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Seeking University Jobs in Mathematics?
NegativeK asks: "I'm currently a high school student, soaking up all of the math I can. Via a state program, the education department pays for my enrollment in a semi-local university, which is allowing me to take four mathematics courses at a time. My question is this: am I chasing a white-elephant? How much does it take to get a job in theoretical mathematics? What does it require to get a stable job in a university to do math research? This also applies to other theoretical positions; how competitive is the workplace in a research university?"
Well I am a junior math major at a not so pristegious university and I would say that I am in the same boat. I posted a topic similar to this on the alt.math newsgroup and I got about 50/50 = "go for it" / "Stick w/ computers and keep math as a hobby"
If I were you I would take a few more classes until I make a lifelong commitment. Math is one of those subjects where the upper division work differs greatly from most of what you see in ugrad/hs.If that hasn't scared you enough then try the AMS Job Search just to see what type of positions seem to be open in your state.
Also (although you seem quite gung ho about theoretical research) keep your mind open about other subjects for your graduate degree. Bioinformatics departments seem to want mathematicians at least here at UCLA. Not to mention if you read in last months issue of AMS's "Notices" (would link but unless you are behind a a school's firewall you can't view it) they have an article about the shortage of Phd's in Math Ed. (which is more cognitive science than math). So, I know where you are comming from. Pure Mathematics is quite a leap of faith but it's one that I am {smart|stupid} enough to take.Will anyone care enough to pay you?
P.S. I Can. No one cares.
You are being MICROattacked, from various angles, in a SOFT manner.
It's all about tatics, Reffer to this Use that as a guide and I'm sure you'll get a nice cushy job at a good college. All the best mathematicians do it man! ;)
~Anztac
You said yourself you're trying to soak it all up. So why are you asking about how you can limit yourself?
Archimedes prophetically predicted the fall of the roman empire because they only funded practical mathematics research. The Romans, lacking any theoretical mathematics to base new ideas on, did in fact decline. Their technology had hit a wall, much the same way that we have with unification. The mathematical underpinnings of chaos theory languished as an oddity 50 years after being discovered in a dead mathematician's mother's attic, before being used.
If you think about it, the romans had everything they needed to build steam locomotives. They had advanced road building, knowledge of steam dynamics, the ability to forge pressure vessels and an unrivaled industrial base. What they lacked was vision and the will to do anything that might seem impractical.
Hats off to you and godspeed.
If voting were effective, it would be illegal by now.
However, the statistics are a bit pessimistic. About 50% of the applications are pretty wildly unqualified (the extreme example being MS holders applying for a Ph.D. position). If the search is looking for particular expertise and you have it, another 50% of the survivors will get tossed out. Obviously, it's still tough, but not impossible -- especially if (a) you're good at what you do and (b) you persevere.
You can also do research outside universities. In fact, if you don't have a desire to teach, it can be better to avoid academia. Some industrial research labs want mathematicians. There are also pure industry spots: for example, I think Wall Street is quite fond of math right now (though a lot of it might not be research, depending on how you define "research").
A lot of the above applies to other "paper and pencil" disciplines, such as CS theory.
An upcoming bright spot is biology. After centuries of trying to get a handle on a complex topic, the bio folks have finally started to develop models that are tractable with the help of computers. If you develop an interest in that particular sort of math, you might discover that there is huge demand by the time you graduate. The field is hot enough that we've added a new bio/math major.
Above all, though, my advice to all people seeking a career is the same: follow your heart. You're going to be doing it for 40 years or so, and that's a lot easier if you're having fun. Also, getting from high school to a math Ph.D. is going to take around 8 years, maybe more (I took 13, not counting time spent working, but I'm in a time-consuming field). Who knows what the job situation is goinig to look like 8 years from now? Maybe Enron Jr. will be hiring all the mathematicians it can get its hands on to develop models of how to scam the energy market. :-)
chance of you getting a great math job: are you a genius who is willing to devote alot of effort to it?
chance of your math major being usefull while trying to find very good computer jobs (I'm talking the real stuff): very good
chance of your math major with a cs minor landing you a freaking nice job (assuming of course you actually are very bright): very high
so in the end, I'd say learn your maths well; and learn your CS well. If you know both you can get a good job doing something that it sounds like might be intersting to you (might not be extremly well paying, might be though)
I live in a giant bucket.
OK, I will add another question to this. What are the chances of landing a similar position in Computer Science? Some theoretical stuff such as PL design or something like that. I heard that the .com boom pulled a load of gradschool people out of the universities pursuing the $$$ and that there was a shortage of researchers. I would love to do my PhD, but academic job availability afterwards is a issue I have to consider.
The dangers of excessive individualism are nothing compared to the oppressiveness of excessive collectivism
I think CS could have been great, but the cheaters completely destroyed it for me.
Most universities expanded dramatically in the 60s... that faculty is retiring over the next five years. Many mathematics departments are losing 40% of their faculty within a five year window.
Jobs are going to be available.
Tarsnap: Online backups for the truly paranoid
I got a PhD in (Pure) Maths at Brown in 1997 and I got a tenured position (in Europe, though) 2 years ago, so I suppose I'm qualified to say something: if you like the idea, definitevely go for it!
The market is really, really, really cyclic: there are years when Harvard graduates with decent teaching experience cannot get a job (like the end of the 90's) and there are years when it's difficult to find decent candidates.
Here in Europe it's easier since the cycles are different in each country, so people move around.
If you want to stay in the US (which I didn't, BTW), I'd advise you to get a MSc in Computer Science while working towards your PhD: at least at Brown (but I suppose this is common), you may do that for free. In this way, if the job market is really bad, you can always find a decent (and so much better paid) job: a good part of my colleagues did so, and many ended up getting a job in the real world.
Feel free to write me if you want to ask some more.
If you can show a breadth of research in your field, you'll boost your chances. I saw the review process when we hired faculty. Most applicants had one research idea, which had been fed to them by their advisor. The best applicants had several viable (fundable) research ideas to pursue.
If the universities you're interested in have a boat-load of money coming into the math dept., then it may not be so difficult because the resources will be more likely available to you. However, in some universities, where the math depts are small, it pays bigger dividends to have more knowledge when matriculating. This is because you'll have more of the professors' attention and therefore more funding for any research you want to do.
"...today consumers have been conditioned to think of beer when they see a bullfrog..."
I'm going to receive my PhD in economics this May at the University of Michigan, which is probably ranked somewhere between 10 and 15 nowadays. I'm not looking for an academic job, but I've heard from my classmates who are that they haven't been doing very well. If you want a position at a good research university, you better be coming out of a top-notch program.
Sig (appended to the end of comments you post, 120 chars)
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High School: Very high GPA, Very high SATs, Very good letters of recommendation, so that you can...
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Get into a college/university with an excellent undergraduate math program. Then, get very high GPA, Very high GREs, and three letters of recommendation from faculty with PhDs, so that you can...
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Get into a university with an excellent graduate math program. Ignore the university's overall reputation; go solely with the department's reputation. Math isn't my area, so I can't give a recommendation. However, some departments in the really prestigious schools suck. Some departments in somewhat obscure state schools trounce the Ivies. Get solid advice. Then, get publications. The more pubs the better. Do an outstanding dissertation in a reasonable amount of time. Get excellent letters. Then...
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Get a job. I like to tell our recent PhDs that once they get a job, all they have to do to keep it is to do 2 dissertations per year plus bring in money plus teach! There will be several hundred applicants for each job. Post doc experience can help. Then publish, publish, publish, get grants, get grants, get grants. Teaching is secondary. In many places, reverse the order: grants count more than pubs. Some places are even specifying how much in grant money you must bring in.
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Get tenure. Tenure is all or none: if you get it, life is good and it is why people put up with all the crap above and the below-industry salary and the outdated infrastructure and the administration. If you don't get it, you are a failure and will find it hard to get any other job in academia.
If you like doing your own research, you cannot beat a tenured faculty position. If you don't mind someone else telling you the general research area, then go into industry.Goddamn you lazy fvck, go do your own research.
This isn't Monster.com
Our experience is that getting jobs with a math degree is not that difficult (if you look hard).
Each of the 20-30 Ph.D. graduates from our department (http://www.math.twsu.edu) has received a job; about half were in industry and half received tenure-track positions. Although our university is not as well known as many others, our Ph.D.s have tenure-track (or tenured) positions at Georgetown University, the University of Arizona, Middle Tennessee State University, Georgia Southern University (?), etc. One of our (1996) Ph.D.s is a vice president at a private company ($20 billion(?) annual revenue) based here. Other of our Ph.D.s work in industry in Boston, Alabama, etc.
Our Masters and BA/BS students also are doing well, working at universities, for insurance or reinsurance companies, the aviation industry, software companies, etc. One of my undergraduate students attended a NSF R.E.U. at Cornell, wrote papers with faculty at Cornell and with me; he graduated last May, got a job in KC, "reinvented" the job so he can do math and programming, and may make a substantial contribution to his employer. His long term plans may include earning a Ph.D. in math.
The reputation of the university is important, but a student's effort and ability is much more important. I think the future is bright if you work hard, have ability, learn as much as possible about computers/software, look for opportunities (e.g. REUs, postDoc positions at Cal Tech, Stanford, Brown, etc.), considering earning an additional degree (e.g. EE) while completing your Ph.D. in math, etc.
PS A lot of university math faculty will retire in the "near" future. We are trying to fill three junior/senior positions right now. (I hope the state does not run out of money.)
and I mean advanced math, you can do anything. CS and engineering both are based on it.
BC
the job market for mathematics is just about to explode. the majority of faculty members are within 10 years of retirement, and there is simply not enough new phds coming through the pipeline to meet the demand.
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however, if you are not passionate about mathematics then your chances of obtaining a phd are in every neighbourhood of zero. in fact you would not likely graduate from an honours undergrad program.
if you are, then i urge you to follow your dreams and work very hard during your undergrad degree. you will (presumably) be broke and extremely busy for 4 difficult years, but once you get into grad program life looks very very good. excellent grad students can get paid circa $us 22k a year to go to school and there are plenty of opportunities to travel.
the life of a tenured professor, teaching and doing research, is one of the most honourable and privileged careers in our society. note that i didn't say lucrative.
so go for it, and good luck !
ps: be sure to take a foundations of mathematics from an actual logician and read as much history as you can
the grammar and syntax of mathematical theory may be there, but if you are looking to go into a CS field, it's more often a liability. most CS and engineering jobs require understanding systems and flows, not simply solving a system of equations.
sure, it helps, but of the advanced science/theory type majors turned programmers, about 75% i've come across are virtually worthless and 25% are not. this includes inefficient code, poor design, and lack of appreciation for the art of programming.
Just remember Don Knuth earned a Ph.D. in math and he seems the know the "Art of Programming."
is get a job as a mathematician. I speak from experience. I graduated Magna Cum Laude with distinction in 2000 from Boston University with a degree in mathematics (I also received the College Prize in mathematics.) Further, I was awarded a full scholarship to Brown University to study mathematics as a Phd student.
I attended Brown for a semester, and had to leave.
(I had grown weary of certain distasteful aspects of the field, and subsequently could not commit to the level of effort required of a grad student. It's a shame really, because I understood most of the material and it was truly beautiful.)
Mathematics is an intensely rigorous, very narrow-minded and extraordinarily challenging field. It is also extremely isolating, and highly distancing. At the same time is in incredibly fascinating and richly (intellectually) rewarding.
However the job outlook for mathematicians is not good last I looked. Old faculty have been "about to retire" for the better part of a decade and only in very recent years has there been anything like a good year for academic hiring. Both BU and Brown (which are both considered Tier 1 Private Universities for mathematics by the AMS last time I checked) had several extremely talented grad students who were on repeated post docs because they couldn't find positions at other universities.
I won't go into my personal philosophical differences with how mathematical research is done today, as that would be more biased than the above diatribe, but I will tell you what is right with the field. First off, given the above, the field generally rewards extremely talented and diligent members of its community. If you work very hard and are incredibly brilliant then the job market (more than likely) won't matter. (this is of course, assuming you can avoid getting embroiled in the math.) In my personal experience talent can even get you past the politics. (I've seen professors express loathing for certain other faculty but at the same time give them respect for the quality of their work.)
I guess what I'm trying to say is that if you truly love the field and if the people around you (your teachers and mentors) think you have what it takes then go for it. The worst case scenario is that you end up with an undergrad degree in mathematics and have to go get a job. Math students are very highly prized in the technical job market as they have excellent thinking, reasoning and analytical skills. They also tend to be ruthlessly efficient. (okay, that last bit was blatant self-promotion, shoot me.)
On the other hand, if you have the math background, there are a lot of places where algorithm design can use that expertise. Often, it's the non-intuitive, mathematically based algorithms that perform the best, rather than the intuitive (sometimes brute force) algorithms those without the background are likely to design. Take quicksort for an example!
But you're just a high-school student. I don't mean to belittle you with that, but to devote your career to academics at this point is a bit early. Certainly, get your degree in math if that's what you love. Go to grad school in math and then you'll start to get the flavor of what life is like in academics. You'll also (hopefully) learn about the job market there.
Yes, you probably can stay in academics all your life. You might not like it, though. You might have to do research in areas you aren't interested in; for part of your career you might have very little time to do anything but teach (while at the same time you really also have to be publishing!). You'll almost certainly be looking at moving around a lot, first to grad school, then to a series of postdocs at different institutions, then start moving up the ranks towards tenure (which often involves moving sideways to other institutions, too.) If you love travel and not settling down, it's great. If you're looking for stability, it may not be for you.
You'll also be able to go into many industries or branch out into some other area. Mathematicians are in demand in a number of different areas (some of which you may not enjoy, though.)
Don't box yourself in at this point. In fact, it's hard to box yourself in until grad school. So do what you enjoy, discover new things, have fun!
I graduated 9 years ago with a pure math / CS double major. I must say that my biggest regret is that I didn't study more of the applied stuff. The pure stuff was a challenging exercise, and certainly did wonders for my thinking skills, but it's just not that useful in day-to-day.
When I find some free time I'll be auditing the local college's courses.
I figured I'd chime in with my two cents worth since not too long ago I found myself in exactly the same spot as you. I loved mathematics but was very skeptical about being able to make a living doing pure math. Heres what I did:
;) ). I enjoyed TCS so much, in fact, that I ended up doing my Ph.D. in computer science and not mathematics.
;) ).
As an undergraduate I double-majored in pure math and computer science. I took every theoretical computer science course I could get my hands on and by my 3rd/4th year of undergrad I was pretty much doing exclusively math. Yes, 2nd year specifically involved suffering through many 'coding' courses, but in the long run this isn't such a bad thing. A computer is a wonderful tool for a mathematician and knowing how to program one well is actually a very desirable skill (note, I still hated the programming classes
Don't let anyone fool you... theoretical computer science *is* math; and to be honest, its math that I found more interesting than any of my 'pure math' courses. As far as courses, on the math side I took as many abstract algebra courses as I could and on the CS side I focused on automata theory and formal languages (with a good helping of recursive function theory and semantics).
There were a number of posters above who mentioned mathematical biology and bioinformatics. For me, anyway, this was bang on the target. There is a huge need for competent mathematicians who are willing to learn a little bit about biology. We are at the point where biology is beginning the transition from a qualitative to a quantative science and we *need* good models.
Again, don't be fooled into thinking you have to do applied math. Sure, coming up with a model is 'applied' in some sense, but once you have the model you get to investigate it and try to prove properties that you think it has (e.g. recent work involved showing that the gene-descrambling process in hyptochious ciliates is computationally universal. Proving that is fun mathematics).
And of course, once you get a job and a grant, theres nothing preventing you from also researching other topics too (my 'academic hobby' is foundations of mathematics... but you don't get too many grants for that
Job prospects in Computer Science (academically speaking) are good right now; though its certainly tougher as a theoretician than, say, a software engineer. But, if you can market yourself correctly, I think its easier than pure math.
I hope that stream-of-conciousness rambling was of some value to you.
Don't just choose a grad school by its reputation. Back in the 1970's, I chose UC-Berkeley because its math dept was ranked #1, it had all kinds of famous people there, etc. When I got there, I found that with a very brilliant group of about 400 grad students, only about 15 Ph.D.'s were awarded yearly. It was near-impossible to find an advisor once you passed the qualifying exams and it was an incredibly distressing and discouraging experience. Like most people, I didn't finish (a master's is only a consolation prize that means near nothing, as you probably are aware). It may have been that I didn't have enough ability -- I'll never know for certain, but I am quite sure that more had ability and the potential to do good work than completed their Ph.D.'s.
When you choose a grad school, look at how many students get Ph.D.s vs. enrollment NOT just who the faculty are and rankings. Very very important!!!
Best wishes to you, and don't repeat my mistake!
OK, I may be biased (I work for one of them) but they can be quite helpful. Most if not all have reduced rates for students. I know that SIAM has activity groups focusing on different areas of Mathematics. (Anyone care to guess who I work for?).
I am a 2nd year undergrad at a local university studying Computer Science, and I work tech support here. I can't form a real accurate opinion of what we do for our members, as I'm not all that interested in it, or do I work with members much. But I know we have conferences all over the country and have Job listing and such. Plus it's a good way to network with other geeks... Umm... I mean Mathematicians.
I suggest you check out some websites, see what you like, and perhaps pose the question towards some of them.
Society for Industrial and Applied Mathematics
American Mathematical Society
Association for Women in Mathematics
Mathematical Association of America
Also, here is a direct link to the AMS's link page
Good Luck, and feel free to email me with questions.
Am I Over-Moderating??
He ended up working for the NSA.
I hear from friends of friends that he hates it.
So what is the moral of this story? The great thing about college is that you get to explore a variety of subjects. Since you will obviously already have college credit going in that will give you that much more freedom to explore. Take classes in CS, engineering, art, dance, whatever. Take CS theory classes rather than programming courses. You might find that you really like it.
As far as what school to go to (it is probably too late for this if you are a senior) I would suggest being an average sized fish in a big pond rather than the big fish in a little pond. The great thing about going to a prestigious university isn't that you get a diploma from such and such U. The great thing is the people that will surround you. I learned more from my peers than from my professors. Living in the dorms was amazing, both my wife and I wish we could go back in many ways. I would not have had the same experience going to the local commuter school, regardless of how good it is.
Lasers Controlled Games!
This is nonsense. The steam engine is a classic example of a major technology advance made by people being practical, not people doing theoretical research. The Romans could have developed steam locamotives, but they never got past an open steam engine which is little more than a toy.
As for the "collapse" of the Roman Empire, that's Western conceit. For various reasons the core of the RE moved from Rome to Constantinople/Istanbul (think of the relative importance of New York and Los Angeles in 1900 and 2000 - now multiply that a thousandfold since the US doesn't have an emperor) and the RE made an economic decision to reduce troop strength in the western provinces. At the same time, it was extremely difficult to see any difference between the "Romans" and the "barbarians" in the border areas. By the time Rome was sacked, IIRC the Western and Eastern Roman Empires were essentially separate entities.
The Eastern Roman Empire became the Byzantine Empire, which lasted until the 15th Century, and some people see a continuous track until the 19th Century.
The Western Roman Empire "collapsed," but it would have made little difference to most people living at the time. I have some friends who argue that the subsequent dark ages were due to the spread of Christianity and its hostility to pagan ideas (including all of the culture of Greece and Rome), not the collapse of the WRE.
Closing the loop, Europe escaped the dark ages after some people were accepted at Islamic universities (in Spain, IIRC). By this time, the Byzantine Empire/Eastern Roman Empire would have converted from Christianity to Islam.
For every complex problem there is an answer that is clear, simple, and wrong. -- H L Mencken
That is what it is all about. Physics is really "applied math". Amazing how the math can actually model the universe. There's some really subtle stuff floating around, things like e, pi, etc. how they relate to each other and reality is sometimes awe inspiring.
While I've never been emnployed as a physicist or "scientist", I have worked in the field of semiconductor design which, if you include the physics and chemistry, is once again mostly "applied math".
Good judgement comes from experience, and experience comes from bad judgement.
- W. Wriston, former Citibank CEO
If you really love mathematics, then go ahead and study it.
But take a few other courses (eg, CS, engineering).
In my experience, it's insufficient to be in the top 1% of mathematical ability to succeed in pure mathematics as a career. As a high school student, I was in that group.
But to succeed, the requirements are more like being in the top 0.01% of ability (finishing the Putnam with a rank described on one hand).
Of course, you run a higher than average risk of being too eccentric to adapt to conventional society. As I remember, my math profs tended to be out on the edge of the Gaussian in more ways than one.
"Provided by the management for your protection."
I've worked with a lot of other people's code over the years, and I've noticed the people without solid math backgrounds (e.g., self-taught hackers, and grads of CS programs without a strong math component) tend to write code that is less organized, harder to debug, and less reusable than the code written by those with strong math backgrounds. You don't have to know a lot of math to write code that works (in most applications) but having what academic mathematicians call "mathematical maturity" will almost certainly make you a better and more elegant coder.
The correlation between ignorance of statistics and using "correlation is not causation" as an argument is close to 1.
I've heard that a certain government agency is always hiring math freaks. I've also heard that they are the largest employer of math freaks in the world.
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Even the strongest students there had trouble getting jobs in academia. Those that did were all excellent teachers and got jobs at liberal arts colleges.
Starting grad school in the early '90s, I was told that it was a good time to do so - although there weren't too many jobs at the time, there would be waves of faculty retiring around when I was finishing, opening up plenty of jobs.
There were two reasons those jobs didn't materialize. The first is that departments were cutting budgets and tenured positions, replacing them with lecturer jobs. The second was that there was a wave of highly trained mathematicians from the Former Soviet Union who were snapped up into many research positions at bargain rates.
I remember the graduating students in my department applying to hundreds of jobs, and open positions in turn receiving hundreds of applications. It was brutal.
Is there anyone in the math world now who knows how it compares now to 5 or 6 years ago?
Go bored by my second semester; dropped out, started heroin, managing rock bands; got in and out early on a few dot-coms; now I'm retired in the carribean at 36.
But the math thing will probably work out for you, stick with it.
Besides most people who like math, hate sunlight.
Cheers!
HS/Lower Division math cources are nothing like upper division/ grad level courses. What lower division skills are usefull/needed in pure mathematics?
2. What about just teaching?
Are there any stories here on /. about people who got a M.{S | A}/Phd and have been happy at the Community College/High School Level
As I stated in a previous post I have none of the requirements that people listed (Tier I school, 1600 SAT, Published work) but I have a love of Mathematics and teaching (and computers). Is there a life in this?
You are absolutely right.
You may also accept that all of Rome's and the WRE's problems potentially had technological solutions.
Imagine steam locomotives. Troop strength ceases to be a problem because they could move all their troops where they were needed in timeframes that would stun the barbarians attacking them. The massive corruption of Rome would be mitigated by the plenty provided by improved logistics.
"Europe escaped the dark ages after some people were accepted at Islamic universities"
So, the Roman Empire did not collapse, but Arabic universities brought the people who would have been considered to be inside the borders of the Roman Empire out of the dark ages...
Lack of a theoretical mathematic foundation caused the people that inhabited the area considered to be the Roman Empire to experience a sharp drop in their standard of living, the dark ages, and were brought out of the dark ages by the re-introduction of theoretical math, and with it the technologies that improve standard of living.
Yes, you are absolutely right, but you have failed to look at it in any way other than by wrote. It may serve you well to introduce some "what if" variables into the history you have memorized to see if you can deduce the actual causality of historical events.
For instance, a baby deprived of mother's milk will surely die of starvation. You would say, the baby starved to death, and you would be right. I would say the baby died of neglect, and that even if fed, would die for lack of its mother's love. You are right but you have not addressed the causality of the situation.
If voting were effective, it would be illegal by now.
i used to be a math graduate student at a big ten university. spent 7 years on the ph.d. before deciding to quit. there are jobs available. to get a job at a top 20 school (basically a level I school) you need to be very good and should have gotten your ph.d. from a top 20 school. you need to have a passion for the research or else you won't get tenure. for schools like fsu or university of nebraska you have to be decent, not exceptional, to get those positions. the research quality isn't as good at level I schools but there are good mathematicians there. there just are a lot of mathematicians there who are mediocre. the other type of schools people don't really do much research so you don't have to be good at all. be a decent teacher and occasionally publish and you will be set. if you have the brains and the passion you will get a job. but you shouldn't go to graduate school in math for the money or the jobs. do it for the love of the subject. pick up some engineering or computing in undergraduate and maybe take a course or two in graduate school you will definitely be set. assuming you actually know anything. but once you have a taste for academics, imho, the corporate world just plain sucks.
Depending on how theoretical/practical you want to be there are A LOT of great paying jobs in the field of cryptanalysis/cryptography/etc. that take people with a bent towards mathematics and computers.
I know how to implement crypto systems, however I have leaned heavily on a co-worker that has a Ph. D. in mathematics to do the proving stuff that shows why you can't break the system, and to explain to me 3/4 years ago why WEP was bad...
Hrm, it's not like mathematics is developed in a vacuum. Much of it has in fact been developed as a solution to a problem in, say, physics. Newton, for example, developed much of the early theory of differential calculus to express his ideas in classical mechanics. Fourier developed fourier analysis to study problems in, iirc, heat conduction. Etc. etc. Of course, there are also plenty of examples where a field of pure mathematics thought of as little use in the real world suddenly finds some interresting applications. For example group theory and abstract algebra in quantum mechanics.
And about steam locomotives, as the previous poster claimed, no amount of theoretical mathematics is going to build you a locomotive. Steam locomotives were mainly developed with the simple knowledge that if you boil water you get pressurized steam. And a lot of good ol' engineering (i.e. trial and error, and using what worked previously). Add to this that the romans were unable to produce steel in sufficient quantity and quality (it takes a lot of steel to produce trains and a railroad network, you know!), they probably new little about lubrication of the mechanical parts (I think they used some kind of grease produced from animals to lubricate their wagons and other things. Clearly this is not enough for a locomotive). Etc. Even today, modeling something like a steam locomotive is a very non-trivial problem. Depending of course on what you want to know. Material properties? Check out solid state physics, definitely 20th century stuff. Steam dynamics? Navier-Stokes equations for fluid mechanics have been known for quite a while, but solving them for your locomotive entails solving a non-linear partial differential equation in a very complicated domain. If the previous statement doesn't raise the hairs on the back of your neck, attend some course entitled something like "advanced numerical methods for partial differential equations" to get some insight into the theory. And then get a supercomputer to actually solve the problem. In short: Waaay out of the league of the romans, theoretical mathematics of not.
Of course you might argue that mathematics has allowed us all these kinds of stuff. Well, yes, but as I said in the first paragraph, mathematics is not developed in a vacuum.
If you really love math, and you really love computers, you may be missing out on another great subject: Physics.
Physics and math go hand in hand. Well, mostly. Mathematicians are more pedantic in their approaches. Physicists like to jump to conclusions early and rely on shaky logic.
Which way is right? Both seem to have their redeeming values. While Physicists are often wrong about things, they also introduce ideas that eventually turn out to be right (like the Dirac delta function). Mathematicians, however, like to stick with things they know and trust, and end up being a lot more trustworthy.
Physicists are like the hackers of the math realm, trying to figure things out by guess-and-check, and going with what works rather than with what is accepted or "right".
The radical sect of Islam would either see you dead or "reverted" to Islam.
A vacuum is exactly what Rome provided or at least that's what Archimedes said. Archimedes was one of the people who understood steam dynamics. I may be completely wrong, but I belive he was the first true mechanical engineer with a strong math foundation. Perhaps that honor should go to Imhotep.
:)
Please grant that without theoretical math, there are no technological advances. Grant that Archimedes had enough knowlegde to at least experiment with steam power. Grant that Rome had the industrial power to provide Paullinus with an army that sailed to briton with 10,000 soldiers, all equiped, at a minimum, with a three pound bronze drusus to defeat a rebelion of 80,000 rebellious Britons.
Bronze is certainly not the Ideal substance to build a locomotive with but it would not be impossible.
A chariot from about 1400 B.C. was found in the tomb of Yuaa and Thuiu, along with traces of the original lubricant, mineral oil, on the axle.
Tribology, the study of lubricants, is an ancient greek word.
The first locomotive rails were made of wood capped with copper, then later iron.
And if it takes a supercomputer to build a locomotive, Babbage must have gotten a lot farther than I had thought
If voting were effective, it would be illegal by now.
I will heartily second that, especially at lower levels. I finished two years of engineering, before switching to busineess graduated and really enjoy my job. It is really nice to understand the simple math that goes into financial formula's, its mostly basic stuff, like a sum, first year calculus or similar, but so few of my peers have any understanding of this, it makes my little bit of extra quite useful. That being said, my advice would be to do what you will enjoy, otherwise no amount of money or job security will compensate you for missing out on doing what you love.
Degaussing scares the bad magnetism out of the monitor and fills it with good karma.
Seriously. The worst thing you can do at your age is say "I am only interested in X, all my life shall be X, and yea verily it is good." College is a time of experimentation (yes yes, wine women and song, but I mean specifically in terms of fields of study). Math is a great tool in tons of other fields, so you should at least dabble in a few other fields of study while you're an undergrad. You never know, you might end up developing a love for physics or the philosophy of formal logic. My math skills are nothing to brag about, but I'm really happy as a computational chemist[1] to have linear algebra, for example. (Actually that's what I was doing in academia, right now I'm "slumming" as a programmer.) My ex-roommate got a BSc math and just went to grad school in south africa taking a curricula in applied oceanography. You might even pull an Escher and become an artist. So when you're 17 or 18, don't be rigid about your path in life. Heck, when you're 30 don't be that way. Life is full of possibilities...
On an IMHO level: making a living as an academic is hard. The pure pursuit of knowledge is great, and vital in the long run, but sometimes it's hard to pay the bills, you know? So, again IMHO, you might be better off finding a career that uses a lot of math but in an applied setting (like as a scientific programmer in the pharmaceutical industry, lots of interesting code, fair bit of math, and you might indirectly be saving lives with every line of code you write).
[1] many jokes about "chemist math", the dirty secret of most chemists is that we all suck balls at anything more complex than a partial derivative. except for the physical chemists, but they all wear black and mope in the corner... ;-)
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Try it and see if you are good at math. At least here in Germany (and I think it's the same in other countries), if you have a university degree in mathematics, you can get a decent job in the industry pretty easily, no matter on what aspect of mathematics you have focused on at the university. This fallback option makes aiming at a career in theoretical mathematics less risky than it appears initially.
Sliced the other way, (i.e. what will make you happy?), here's my more detailed story. I got an Sc.B in Theoretical math in 1997. About 1995, (end of my sophomore year), I realized that, although I was quite smart, and at an Ivy, in the top 20 for math, essentially, I wasn't going to be able to make it in the math academia world. This was not obvious to me in high school, (and I did some reasonably heavy math in high school through the UMTYMP program in Minnesota) but was obvious after meeting a few ultra-smart classmates, and talking to some professors.
Listen to those people who are telling you that you need to be at least in the top .01% (That's .0001 of people) to really make it as a mathematical academician. You might be one of those people; if so, it will probably be really clear to you sometime in college. If not, don't worry. For myself, I realized some portion of my brain was motivated by, and interested in money.
So, I ended up starting a company. I'm much happier than I would be struggling to get a job at a liberal arts college doing a teaching position for a job that I'm only 80% good at.
I just wanted to say thanks to all that provided helpful information. =) Through the gathered knowledge, I believe that I'll continue with math in mind, take a few CS classes, and keep with my study of particle physics for the heck of it (all subject to change.) =D Again, thanks for your input.
This statement is false.
When did this topic get posted, and why did I only see it now?
I am in my second year in a tenure track job in mathematics, having completed an undergraduate degree at Dartmouth and my PhD at Cornell. Not only have I gone through the hiring process, I am now on the other end of it as we complete faculty searches for the next year.
First of all, you should not become a professional mathematician unless you love it. Research in this area is infamous for breeding manic depressives because you can work for a year on a result., have it fall apart, and have nothing to show for it when you are done (I speak from experience here). Teaching jobs are much more stable, but unless you keep up even minimal research, you tend to calcify and it adversely affects your teaching. If you are willing to starve for your art, just like a struggling artist does, then proceed.
This is not to say you have to starve - just that if you are going to be any good, you have to have this attitude. Depending on the area you go into, there are tons of research jobs in and out of academia.
The list goes on.
Academia is usually the standard place math PhDs go. Even here there are a lot of choices. You have
Now it just comes down to marketing yourself to the job (Thought you could escape that in academia? Wrong!). If you apply to the first, it is a matter of how many papers you have and how many more you can get. The second wants a mix of papers and teaching. The third really just wants to see how you can teach, and expects you to show that you can come up with innovative and new ways to motivate students (Buzzwords like seminar style, collaborative learning, and Moore method get thrown around a lot).
You also need to find ways to distinguish yourself for the jobs you are applying. If you apply to a school where math and CS are one department, the CS masters is a plus (helped me). But if the CS program is in the engineering school while the math program is Arts and Sciences, it is useless. Masters in similar, but related, fields are nice in this regard (Statistics, OR etc..), but departments are starting to get wary of them and their quality. As a case in point, a lot of CS masters for math PhDs are all theory (and so just more math), whereas Cornell would not allow me to count any theory classes to my masters (engineering/systems only).
These are all important issues you need to think about when you start graduate school. Any respectable graduate program realizes this, and will run seminars on how to develop teaching portfolios or research CVs starting your first year. Its in their best interest as a graduate program that you get a job, as you can refer future undergraduates back to them.
After all that, you still have to accept the fact that it is all cyclical, and you can never predict what will happen. A lot of professors were hired in the 60s for the GI bill, and tthey were supposed to retire ten years ago, but never did (you can hang around longer in academia). Then in the early 90s the collapse of the Soviet Union brought a lot of world class mathematicians into junior colleges (will prof for food).
Because of these two factors, when I entered grad school in 94, there was nothing but doom and gloom about how bad the job market was. So no one went to grad school. And many others left grad school to make money in tech. The result? Six years later I had my choice of professorship jobs, and now have my dream job while those that want to tech are moving about.
Enough of my ramblings ... It all comes down to one thing: do you love math. If so, then go for it. If not, maybe you should look at something else.
If you don't need to stay local, or even in the country you might want to try University of Waterloo
There's a math faculty (you get a BMath) which includes a Pure Math department. It's a pretty nice place, and you get to drink real (Canadian) beer when you're only 19. Plus almost all of the math faculty is in co-op, which means that you also do work terms where you get paid... very handy.
Actuaries - making accountants look interesting since 1949
i'm a 2nd year grad student in math at carnegie mellon, so i hope to have some perspective on employability in a couple years. i write to recommend a math summer program which exposes high school students to "real" math (and doesn't require calculus). The Hampshire College Summer Studies in Mathematics is where I started to think I should be a professional mathematician. It is heartly endorsed.