymium, I told my son that people would view a math/econ major very differently than an econ major. In his case, he did math major lite (9 courses including real analysis and algebra but not differential equations or complex analysis). He did find it easy, but he was at an LAC (one of the most selective) but the competition was not as great at a school with a top math department (when I was an undergrad, I took a course from John Nash’s advisor and there were five people who placed in the math olympiad in the class). I didn’t find it easy. I also didn’t find it competitive, for the most part, but the difficulty came from the challenge of mastering relative abstract material.
I honestly am perplexed about advice relative the the gender gap in math. I’m sure there is unconscious sexism there. We’re not talking about folks with the greatest EQ or self-awareness, usually. A bit like software. So the question is whether your D brushes shoulders and learns from with the best or whether she has a more secure learning environment in which she develops the intellectual confidence and skills without the implicit put-downs. At some point, whether she is female or male, she will be competing with everyone.
I think the LAC/uni divide here is being caricatured (and misrepresented) as nurture without challenge vs. challenge without pity. Maybe I’m wrong, but that’s not quite how I see it. So here’s another analogy. I think research universities present students with a wide assortment of hole-shapes to plug themselves into: round, square, pentagonal, oval, free-form, etc. The hole shapes represent different topics combined with the different instructional styles of faculty members. It’s each kid’s responsibility to figure out how to plug him- or herself into each hole, and which holes to avoid because there’s no way to reshape oneself that much. At LACs, in small departments (like math, at most LACs), when you get above the introductory level learning is very much a collaboration between the faculty and students, with the faculty effectively cutting holes (or trying to) to fit the students they have. The goal is not to coddle the students or go easy on them. The goal is that at the end of the process their students are as prepared as anyone to compete at the next level. But the process of getting there is more individually tailored. At the cost of some access to the cutting edge and being part of a larger community of mathematicians.
I once wound up at a dinner with an entire small department of a top LAC. Just listening to them chat, I was astonished at how well they knew their current crop of majors, and how personal their attention to the students was. At this social occasion, what they talked about was what each student needed from them, and how to provide it. It was completely admirable. Of course, this group was less than a quarter the size of what a decent university department would be, only one of the professors really had a high profile in the field, and among them they didn’t really have cutting-edge expertise in every part of the field. But their students were getting their needs met in a way that doesn’t happen even for star undergraduates at equivalent universities, at least most of the time.
I would not say that it’s always better in terms of ultimate outcomes for equivalent students, but I am convinced that it’s not always worse. And the recent experience of one of the kids I know well bears that out. No one, including her, would have suggested that her highly regarded LAC had faculty strength or critical mass in math and computer science equivalent to Harvard, MIT, or Berkeley. But the job she had when she graduated was the exact job she dreamed about getting when she started college, and her co-workers come from Harvard, MIT, and Berkeley more than anywhere else. And everyone has strong suits and weak points, but overall she was not less prepared than they for the sophisticated, job-related training they have been receiving.
Cutting edge expertise? In math?
If that even exists, how relevant is it to an undergrad math student?
I will note that it is very difficult to have any meaningful contributions as anything but a doctorate student in academic mathematics, simply by virtue of the fact that you actually have to learn all the fundamentals before you can make a real advancement. Performing experiments is less helpful than in science because math uses proof rather than evidence. You can still get your name on papers by making a “logistical” contribution (which is meaningful, as you do have to learn a lot to write intelligently on a math topic and writing/grunt work is a valuable skill to learn for real research) or by working in more experimental/applied subfield of math like engineering or economics.
Getting into a top graduate school in math is an odd affair, to say the least. It’s hard (though far from impossible) to prove that you have meaningful research experience for any highly academic subfield. Applied is easier, but also tough.
On sexism: Anecdotally, I noticed far less sexism in math than engineering. While high-level engineering classes were severely skewed towards male (80-90%, 60% in more medically oriented engineering), math classes were only slightly skewed male (50-60% male). Very skewed in graduate school though - in general women are smart enough to know that math grad school is a bum deal, economically. Men, a lot of them either don’t know or don’t care.
To clarify, the department I described was not a math department.
I do see the merits in a more LAC-style approach to undergraduate mathematical research, which focuses more on designing a project that undergraduate students can complete than in doing “real research.” Since you probably won’t be able to do any real advanced math as an undergraduate, it might just help to be taught how to actually do more advanced research in a controlled and directed environment rather than in a realistic one. It really depends on the student.