The Should I Become a Mathematician? Thread

mathwonk

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

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

So we should smoke pot?

ironman1478

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

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

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

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

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

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

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

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

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.

Locrian

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.

00Donut

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.

abelian

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.

mathwonk

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

Advent

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