The Should I Become a Mathematician? Thread


by mathwonk
Tags: mathematician
homeomorphic
homeomorphic is offline
#2953
Feb10-12, 03:09 PM
P: 1,052
Probably, math ability fades slightly with age, but I don't think it fades that quickly, plus, older mathematicians can make up for that with more breadth and so on. There seem to be plenty of examples of good work by older mathematicians.

People SHOULD be discouraged from pursuing math as a career, on the whole.

When you are growing up, it's easy to have this naive view of pursuing your dreams, but in many cases, it's just not realistic. My piano teacher just got his doctor of music and was looking for jobs. He says the number of positions available for piano professor in the country was something like 8. In the whole country. So, unless you started playing at age 4 or are at least are willing to put in 10 hours a day and have no life outside piano what so ever, you can probably forget about it.

Now, math isn't quite that bad, but there's a similar process of weeding out that goes on, leaving few survivors at the end. I just mentioned piano, just to shatter the naive childhood attitude of just saying "I want to be so and so when I grow up."

You can't always get what you want.

However, if you are really determined to do it, do it. Just don't say I didn't warn you if, at some point, you find it all a bit overwhelming and feel tempted to quit. Try to plan ahead. Start thinking about research as soon as you can. I didn't think about it enough until too late in my PhD. That doesn't necessarily mean you have to know what your thesis topic will be in undergrad already, but it helps to think about things like learning how to typeset in Latex, drawing mathematical illustrations, and so on. Practice typing up notes in Latex or something. Also, I think it might be helpful to think about what kind of skills you will need and how to learn things with research in mind, early on. I thought about it all a bit too late. Come up with exercises for yourself and try to invent things--don't just rely on books for that. That will give you some of the skills you will need.

If Atiyah was tempted to quit, anyone may be tempted to quit.
Mépris
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#2954
Feb11-12, 01:26 AM
P: 826
Has anyone read this Lagrange book? Thoughts? [edit: after a search of this thread, I see you (mathwonk) have read it - any further thoughts, relating to this and Euler's book, i.e, any non-essential parts I could simply skim through instead of deeply studying? if I had it my way, I would read it all - trust me, I get very obsessive about this - but time is not on my side. no, I'm not dying but I need have other subjects to take care of]

Opinions on this text as well? I already have this book home and was wondering if the exercises in it would be suitable to supplement my reading of Euler. Viswuze, if you're reading this, note that I tried to get hold of the Allendoerfer/Oakley book but found no edition that ships to my country.

Lecter, I can see where you're coming from but there is simply too much information in this gem of a thread that it would require a herculean effort to compile it all in one article. In fact, I'd be willing to bet that there's enough valuable information/opinions here to make a few articles, directed to students in high school to those who already have doctoral degree!

Further, who can decide what information should "make the cut" and what should not? This is indeed mathwonk's thread and he is among the main contributors (or "guides"?) in it but there is, as I said, just too many good posts here for anyone to realistically put it all together in a concise way. It could be done but I think it should be a collective effort and even then, it will take a lot of time and one may accidentally omit one thing or another. At any rate, what I mean to say is, even if the people involved were to confine themselves to this thread alone (there's so much more information throughout the academic guidance section, and of course, in the whole website), it would be difficult to write "complete articles".

Anyway, this just my opinion and I could have missed something or could indeed, be completely wrong. :-) :-)
sahmgeek
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#2955
Feb11-12, 09:58 PM
P: 65
Hello,

I have a question that may already be covered in this thread but I have not read all 185 pages. If my question has been addressed, could someone kindly direct me to the correct page(s)?

I am seeking advice on a receiving a math degree (e.g. Master's + Secondary Ed certification) however I have very little formal math training beyond high school. I'm one of those horribly misguided individuals with a social science/philosophy degree who thinks they can walk into the world of math/science with foolish confidence . Given that I would need to start from scratch, I wondered if taking the basics at a community college (Analytic Geo/Cal 1, 2, & 3, Linear & Abstract Algebra, Finite Math, and ODE) and, of course, doing very well in the courses, would provide enough preparation for applying to a graduate program. If not, are there other avenues one could take w/o getting another bachelor's degree (I already have an M.A. in another field)? I do know that most of the grad programs (I'm located in New York, NY and will not relocate) allow up to 4 non-matriculated courses so that could help. Also, I realize that these programs are very competitive and I would be up against applicants who already have a math degree. However, I also know that high school math teachers are scarce, especially in NYC.

Perhaps a little personal information about me would help you formulate your response. I'm 35, stay home with my 2 very young children and would most likely need to go back to school part-time. I might have some time during the day to work on math, but most of my free time would occur in the evening, 8pm and later. I am concerned that this isn't enough free time to really study this subject. I am not very concerned about my intellectual capabilities, but with my time constraints perhaps this is an unrealistic goal given the rigorous nature of math. I do, however, like the idea of studying math for it's own sake, even if the end result is purely for personal gain.

Thank you for any feedback relating to this post.
homeomorphic
homeomorphic is offline
#2956
Feb12-12, 12:28 PM
P: 1,052
I am seeking advice on a receiving a math degree (e.g. Master's + Secondary Ed certification) however I have very little formal math training beyond high school. I'm one of those horribly misguided individuals with a social science/philosophy degree who thinks they can walk into the world of math/science with foolish confidence . Given that I would need to start from scratch, I wondered if taking the basics at a community college (Analytic Geo/Cal 1, 2, & 3, Linear & Abstract Algebra, Finite Math, and ODE) and, of course, doing very well in the courses, would provide enough preparation for applying to a graduate program.
You would also need 2 semesters of analysis. Community college profs might not have that much credibility as far as recommendation letters go. Cornell or Columbia would be pretty hard to get into. Maybe there's a place in NYC that offers a masters in math that would more realistic. I don't know.


If not, are there other avenues one could take w/o getting another bachelor's degree (I already have an M.A. in another field)? I do know that most of the grad programs (I'm located in New York, NY and will not relocate) allow up to 4 non-matriculated courses so that could help. Also, I realize that these programs are very competitive and I would be up against applicants who already have a math degree. However, I also know that high school math teachers are scarce, especially in NYC.
I don't think you have to get the whole degree, although it helps. But you have to learn most of the same material.


Perhaps a little personal information about me would help you formulate your response. I'm 35, stay home with my 2 very young children and would most likely need to go back to school part-time. I might have some time during the day to work on math, but most of my free time would occur in the evening, 8pm and later. I am concerned that this isn't enough free time to really study this subject. I am not very concerned about my intellectual capabilities, but with my time constraints perhaps this is an unrealistic goal given the rigorous nature of math. I do, however, like the idea of studying math for it's own sake, even if the end result is purely for personal gain.
Sounds difficult. Taking classes would REQUIRE free time during the day, in most cases.

There are times when I do nothing but work, eat, sleep, and take a few breaks here and there for piano. Usually, at least one day a week, I take it easy (only work a little bit, maybe a couple hours). I suppose a lot of this work is self-imposed, due to the fact that I feel the need to drastically reformulate most of the math I come across in order to make it as intuitive and well-motivated as possible.

Poincare is said to have worked on math research for just 4 hours each day, but it will probably take a bit more work than that for several years to get to an appropriate level.
sahmgeek
sahmgeek is offline
#2957
Feb13-12, 01:26 PM
P: 65
Thanks homeomorphic. Yes, I would need to take time out during the day for classes. That is almost certainly true. I suppose I just need to begin with some basic community college classes and go from there. No sense in trying to plan ahead at this point. It does seem to me that it would be very challenging given my background and familial responsibilities. I can assure you that I am not, nor will I ever be, like Poincare. But that's not the goal...
homeomorphic
homeomorphic is offline
#2958
Feb13-12, 04:28 PM
P: 1,052
I can assure you that I am not, nor will I ever be, like Poincare. But that's not the goal...
I just mentioned him to suggest that 4 well-spent hours a day is probably sufficient, eventually, if you ever plan to do research.
mathwonk
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#2959
Feb14-12, 07:28 PM
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people here are giving good advice on what mathematical background you might well need, but since your goal is to obtain a degree, it may be more efficient, to choose =the school where you would like to get your degree, and ask them exactly what will be required to obtain an MA.
Mépris
Mépris is offline
#2960
Feb17-12, 03:10 AM
P: 826
http://www.alljapaneseallthetime.com...rs-and-players

Something I found a website that MissSilvy referred me to. It's about learning Japanese, as the name would suggest, but I think some of us might benefit from this post. I know I did. (math, physics...schooling related, in general)
gnarly
gnarly is offline
#2961
Feb18-12, 10:28 AM
P: 3
Quote Quote by Mépris View Post
http://www.alljapaneseallthetime.com...rs-and-players

Something I found a website that MissSilvy referred me to. It's about learning Japanese, as the name would suggest, but I think some of us might benefit from this post. I know I did. (math, physics...schooling related, in general)
So we should smoke pot?
ironman1478
ironman1478 is offline
#2962
Feb19-12, 03:29 AM
P: 24
hello physicsforums.com,

i just have a question about proofs in general, but i didnt think it warranted a thread and i think this is the right place to put it.

if i am doing a proof and i get to the end, how do i know i am right? i am doing extra problems from my linear algebra book and from "Elementary Geometry from and Advanced Standpoint" and whenever i do a proof, i have no way of knowing that i have done it correctly since there is no solution given in both of these books. its not like finding a solution to an equation or a physics question because usually i can just plug my solution back into an equation and confirm my results, but with proofs its a bit different.

sry if this is a stupid question, but i am hesitant to continue doing problems from the books because i feel like i might finish the book, but i would have learned nothing since i did the problems incorrectly.
chiro
chiro is offline
#2963
Feb19-12, 04:13 AM
P: 4,570
Quote Quote by ironman1478 View Post
hello physicsforums.com,

i just have a question about proofs in general, but i didnt think it warranted a thread and i think this is the right place to put it.

if i am doing a proof and i get to the end, how do i know i am right? i am doing extra problems from my linear algebra book and from "Elementary Geometry from and Advanced Standpoint" and whenever i do a proof, i have no way of knowing that i have done it correctly since there is no solution given in both of these books. its not like finding a solution to an equation or a physics question because usually i can just plug my solution back into an equation and confirm my results, but with proofs its a bit different.

sry if this is a stupid question, but i am hesitant to continue doing problems from the books because i feel like i might finish the book, but i would have learned nothing since i did the problems incorrectly.
Hey ironman1478 and welcome to the forums.

This is not a stupid question.

If you don't have access to someone else like a professor, instructor, lecturer, TA or even one of your peers then I strongly make the suggestion to post your query on here in the relevant mathematics forum.

If you provide all the steps then I gaurantee someone will take a look and critique it.
Nano-Passion
Nano-Passion is offline
#2964
Feb19-12, 10:38 AM
P: 1,306
Quote Quote by ironman1478 View Post
hello physicsforums.com,

i just have a question about proofs in general, but i didnt think it warranted a thread and i think this is the right place to put it.

if i am doing a proof and i get to the end, how do i know i am right? i am doing extra problems from my linear algebra book and from "Elementary Geometry from and Advanced Standpoint" and whenever i do a proof, i have no way of knowing that i have done it correctly since there is no solution given in both of these books. its not like finding a solution to an equation or a physics question because usually i can just plug my solution back into an equation and confirm my results, but with proofs its a bit different.

sry if this is a stupid question, but i am hesitant to continue doing problems from the books because i feel like i might finish the book, but i would have learned nothing since i did the problems incorrectly.
Do the odd problems so you can check if you got the correct answers in the back.
Check if your book is on cramster.com, they have step-by-step solution to virtually every problem.
homeomorphic
homeomorphic is offline
#2965
Feb19-12, 12:17 PM
P: 1,052
i just have a question about proofs in general, but i didnt think it warranted a thread and i think this is the right place to put it.

if i am doing a proof and i get to the end, how do i know i am right? i am doing extra problems from my linear algebra book and from "Elementary Geometry from and Advanced Standpoint" and whenever i do a proof, i have no way of knowing that i have done it correctly since there is no solution given in both of these books. its not like finding a solution to an equation or a physics question because usually i can just plug my solution back into an equation and confirm my results, but with proofs its a bit different.

sry if this is a stupid question, but i am hesitant to continue doing problems from the books because i feel like i might finish the book, but i would have learned nothing since i did the problems incorrectly.
You have to try to figure out for yourself whether it's right or not. What good is knowing math anyway, if you always need someone to tell you whether you did it right? In the context of a job, the person who told you whether you were right may as well just do it themselves. So, you should aspire to be one of the people who knows what is right, rather than one of those who has to be told when they are right.

Just check all the steps and see if each step follows logically from the previous ones.
jbunniii
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#2966
Feb19-12, 12:45 PM
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Quote Quote by homeomorphic View Post
You have to try to figure out for yourself whether it's right or not. What good is knowing math anyway, if you always need someone to tell you whether you did it right? In the context of a job, the person who told you whether you were right may as well just do it themselves. So, you should aspire to be one of the people who knows what is right, rather than one of those who has to be told when they are right.

Just check all the steps and see if each step follows logically from the previous ones.
Easier said than done if you're working outside your comfort range, which is how you learn anything new. This is why peer review exists. Logical errors can be subtle and hard to spot, especially one's own logical errors.
homeomorphic
homeomorphic is offline
#2967
Feb19-12, 01:09 PM
P: 1,052
Easier said than done if you're working outside your comfort range, which is how you learn anything new. This is why peer review exists. Logical errors can be subtle and hard to spot, especially one's own logical errors.
You don't have to be perfect in order to learn something. You don't have to eliminate all mistakes.

I learn boatloads of new stuff that is outside my comfort range all the time and I never need anyone to tell me if I'm doing it right. It doesn't matter that much if I get something wrong because misunderstandings are almost always temporary if you keep learning in a rigorous and questioning manner.

Peer review is there, but it's only the last stage. If you can't tell right from wrong by yourself with reasonable reliability, you will never get to the peer review stage.
PrinceRhaegar
PrinceRhaegar is offline
#2968
Feb19-12, 04:15 PM
P: 3
Hey guys. So I'm in my second semester of college as a mechanical engineering major, but I'm thinking about switching to math. The reasons are simple; recently I've found that I'm better at math than any other subject (especially physics, which is likely what I'll be spending most of my time doing for the next few years considering my current major), and I just think math is cooler than any other subject I've seen so far. The reason I'm really hesitant to do so is because firstly, I have no idea what I'd do with my degree after I graduate, and secondly, and this may seem a bit shallow, I know that I'll likely be making more money as an engineer than as a mathematician, especially right after college. So I guess my question to you guys is what are some of the more lucrative career options for someone with a math PhD (I know that I'll be going to grad school regardless of my major), and what would I likely see myself doing for those first few years after I graduate? Thanks for all the help, sincerely.

EDIT: I should probably add a few more points. In a perfect world I'd major in math and get a job as an engineer (or at least in an engineering company). This is because I love math and I feel like I'd get a TON of satisfaction out of doing useful stuff for the world while also doing what I love. So I guess I should rephrase my question; how easy is it for someone with a math degree to work in an engineering firm? And I know that this will likely vary greatly from person to person, but, mathematicians of the board, how much satisfaction do YOU personally get from doing the more "normal" things that a mathematician does (research, possibly teaching, etc.).
alanlu
alanlu is offline
#2969
Feb19-12, 04:30 PM
P: 65
You can count the money you make when you apply it to *.

Try using a Lebesgue integral to count your money.

Or if you want you can be an enlightened hobo.
20Tauri
20Tauri is offline
#2970
Feb19-12, 05:21 PM
P: 177
ironman1478, that is one of the tricky things about studying on your own. If you knew how to do the proofs correctly already, you wouldn't be studying, so it can be hard if you don't have access to the answers. I'd suggest getting a friend, prof, or a forum group to take a look at your answers. Sometimes you can also find proof solutions by Googling if it's a relatively common problem type, or you could check Proof Wiki. The homework section of Physics Forum also is good for this stuff, as I think others have mentioned.

PrinceRhaegar, I have heard the more lucrative math careers are in finance. You can make quite a lot of money as an actuary, although I don't think it's something you would do if you had a PhD.


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