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The Should I Become a Mathematician? Thread

by mathwonk
Tags: mathematician
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Whovian
#3367
Jan5-13, 04:10 AM
P: 642
I was about to ask where Number Theory was in the list of major branches, when I realized it was basically a subset of algebra.

Anyway, I've gone through pretty much one's basic high school curriculum, have some rudimentary understanding of number theory (hate it,) am in an intermediate combinatorics class at the moment, have gone through a basic calculus course with little bumps (other than that I'm still struggling with Riemann integrals, working on that,) and have some knowledge of integral multivariable calculus. No idea where to head to next.
mathwonk
#3368
Jan5-13, 10:30 AM
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rather than a branch of algebra, number theory is the study of a certain fundamental example, namely the integers, that can be studied by many different techniques. i.e. there is algebraic number theory, a branch of algebra, and analytic number theory, and also arithmetic algebraic geometry.

Basic advice: Try not to make up your mind too soon in favor of, or strongly opposed to, any particular topic, especially not while you are very young and naive. The more you know about it, the more interesting a subject becomes.
Dens
#3369
Jan7-13, 11:49 PM
P: 74
mathwonk, I am a junior and planning to graduate next year. I have a major problem.

My university has research opportunities, but I am unable to apply for them because I had to do summer classes. I am terribly upset because if I were to apply, I could get the research position easily (I have two profs who can take me) and I don't want to throw away this precious opportunity, but at the same time if I cannot throw away my summer classes either. Extending my college career could heavily influence my future, so pulling off another year is unfortunately out of the question

Summer term is splitted into two. I plan to have two courses per term. One computer science (like freshman level) and probably an art class. for one term and the next another freshman computer science class and maybe an easy stat class. I could technically run into the risk of weighing the research over my grades. So I could sacrifice grades for research, is this a terrible idea? Research is taken up the whole term
n10Newton
#3370
Jan18-13, 08:11 AM
P: 108
@Dens What you want to do in future it depends on you. If you want to study Mathematics and doing Research then stop the Summer courses in Arts & CS.
mathwonk
#3371
Jan18-13, 02:49 PM
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for some reason, the way you present it, i cannot tell what is better. you say that taking the summer courses is necessary. whereas the research is not as necessary. some kind of compromise is usually possible. but you need to be asking these questions of the professors you are going to be working with, in the research opportunity and the courses, not me. in this situation they know you and know the circumstances and can better advise how to work this out.
3.141592
#3372
Jan20-13, 04:27 PM
P: 76
Hello,

I don't mean to intrude and hope this is not rude but I was not sure where else to post this.

Can I put in a polite request for a 'who wants to be a statistician' thread please?

Apologies in advance for incorrect place of posting.

Thankyou.
tinylights
#3373
Jan21-13, 03:47 PM
P: 18
Sooooo, I'm a hopeful math major who just started Calc II.

And it's unexpectedly challenging.

I aced Calc I, lowest test score was a B and I feel very comfortable with all of the concepts. But even in the very first week of my Calc II class, sitting down to do the homework, I am spending what seems like an eternity on each problem and struggling my way through them. (We're doing integration by parts primarily, with some new trig identities thrown in there.)

Is there still a chance? Do I have what it takes to be a math major? All of my friends told me Calc II was basically impossible, but I didn't listen... I'm feeling very worried.
homeomorphic
#3374
Jan21-13, 05:01 PM
P: 1,245
Is there still a chance? Do I have what it takes to be a math major? All of my friends told me Calc II was basically impossible, but I didn't listen... I'm feeling very worried.
There's always a chance. As I've said before, the bad news is it's going to get 10 times harder when you get to real analysis, then another 10 times harder if you get to graduate school, and then another 10 times harder when you get to research. This isn't much of an exaggeration, although you shouldn't take me completely literally here. The good news is that it is possible to get 10 times better each time. I know at least a couple research mathematicians who failed calculus and others who maybe didn't fail, but didn't do that well.

But it's not easy. Of course, if you just want to get a bachelor's degree and then get a job, you only have to improve your math skills by a factor of 10, rather than 1000.

I can't say that having great difficulties with Calc 2 is a good start, but it is possible to improve and catch up. When I studied that stuff, it wasn't a breeze, since I wasn't that good at math at that stage. By now, Calc 2 seems trivial, but even back then, the idea that it was "impossible" would have sounded like a bit of a stretch.
mathwonk
#3375
Jan22-13, 10:17 PM
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@3,14,

why don't you start the thread you want?
mathwonk
#3376
Jan22-13, 10:20 PM
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tiny lights: math is hard. i myself, an obvious beacon of the math world (hysterical laughter), got a D- in second semester calc.

i'm just saying, struggling or not, no one can force you to give up. you may not get a fields medal, but if you enjoy the work,..,...

but it depends on you. some of us would be happier elsewhere, just not me.
tinylights
#3377
Jan23-13, 08:49 AM
P: 18
Thank you both, it makes me feel a lot better to know that a certain amount of struggle is okay. I'm just going to try my best and see where I get, and hit up my professor's office hours like crazy.
dkotschessaa
#3378
Jan30-13, 06:51 AM
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P: 604
Quote Quote by tinylights View Post
Thank you both, it makes me feel a lot better to know that a certain amount of struggle is okay. I'm just going to try my best and see where I get, and hit up my professor's office hours like crazy.
What helped me during that time was to realize that calculus was just a part of mathematics, and doing actual calculations was a small part of that.

By this point, I'm finally doing stuff that either a) isn't calculus (foundations, logic, set theory) or b) that involves very little calculus (probability - we haven't even used calculus in the course yet. The stuff that isn't calculus - the more abstract stuff - seems easier for me (though harder for those that were good at calculus, and who seem to dislike abstraction).

The stuff that *does* involve calculus involves using some technique over and over again, rather than blazing through a thousand different concepts like you do in the calculus sequence, without time or pause or reflection. So you'll get better at that thing.

I also do peer-leading and tutoring for calculus, which forces me to review and understand things better, and certain concepts are only now sinking in - I suspect they'll continue to 'sink' for awhile.

-Dave K
Snow-Leopard
#3379
Jan30-13, 12:26 PM
P: 53
Quote Quote by mathwonk View Post
Becoming a mathematician.

Being a mathematician means doing mathematics, but the activity is not the same as the job. Being a professional mathematician means being a professor, doing research and teaching and writing, or working in an industry using math tools to do things like design cars, or solve turbulence problems for aircraft, or to estimate the actual pollution in streams from samples. I only know about the professor side of it since I have been teaching and working in a university setting most of my life, but the behavior of learning and practicing mathematics is probably not too different for all intended lines of work. Ironically, a professor often has so many duties associated with teaching, grading, evaluating people, recruiting, etc,.. that he/she has to scrounge time to actually do math.
Here you listed many Things but
1.How you get the idea that your future is in Professor Post?
2.What type of work a mathematician do outside his academia i.e, as research?Are they paid just for doing/solving hard type equations?
3.How you get prepared for your Lecture? What you add extras every year that means if you repeat same lecture again and again every year then student may understand that the Prof. is just memorized everything and write downed!
Snow-Leopard
#3380
Jan30-13, 12:48 PM
P: 53
Quote Quote by mathwonk View Post
Matt's remarks on differences in expectations in US, UK remind me of a talk I heard at a conference. The speaker said something like, "this proof uses only mathematics that any sophomore undergraduate would know", then paused and added, "or here in the US, maybe any graduate student". This is true and getting worse.
What do you think the Reason behind it! Syllabus overview or others!
Snow-Leopard
#3381
Jan30-13, 12:55 PM
P: 53
Quote Quote by mathwonk View Post
From 1960-1964 there were undergrads I knew at Harvard, maybe even the typical very good math major, who took the following type of preparation: 1st year: Spivak calculus course, plus more; second year: Loomis and Sternberg Advanced calculus, Birkhoff and Maclane, or Artin Algebra; 3rd yr: Ahlfors and maybe Rudin Reals and Complex; 4th year: Lang Algebra, and Spanier Algebraic Topology.
What do you recommend today as an Undergraduate 4 year Mathematics Course.
Also at this time Harvard is Rocking in PUTNAM Mathematical Competition do you know syllabus of that institute and their recommended text.
Snow-Leopard
#3382
Jan31-13, 01:28 AM
P: 53
Quote Quote by n10Newton View Post
Can you list some journals also.I read the thread whole but not found any,when I was in Pre-University i read the canadian CRUX for IMO preparation. Currently I am going through journals from MAA. Name some others.
Try the Monthly by American Mathematical Society if you understand the Journal by Mathematical Association of America.
Snow-Leopard
#3383
Jan31-13, 01:58 AM
P: 53
Good Thread mathwonk but only clear till Graduate Education.
Mariogs379
#3384
Feb1-13, 12:54 PM
P: 27
@mathwonk, do you know of a good real analysis book for R^n? I hear Baby Rudin's treatment of it is awful...(not that I liked the first half of Rudin...)


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