
#2971
Feb2012, 02:48 PM

P: 1,696

I personally wouldn’t call actuarial work lucrative, but if you can get a job and some experience it has been very stable historically. It certainly pays better than most office jobs.
There are people with math PhD’s that get jobs as actuaries, but they’re rare. Actuarial mathematics is very specific and, if you’re in the US, you’ll learn it from the exams anyways. So why spend the extra years of poverty? The fantasy people have entering grad school wears off long before a math PhD is earned, so a Masters in math is much more common in this line of work. To PrinceRhagar, getting a PhD in math with hopes of working at an engineering firm sounds like a recipe for disappointment to me. Don’t get me wrong, with enough craft and luck I’m sure it’s possible. It’s just not probable. Still, you’ll have lots of other options, too, so maybe it’s worth a try. 



#2972
Feb2212, 09:38 PM

P: 17

Ironman, I sometimes struggle with the same thing. I do a proof, one which I feel is especially hard for me at the time, and in the end, like as soon as I finish it, I'm sitting there wondering whether or not whatever I did was correct. Usually what I do in these situations is examine every single step in my proof as much as I can, like, I will review the exact form of any theorem I may have used, critically examine and "poke at" any kind of things I may have "constructed" to aid in my proof, and so on. Also, another thing which is, in my opinion, extremely helpful is to walk away from your finished proof for like 2 days, then come back to it and read it over. Many times, you will not be able to see a mistake you may have made in your proof if you examine it immediately after you've finished it. Walking away gives your brain time to let other ideas and stuff in, like you stop thinking about math. There have been times where I do a proof, and I examine it immediately after and find no mistake in it. But then, days later, I do the same thing, and I find this HUGE mistake in it, and it's because when I checked immediately after finishing it, I was walking through the same path I went through when I made the mistake, and so it doesn't seem like a mistake, if that makes any sense at all... So yeah, my advice is that you walk away for a couple days, and then re read your proof. I feel like gaps in your understanding are much easier to find when you do this.




#2973
Feb2612, 02:44 PM

P: 14

What's a good resource to learn about simple closed curves and intersection numbers (geometric and algebraic)? I don't know if this is obvious but I'm looking at this from a surface topological perspective.
Thanks. 



#2974
Feb2712, 09:41 PM

Sci Advisor
HW Helper
P: 9,428

milnor's topology from the differentiable viewpoint, differential topology by guillemin and pollack, and algebraic curves by william fulton.




#2975
Feb2812, 02:19 PM

P: 20

I've only read half topic but it has an insane amount of advice, references, and enjoyable stuff. Thank you all, seriously.




#2976
Mar712, 03:26 PM

P: 38

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, onetoone functions and their inverses, trig, imaginary numbers...
http://www.amazon.com/IntroductoryA...3&sr=83spell Though I have yet to read Spivak, I imagine this would be wonderful preparation for it. 



#2977
Mar1512, 08:10 PM

P: 828

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 moneywise 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. 



#2978
Mar1612, 03:14 PM

Sci Advisor
HW Helper
P: 9,428

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. 



#2979
Mar1812, 07:41 PM

P: 524

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




#2980
Mar1812, 08:26 PM

Sci Advisor
HW Helper
P: 9,428

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.




#2981
Mar1812, 10:07 PM

P: 21

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 onestep 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 3year 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 problemsolving 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? 



#2982
Mar1912, 08:08 AM

P: 524

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 selfstudying, 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 



#2983
Mar1912, 06:48 PM

P: 21

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. 



#2984
Mar1912, 07:47 PM

P: 65





#2986
Mar2012, 09:48 AM

Sci Advisor
HW Helper
P: 9,428

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.




#2987
Mar2412, 08:39 AM

P: 83

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 subpar 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. 



#2988
Mar2412, 09:01 AM

P: 1,056

But it's not a joke. It's not uncommon for the dropout 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. 


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