I really would like to get a mathematics phd.

[Philosopher_k]

The thing is, i am not really that interested in becoming a professor. Well, more specifically, i am aware of the lack of positions in teaching. I am currently a senior in high school and have a bit less then a year before i need to decide on what i am going to go to university for. Here are some thoughts i have:

Major in mathematics and engineering...Proceed to get a math phd and then become a professional engineer.

Major in mathematics...proceed to get a math phd and then become a quant or an acturary.

I really can't think of anything else that would allow me to get a math phd and then move into a professional field. I have given this some thought, and i am not interested in experimental physics or industry. So is it viable? Specifically the first option, as i enjoy the thought of becoming an engineer. The thing is i also enjoy the thought of having a dr. in front of my name (call it narcissism if you will).

 

[mathwonk]

If you want to be an engineer, you may find it quite trying to persist in a pure math field far enough to get a PhD. But I suppose you could get a PhD in a more useful area like differential equations and then that could be quite useful in engineering. To get a PhD you usually introduce some new mathematical idea, or explore some unknown facet or a mathematical topic. I am sure someone knowledgeable enough could help you design a PhD project that would be interesting and valuable to an engineer.

Could someone more experienced in engineering chime in here? Do any engineers here have a PhD in mathematics? Maybe you should ask this in the engineering thread as well.

 

[Philosopher_k]

Thanks Mathwonk. I am aware that you need to come up with an original idea to get a math phd, and that's exactly what i would like to do. The thing is i doubt i have it in me to spend my entire career in academia, sure 10 years would be ok, but i doubt i could contribute much to the field of mathematics over an entire career.

The other thing is, i am not that interested in applied mathematics, as in differential equations and fluid dynamics, more esoterical subjects like geometry, topology and manifolds.

 

[hadsed]

If you're interested in those topics then you probably wouldn't like engineering since it doesn't have too much to do with it.

You may take a liking to mathematical physics though..

Also, it sounds a bit like you have a few misconceptions about academia. If you get in, you'd have to do something pretty stupid (or just not bring anything else to the table) to only last 10 years. If you're really good enough to be an academic in mathematics and you really love it, there's no place better.

 

[Philosopher_k]

I would be interested in getting a phd in those topics, but i would enjoy applying the mathematical knowledge to other fields. Maybe the financial option is more viable?

 

[chiro]

The thing is, i am not really that interested in becoming a professor. Well, more specifically, i am aware of the lack of positions in teaching. I am currently a senior in high school and have a bit less then a year before i need to decide on what i am going to go to university for. Here are some thoughts i have:

Major in mathematics and engineering...Proceed to get a math phd and then become a professional engineer.

Major in mathematics...proceed to get a math phd and then become a quant or an acturary.

I really can't think of anything else that would allow me to get a math phd and then move into a professional field. I have given this some thought, and i am not interested in experimental physics or industry. So is it viable? Specifically the first option, as i enjoy the thought of becoming an engineer. The thing is i also enjoy the thought of having a dr. in front of my name (call it narcissism if you will).

Hey there and welcome to the forums :)

I'm currently a math double major so I can give you my 2c for these but not no so for engineering specific courses.

The main branches of math are pure, applied, and statistics. As you are probably aware, they are three vastly different fields, but like most of science they can also be very intertwined with each other.

As for career choices I will expand what I know about them from coursework and other investigation:

Actuary:

The Australian system is slightly different but the course grunt work is largely the same.
Here we have three parts of exams: Part 1 has 8 exams, Part II has 1, and Part III has three exams and a work experience component.

Do not underestimate the difficulty of these exams. You might get through A level probability and statistics courses but if they are a little light on what is covered, they may not be sufficient for exams. A thorough rigorous stats sequence will most likely prepare you for the difficulty that lies ahead.

Apart from standard statistics you will need to do exams in business finance/accounting, financial economics, introductory micro and macro economics, and financial mathematics.

On top of the above you do actuarial statistics. These relate purely to statistics as applied to insurance (life, general, etc) and superannuation (eg pensions).

I would look up your actuary professional society like the Society of Actuaries or the Casualty Actuary Society.

Having done a year long stats sequence (I'm planning one major in stats, other in applied/pure), it can be a grind especially if you're not into that kind of thing.

With regard to your suggestion of becoming an engineer then doing PhD work in mathematics, I highly doubt that you could do this. The scope and context of the two fields is wide apart enough to put you at a disadvantage if you chose this, but I wouldn't rule it out.

If you do major in statistics there are quite a few options available to you. Some more specialized fields (apart from actuarial) include bio statistics (pharmaceutical, hospital, research in health field), financial statistics/mathematics (banks, investment companies etc) data analysts (data mining, market research etc) and other jobs that make heavy use of data and its appropriate analysis thereof.

I'm not sure about employment where you are, but with regards of employment statistics and applied mathematics is going to be your better friend than doing pure (at least that's the case where I am). One place where this is different would be the National Security Agency where as far as i recall, they are the number 1 employer of Mathematicians in the states.

One thing I would recommend no matter what you do is to pick up a programming subject regardless of what course you do. If you do telecommunications / computer / electrical engineering you will take a few and if a math major hopefully at least 1, but if you do a math course where you don't need to take a programming unit, you should take a programming course as an elective: it will come in handy.

Also note that a major in math or engineering doesn't necessarily restrict you to jobs with "math" or "engineer" in the title. You could get work in an analyst role, then become a programmer with experience.

If you are interested in the financial side of mathematics you should ask two fish quant since he works in the industry: he frequents these forums a lot and gives great advice.

Also one thing that I should add: in the kind of careers you are interested in, I would recommend you do some sort of public speaking. Its probably going to be forced upon you in any engineering or mathematics program worth its salt, but if for some reason you sneak through without the experience, it should be your duty to gain and develop your experience in this area.

It doesn't matter if you want to be an actuary or an engineer or statistician, or whether you want to end up in academia or other areas of the private or public sector, people will expect you to be able to be very good communicators especially to audiences that do not have the breadth or patience for tough mathematics.

Whatever route you choose, they are all good choices and I wish you the best for your future.

 

[Philosopher_k]

Thanks chiro. Is it possible to take the acturarial exams while you are persuing a math phd? (from your tone, i doubt it)

Also say i want to become a quant, do i just take the normal pure math courseload and then when i get the job they will train me? or am i expected to double major in economics/finance or something.

 

[chiro]

Thanks chiro. Is it possible to take the acturarial exams while you are persuing a math phd? (from your tone, i doubt it)

Also say i want to become a quant, do i just take the normal pure math courseload and then when i get the job they will train me? or am i expected to double major in economics/finance or something.

If you do say a math degree and have at least one major in statistics in your 3rd year (I think you call it sophomore but I'm not sure) you could with some preparation have a good chance of passing the P exam (probability exam). Also if you do a good amount of study for FM (financial math) you could take that in either your sophomore year or when you graduate.

The professions recommend that you put in 300-400 hours of study into each exam.

If you are doing the normal math track you will most likely do a full single calculus session (Calc I and II) and then in 2nd year do a full intro probability/statistics session. Most people do not do a proper statistics session until 2nd year and this includes the honors candidates simply for the reason that you need a solid calculus foundation for the continuous probability analysis and especially with multivariate analysis (ie calculus in many variables).

If you do your A-level intro stats sequence and go well in it, then its going to be a somewhat good indicator of whether you will consider going the actuarial route (in fact any statistical route). Statistics is known to be hard and also to be boring. Some people find that its both boring, others just one or the other, and some lucky people find it neither.

So in answer to your questions yes you can take the exams while in uni (P and FM), but apart from these two I would not recommend any others since the other material builds on these, and will be much harder.

With regard to quantitative analysis you will more than likely need a PhD in a quantitative discipline like mathematics, engineering, physics, statistics or something along those lines.

With respect to the actual mathematical and economic content, I have to say that I am not qualified to give you any advice on the specifics, but hopefully two-fish can come in here and give you some advice with real authority.

But I can tell you about the other thing that quants often do which is program.

I used to be a programmer in accountancy programs and game design. Although these fields are far removed from one another, both of them required common skillsets that can be quite deep in nature and take significant amounts of time to develop correctly.

Bottom line is if you want to get into a modelling role (ie quant, some types of analytic work etc) you 1) need to know how to program and more importantly 2) know how to do it well.

It's one thing to be writing your own program that you fully understand line by line with good design principles, good abstraction, minimal redundancy, good documentation blah blah blah but its another thing to be working in a team of 5 maybe a dozen other people who are contributing to a repository of a million plus lines of code where the majority of code is not your own and you are under pressure from the program not working because of a myriad of reasons of which some may not be under your control.

There are actually quite a few books on writing code in C++/Java for derivative securities code, but if you want to get into some sort of mathematical modeling, I would recommend you learn how to program.

There are a couple of ways you can do this. One is the formal route through elective or perhaps a major in computer science in your undergraduate degree.

Another is through a masters or through some sort of computational science project or part of your PhD. For these options there are ample opportunities to gain some of these skills, which you will no doubt build on to become a good solid commercial grade developer. I'm not suggesting you need to become a systems architect, but you will need to become at some point commercial grade if you are writing that kind of code.

 

[mathwonk]

you might also check out medical applications of math, such as to genetics, and genone mapping. (I know diddly about this subject, but I do know the UGA application from the biosciences group for a big genome project grant was initially turned down for lack of sufficient math input.)

by the way, when you look at it abstractly, i.e. when you look at a differential equation as a vector field on a manifold, it begins to be (differential) geometry.