The Should I Become a Mathematician? Thread

Bearded Man

I have a good PreCalc book to recommend people. It starts with logic and set theory then moves to the field axioms. It covers a wide variety of topics from there, including the fundamental theorem of Algebra, logs, one-to-one functions and their inverses, trig, imaginary numbers...

http://www.amazon.com/Introductory-A...3&sr=8-3-spell

Though I have yet to read Spivak, I imagine this would be wonderful preparation for it.

Robert1986

Not true (the part about making less as a mathematician.) I read a Forbes article and the three majors that made the most money in the private sector were: Engineering, Math/CS, and Pharmacology. And, to be honest, I would imagine that there are some engineering disciplines that are causing this engineering average to go way up. ME is probably pretty good money-wise but not as good as ChemE, AE or BME, I would imagine.

Now, let's say you major in math. You say you are going to grad school. Now, what can we have you do so that you can a)make money and b)have a career you enjoy. Well, at my school, we a Ph.D. program called "Computational Science and Engineering." It is like a mix between Engineer CS and Math (and you basically get to pick the field of engineering and proportions of each component, within some loose guidelines.) It is a pretty hard program I understand, but I think if you do it you could major in math, do a lot of math in grad school and come out and get a job in an engineering firm. Everyone wins. Here is the website for the program I mention: www.cse.gatech.edu.

mathwonk

making money is largely about being flexible and making choices that enhance your earning potential. there is no salaried job that earns the big bucks. professors do better than average but do not earn a lot at most schools. but they get lots of freedom to control their own hours, as long as they bring in grant money for the school. raising your income in a university setting eventually forces you to go into administration where salaries are higher.

if you work in an engineering or internet company with your math major, your income will still depend on your willingness to do more for the company than just what you majored in. If you want to earn more you will find yourself needing to learn to manage more people, make good decisions, and help broaden your company's markets. I.e. again the bigger bucks are in administration than in day to day nuts and bolts work.

The most valuable thing you can learn from a math major is not how to solve canned polynomial or differential equations, but how to apply logic and creativity to analyze and solve a variety of problems.

dkotschessaa

Was looking for the "like" button for mathwonk's last post. Been spending too much time on Facebook and not enough time here.

mathwonk

In the same vein, if you are a researcher getting older, and your friends want you to become an administrator, but you would rather remain a researcher, think about it. Your seniors served as administrators and helped you advance your career. Maybe it is your turn. Not only will your pay go up, but you have chance to choose the direction of your research group, and to support the young talent in your department.

analyzer

Hello, everyone. I probably want to become a mathematician. When I was in high school, mathematics was the only subject in which we were required to think. I should mention, though, that most of the mathematical problems we were faced with were one-step and done, and involved no calculus. Perhaps I liked math at that time because I was the best student in my course.

After graduating from high school, I went through a period of crisis. I sort of became paranoid. I used to have delusions. Previously, I had been diagnosed with obsessive compulsive disorder. Now, I am 26. I have been taking medicines for the past ten years.

At 22, I decided to enroll in a 3-year technology program (I believe the equivalent in the U.S. is an engineering technology program). Soon after enrolling, I became discouraged. I couldn't keep pace. The program is offered by one of the few decent universities in my country. I realized that I lacked many mathematical concepts (precalculus concepts).

Then, I went to a less competitive program in another institution. At last, I completed two years of study of electricity and electronics. There, I realized that I'm not good at manual tasks, like soldering little electronic components on a board. But I excelled in the math and programming courses (you should take into account that the insitution is noncompetitive.)

I read over and over that math teaches one problem solving and logical reasoning. My parents are willing to pay the money if I enroll in the math program at the university which I first attended. But I'm not sure.

I have been studying math on my own (precalculus) with the Spanish version of a book titled Algebra and Trigonometry with Analytic Geometry: A problem-solving approach, by Varberg and Fleming. This book features in each section a difficult problem. I have tried to solve some of these problems. I succeed at times. But, for a real mathematician, these are "mickey mouse" problems. So, given the facts that I have unsuccesfully tried to solve some of these problems and that I am already 26, I am hesitant that I can become a mathematician.

On the other hand, I have not had a real job. Currently, I work with my father. He's got a print business. So, if I choose to go to college instead of getting a real job (thus still depending financially on my parents), I may be ruining my future.

Can someone guide me?

dkotschessaa

Analyzer,

I'm not a mathematician (yet) but a few years ahead of you in age having gone back to school for math after quite awhile absent, and with a few of the same difficulties.

I would advise you to absolutely not worry about having problems self-studying, and would say not to compare yourself to "real mathematicians" at this point, because you're just not one yet. What I've figured out is that to be a mathematician you have to learn mathematics (a seemingly obvious statement) and to do that you have to go to school and struggle for awhile. Just go back to school and do the work and study and do not question your innate ability. I am passionate about math despite the fact that I am in some senses quite terrible at it. I studied for about a year on my own, and then it took me another year of school for my brain to start getting into shape.

Don't assume that any mathematician can solve any problem instantly, like they are some sort of huge repository of mathematical wisdom. I've seen brilliant professors struggle with problems in class that were in our calculus book. A lot of the young students are baffled by this because they think that math professors should just be problem solving machines. It's not like that.

What they do know how to do is do the required research and reading to be able to come back and solve the problem. They learned to do that in their studies, just like you will in yours. (And I also recommend G. Polya's "How to Solve it" which has helped me in this area).

When I see people like you worrying about being 26 it makes me nervous, because I am 35 and it makes me think I'm supposed to be worried about something. I am aware that I'm not the norm in age and that by the time I get a Phd I will be in my 40s. But I reason thusly - if I work now and get my Phd in my 40s I will be 40 something and have a Phd. If I decide not to do it, then I will eventually be in my 40s anyway and will not have a Phd. If I had gotten my Phd in my 20s I will eventually still be 40 and have a Phd. So in 2 out of three cases I will be a 40something year old Phd. In the third case I will still be in my 40s and thinking that maybe I should have continued to work at it when I was in my 30s. Now how long do I really want to keep that up? So I'm just going to do it now and stop worrying about it.

I realize I've rambled on a bit here in mathwonks thread. Please, mathwonk, let me know if anything I've said here does or doesn't make sense. I don't want to give bad information, but I think I have an idea what I'm talking about here.

-Dave K

analyzer

Thanks for replying, dkotschessaa. I can see I'm not alone.

You are passionate about math. That's the most important part. For math being hard, one cannot succeed if one is not in love with it.

Regarding my situation, I don't know if I am passionate about math since I haven't even scratched its surface. I want to know more, for sure. But I believe trying to solve hard problems on books on one's own resembles research.

I have gotten stuck with problems for months, and that's discouraging, but one does learn a lot in the way. Besides, one refines one's reasoning skills. And that's what it's all about. A rigorous undergraduate math program should open many doors.

If there's a place where I want to spend most of my energies, that place is university. I don't want to inherit my dad's business. I don't want to do repetitive tasks or manual tasks for eight or more hours a day.

sahmgeek

dkotschessaa

That's a good way to look at it.

Do it man!

mathwonk

Thanks for the good counsel guys. Dave I appreciate and in fact depend on the input from people like yourself. I feel an obligation to weigh in here when someone explicitly asks for my view, and I have something to say, or but only then.

AcidRainLiTE

Hi everyone. I was wondering what you think of Lehigh's math PhD program. I recently applied to grad schools and was accepted into Lehigh (my top choice was Stony Brook but I didn't get in). What do you know about the school? How strong is its graduate math program (I am interested in pure mathematics)? One of my main priorities is to be immersed in an environment with experts in the field and surrounded by bright and passionate peers/grad students. I also really want to feel pushed and challenged and don't want to be in a sub-par environment. I may also like to ultimately teach at the grad level and so I am also interested in how attending Lehigh for my PhD would affect my career options. What do you know about the school? Any advice is appreciated.

For the record, I am still awaiting responses from Pitt, Penn State, and Maryland. It is kind of late in the game, though.

homeomorphic

You should probably be more concerned about feeling TOO pushed and challenged. That's what grad school is all about. One of the profs here jokingly said something like "the purpose of grad school is to suck all the joy out of life".

But it's not a joke. It's not uncommon for the drop-out rate in math grad schools to be 50%. That should tell you something.

Many will enter. Few survive.

I don't know anything about Lehigh's PhD program.

mathwonk

i do not know anyone there personally but a quick look at their faculty list shows they have their own phd's from top places like SUNY, Harvard, Princeton, MIT, Stanford, Rutgers,.....


so I would not worry about how good they are, they seem quite good. Indeed it is really hard to find a school these days that does not have very good math faculty. With all the in migration from eastern europe and asia, they just keep getting and better.

More relevant is whether they specialize in areas of interest to you. So take a look at their fields of specialty.

AcidRainLiTE

It looks like they have a good number of people specializing in Geometry/Topology which is one of the primary areas I am potentially interested in. I say potentially because I really need a bit more exposure to the various areas before I know what I want to specialize in.

On the other hand, it looks like they have only one person doing algebra/number theory, which is a bit concerning. That is, unless the people doing algebraic geometry are essentially involved in algebra with the addition of its use in geometry. I am not familiar enough with the field to know.

One of my other interests is the interface of math and theoretical physics. It looks like they have people specializing in Differential Geometry, which is closely tied to physics. No one seems to be working specifically on Mathematical Physics, though.

I will probably take it if they give me funding.

mathwonk

what is your assessment of university of georgia in athens?

http://www.math.uga.edu/research/index.html

AcidRainLiTE

Looking over UGA's program has made me doubt whether I want to go to lehigh. It looks like they have a larger range of specialties to choose from. They have people working in algebra, geometry, topology, mathematical physics, and analysis. I guess that is one of the benefits of a large university--you get greater diversity of specializations. Since I am still fairly uncertain what I want to specialize in, a university that offers a lot of choices may be best.

I would say UGA would be awesome for me except for one thing. They don't have courses in foundations/axiomatic set theory. Mathwonk, I know you said before that set theory isn't considered a big area of research, but I still find myself very interested in it. I really want know about ZFC, cardinals, the continuum hypothesis, logic & set theory, godel's theorem, the work of tarski, etc. For some reason my mind just 'locks' right into that stuff. To really thrive, I feel I need to be involved in thinking heavily about those things, even it is not my main area of research.