Other Should I Become a Mathematician?

[n10Newton]

n10Newton,, does this help?

http://www.math.uga.edu/undergraduate/lowerdivisioncoursesandsyllabi.html

Thanks for that.

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.

 

[mathwonk]

what are you looking for?

 

[Whovian]

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]

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]

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]

@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]

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]

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]

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]

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]

@3,14,

why don't you start the thread you want?

 

[mathwonk]

tiny lights: math is hard. i myself got a D- in second semester calc (mostly by not attending.)

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]

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]

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]

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]

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]

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]

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]

Good Thread mathwonk but only clear till Graduate Education.

 

[Mariogs379]

@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...)

 

[Snow-Leopard]

@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...)

What do you mean by good, Level Low to Rudin or High. I have used 3 books in this order to Real Analysis, Lang to Rudin to Royden.

 

[Mariogs379]

I guess same level as Rudin would be good but more expository, clearer, etc...

 

[A. Bahat]

Try Spivak's Calculus on Manifolds, or maybe Edwards's Advanced Calculus of Several Variables.

 

[mathwonk]

I have often recommended books by sterling berberian and by george f. simmons. look at the first few pages of this thread as well as at the thread on mathematics books.

https://www.physicsforums.com/forumdisplay.php?f=225

 

[dkotschessaa]

I'm not sure if I've asked this before - but if I want to go for a PhD after I get my bachelor's, wouldn't it behoove me to go straight for it rather than a masters? And to do it in the same place I get my Bachelors?

A couple of considerations:

Being older and married, it's not easy to think about just picking up and going somewhere else for graduate school. And as a PhD student I'd be at least semi-employed. Right now my wife is supporting me. She doesn't mind - sort of - but does occasionally inquire (understandably) just how long this is going to take.

I'm starting to think I would like teaching, even though I hadn't considered it much before. I've been having very good experiences in peer leading and tutoring. Not to mention I've had some really bad professors who make me go "hmm... I could do that better... if I knew the subject anyway."

Worried that if we have kids in the next year or so I'd be somewhat of an absentee parent though.

 

[mathwonk]

Is is usual to enroll directly in the PhD program and not stop for a separate masters. I got a masters by default part way through my PhD program, which was a good thing since I did not finish the PhD that first time through. At my school the masters requirements were a subset of the PhD requirements so all I had to do was apply for the MA after satisfying them.

It is usual to change schools from BA to PhD, just to gain more mathematical exposure, i.e. to meet more people and more perspectives, and to choose a place that has a specialty in your area of interest. But in special cases it is not unheard of to stay where you are, and having a family and a local job is such a special case.

There have certainly been successful PhD candidates at UGA who were undergrads there, indeed some of the best and brightest undergrads just went straight on without moving away.

Regardless of choices, getting a PhD in math is very demanding on you and your family. So choose a good advisor and supportive department. if you already have one, I would not take it for granted that it can be reproduced elsewhere.

 

[dkotschessaa]

Is is usual to enroll directly in the PhD program and not stop for a separate masters. I got a masters by default part way through my PhD program, which was a good thing since I did not finish the PhD that first time through. At my school the masters requirements were a subset of the PhD requirements so all I had to do was apply for the MA after satisfying them.

It is usual to change schools from BA to PhD, just to gain more mathematical exposure, i.e. to meet more people and more perspectives, and to choose a place that has a specialty in your area of interest. But in special cases it is not unheard of to stay where you are, and having a family and a local job is such a special case.

There have certainly been successful PhD candidates at UGA who were undergrads there, indeed some of the best and brightest undergrads just went straight on without moving away.

Regardless of choices, getting a PhD in math is very demanding on you and your family. So choose a good advisor and supportive department. if you already have one, I would not take it for granted that it can be reproduced elsewhere.

Thanks as always for your encouragement (tempered with a kind dash of reality).

One of the things I really like about my university is the environment. I've gotten to know many of them quite well and they've been extremely supportive.

I'm sure it wouldn't be easy. Right now I find it hard to take more than 2 math classes during a semester without falling behind. This makes me nervous about *any* grad program, given the pace. But getting paid, even just a little, to advance my knowledge? Beats working in I.T. again.

It's a bit to early to decide exactly what I'll be doing, but I am trying to map out all the possible avenues right now.

-Dave K

 

[tinylights]

Just to follow up on my math crisis upon getting into Calc II... just got back results for the first test! I got a 95%! Guess I won't have to become an English major after all lol :)

 

[QuantumP7]

My math obsession has totally screwed up my sleep schedule.

 

[dkotschessaa]

My math obsession has totally screwed up my sleep schedule.

It's worse than video games sometimes... No electronics required!