Wikipedia:Reference desk/Archives/Mathematics/2010 December 1

= December 1 =

what's my degree worth?
Hi, I have a degree in Mathematics with first class honours, but it isn't really in anything in particular. I focused on statistics towards the end, to boost my employment chances, but even in my honours year, the statistics project was more focused towards the theoretical end, and I studiously avoided learning anything about computer packages like SPSS and R. I wouldn't rate myself as either a statistician or a mathematician; indeed I wouldn't really call myself anything in the intellectual world or the job market.

Now I'm finding it hard to get a job, and I don't really know what my degree is supposed to be worth, either in terms of specific (interesting) jobs, or in terms of salaries. Everyone is asking for the experience that no one wants to provide. I've looked on the internet, and there's some info out there to help, but I'm wondering if anyone has had a similar experience, and what they did. Thanks, It&#39;s been emotional (talk) 09:57, 1 December 2010 (UTC)


 * Your university probably has a list of resources somewhere. They may also have a job-placement service that you're eligible for (since you're a recent alumnus).


 * Also, I suggest that you teach yourself R. You can list R on your resume.  Ozob (talk) 12:27, 1 December 2010 (UTC)
 * What is R? Kittybrewster  &#9742;  12:44, 1 December 2010 (UTC)
 * Probably R (programming language). Staecker (talk) 12:54, 1 December 2010 (UTC)
 * I'd suggest a one-year MSc in something more job-focussed, such as statistics. Everyone on my statistics MSc got a job and relevant experience didn't seem to be an issue. An MSc is often seen as the minimum qualification, whether in industry or academia. Obviously job markets vary by time and place though. With a first-class degree you probably have a good chance of getting funding for an MSc. --Qwfp (talk) 12:39, 1 December 2010 (UTC)


 * The value of your degree is that it goes without saying that you are smart. Your task now is to investigate the requirements of the employer. If you talk about your degree rather than to listen to what the job is about, then your degree turns out to be a drawback rather than an advantage. Bo Jacoby (talk) 12:58, 1 December 2010 (UTC).

I suggest that although when you had the chance to start the degree, and decided to do so, you also decided to lose money, since if you had done something else you would have gained not only the expense of the degree, but the time during which you could have been on the ramp in something else that you could have also done (like computer science). It gets worse. If you could choose to lose your degree at the moment, so that your history is rewritten to live in your mom's basement for the past n years doing nothing, where n is the time you took to get your degree, I am afraid that choice would still give you a positive expectation if you chose it! You would be RICHER in 5 years if you lost your degree today, and gained nothing in exchange. This is because you would no longer be overqualified for the right job to be on the right ramp to be at the right salary for your intellect and abilities in five years, however as a mathematician you are not going to be able to forego mentioning your degree, or coming up with something else plausible that you would have been doing during the time, whereas if you had been living in your mom's basement playing video games, you would be. (You would say you had some corner grocery store clerkship or whatever). Basically, you're royally screwed at this point. About the ONLY thing you can do, and this does not really put your expected value into the positive, is to gamble. There are two ways of gambling. One, is to stay where you are and try to get the kind of tenure at a University which would give you a better quality of life in 5 years than you would have in 5 years otherwise. I suppose the chances of your getting that are about 2.5-3%. (If you do get it, however, you will be "set", starting at 49-60 thousand and, being the right University, working up to 150-200 thousand or more depending on your level of publication). The other gamble would be to really lose your degree by moving abroad, where the degree becomes "I'm an American with a degree!" and puts you in quite a different boat in many sense from Americans you might be competing with. Come to Paris. That's all I can say. I am sorry about your loss of time, but it was for a better cause: Mathematics is an art, you have been investing your life not into increasing your net worth, or potential to earn, but by doing something beautiful. You have gained understanding. 88.182.221.18 (talk) 17:11, 1 December 2010 (UTC)


 * Thanks for those answers. The last one was uniquely unhelpful, but rather funny. Keep them coming if you have more; I just thought I'd pop back and thank people while I had the time. Also I'm Australian, so I could actually go to America and try that one, although I suspect maths is the same over there, unless you vote Republican, where 48% can win an election, and a trillion dollars does not count as government intervention (I really hope I don't get flamed for this, coz I was just mucking around - I'm not really for one side or the other, but I used to be a way-gone lefty). It&#39;s been emotional (talk) 17:59, 1 December 2010 (UTC)
 * You could think of becoming a maths teacher. One or two years doing a teacher training course and you would have pretty good job prospects. Personally I'd try and delay this option as long as possible though.--Salix (talk): 18:43, 1 December 2010 (UTC)
 * Come back in a year and tell me if you still find my prognosis funny. I really and sincerely hope you do! 88.182.221.18 (talk) 20:54, 1 December 2010 (UTC)
 * Have you looked into Actuarial science? There's a very robust actuarial community in Australia.--  SPhilbrick  T  23:45, 1 December 2010 (UTC)
 * People with skills like yours can earn a lot in investment banking, for example. 92.28.255.105 (talk) 00:09, 2 December 2010 (UTC)
 * If you're a good programmer and can study up a bit on machine learning, there's tons of high paying work at the search companies. 67.117.130.143 (talk) 02:47, 3 December 2010 (UTC)

Thanks, some good ideas to start with. I've looked into these sorts of careers, and they always seem to require either highly specific qualifications or 10 years experience and at least some kind of higher degree (Masters or PhD). It doesn't always measure up to the talk, which was all raving when I switched to maths ("Desperately short of people," "great opportunities even with a minor," "50K+ for doing quadratic equations" and so forth). It&#39;s been emotional (talk) 19:07, 3 December 2010 (UTC)

Not to be too pessimistic, however; there's still stuff out there I can try, It&#39;s been emotional (talk) 20:02, 3 December 2010 (UTC)


 * Without reading all of the above, I will respond only to the fact that actuarial science was mentioned and that you think every opportunity mentioned will take so much additional work. And, apparently you are in Australia but I will only tell you about the situation in the US and maybe it's the same.  Here, you have to pass a series of exams, basically, to become a full fledged actuary.  But, you can work while you are passing these exams.  If you pass 1 or 2 to start you can usually get a job without a lot of special skills, other than maybe being good with Excel.  And, the first exam is only probability, so if you are really good with math and have taken classes in probability, it should not take much studying.  And, you often get paid study time to study for these while you are working and get raises and bonuses once you pass them.  This is what I am going into.  The point is, if it's close to the same there, you could actually get a job without a whole lot of extra work if you are really good at math. StatisticsMan (talk) 21:39, 3 December 2010 (UTC)

Thanks, that was very helpful, and you may indeed be right. I've heard this sort of stuff through the grapevine, but I wasn't sure how much of it to take on faith, as against what the Internet appeared to be telling me. Some good insights. It&#39;s been emotional (talk) 21:38, 5 December 2010 (UTC)

Calculus
A Calculus problem someone brought me today: Let p(x) be defined on [0,1] such that p'(x)=p'(1-x). If p(0)=1 and p(1)=41 evaluate $$\int_0^1 p(x)dx$$. How should I proceed?-Shahab (talk) 12:02, 1 December 2010 (UTC)


 * One solution is p(x) = 40x + 1, for which the integral between 0 and 1 is 21. Another solution is p(x) = 2x^3 - 3x^2 + 41x + 1. How did I find that solution ? What is the value of its integral ? There are many other solutions for p(x), but the wording of the problem suggests that the value of the integral should be independent of the form of p(x). To see why, think of the integral as expressing an area, and look for symmetry. Gandalf61 (talk) 13:11, 1 December 2010 (UTC)

The fact that you're getting information about the derivative of the function you're integrating suggests integrating by parts. And then of course you want to make use of the symmetry that you were given. Michael Hardy (talk) 16:53, 1 December 2010 (UTC)


 * What I wrote above is more complicated than necessary. Notice that
 * $$ p(x) - p(0) = \int_0^x p'(u)\,du $$
 * and

\begin{align} p(1) - p(1-x) & = \int_{1-x}^1 p'(u)\,du \\[8pt] & = \int_x^0 p'(1-v)\,(-dv) \quad\text{where } v = 1-u\text{ so that }du = -dv \\[8pt] & = \int_0^x p'(v)\,dv = p(x) - p(1). \end{align} $$
 * Thus we have
 * $$ p(1) - p(1-x) = p(x) - p(0) \, $$
 * or
 * $$ p(x) + p(1-x) = p(0) + p(1) = 1 + 41 = 42. \, $$
 * So
 * $$ \int_0^1 p(x) \, dx + \int_0^1 p(1-x)\,dx = \int_0^1 42 \, dx = 42. $$
 * But the two integrals are easily seen to be equal, so each must be half of 42. Michael Hardy (talk) 19:14, 1 December 2010 (UTC)

Automorphisms of free products
Are the automorphism groups of free products well understood (say, in terms of the automorphism groups of the product's factors)? I can't seem to find any literature on them. Thanks, Icthyos (talk) 12:31, 1 December 2010 (UTC)