Should I Become a Mathematician?

[thrill3rnit3]

I'm just wondering, did I do the right thing in not skipping geometry? I had the choice of testing out of it, but I decided not to and instead I took it freshman year (high school). I should say I didn't really regret it, since my geometry teacher was like the only math teacher in our school who knows his stuff (plus probably the AP "Calc" teacher)

Now I'm a soph, and I'm on Alg. II/Trig Honors class (nevermind the honors label. It's not really "honors", if you know what I mean). I'm thinking about doing Precalculus over the summer (which would cost me - no, my parents - a painstaking 800 bucks), so that I can take 2 years of AP "Calc" (AB and BC) to add to my college application.

Am I doing the right thing??

 

[symbolipoint]

Skipping Geometry might or might not mean much now; in any case, you already studied it instead of skipping it and it probably helped you at least a little bit, certainly did not hurt you. PreCalculus in the summer might be rough going - not always enough time for some people.

If you are truly interested in Mathematics then you shoud definitely study Geometry. You may see how some things are obtained with Calculus while those same things can also be developed in Geometry without resorting to Calculus.

 

[thrill3rnit3]

I'm doing self-studying so I'll probably be almost if not finished with PreCalc by next summer. I'll take the course just to refreshen my memory, ask some questions, and because my school puts PreCalc as a prerequisite for AP Calc.

 

[mathwonk]

i do not know what your geometry course was like, but i seem to recall no one was allowed to enter plato's academy who was ignorant of geometry. the same should hold for college entrance today in my opinion. just today i have been reading archimedes, for more insight on his anticipation of basic facts now considered a part of integral calculus. euclid is also superb training.

 

[thrill3rnit3]

i do not know what your geometry course was like, but i seem to recall no one was allowed to enter plato's academy who was ignorant of geometry. the same should hold for college entrance today in my opinion. just today i have been reading archimedes, for more insight on his anticipation of basic facts now considered a part of integral calculus. euclid is also superb training.

my geometry teacher emphasized proofs and my dad told me that mastering geometry would be really helpful in the long run, I guess what he says is true...

 

[merjalaginven]

Pure mathematics is the way to the underground. I don't get it all but I do know that if you understand how you are doing it and WHY you are doing it- in every way!- then you are able to understand why everything is so- i mean everything. Pure math is what people do not see, it is the foundation. I want to see like them, not just do what they thought of. ahhh that is the beauty of mathematics. :) they see things others do not-

 

[CoCoA]

I want to be a mathematician (sort of), but I don't know if math would still want me. I am more than 15 years removed from undergrad, no major or minor in math/science/engineering. I have taken some math courses for last 3 years, and I am doing research with a Prof this year; I think I have a minor extension of a minor result. But to go into PhD, I would have to quit work (in my good earning years), get through exams (probably not a big deal), get an advisor (may be a big deal) and write a thesis (probably a big deal). Still, I am applying this year.

Unlike the young students here, I don't expect to solve a major problem - that is like picking the best apple from the top of the tree. But in just the little research I have done, I have started to see so many little apples lying on the ground ready to be picked up - like the little problem I am working on. I don't know, meybe this is because my work crosses over with CompSci, and maybe those problems are more accessible.

 

[mathwonk]

although very different, the last two messages seem more insightful than many. best wishes and good luck to you both.

 

[JasonRox]

Pure mathematics is the way to the underground. I don't get it all but I do know that if you understand how you are doing it and WHY you are doing it- in every way!- then you are able to understand why everything is so- i mean everything. Pure math is what people do not see, it is the foundation. I want to see like them, not just do what they thought of. ahhh that is the beauty of mathematics. :) they see things others do not-

I don't see what your point is, or how that is special.

There are many things others do SEE and mathematicians DO not.

There is no advantage to seeing one thing over another. It's all subjective.

 

[merjalaginven]

It was an opinion.
I did not say that mathematicians were the only people who see things differently. I just said some do.
Between applied and pure mathematics, which was the topic, a pure mathematician is most likely going to understand the concepts more in depth than the person who just uses a formula without questioning what you are really doing. I am not knocking applied math- I would much rather do that any day than proof writing!
I agree, everything is subjective based on our perceptions- that was just my opinion.

 

[Helical]

mathwonk, I was just wondering your opinion (should one exist) on Calculus by Hughes-Hallett et al (required text for my university). It seems to have poor ratings, though quite a few do. Should I get another book to learn from and just use this for problem sets? I find it strange that they would use a book that is so bad but the department at my university seems pretty good.

 

[The|M|onster]

Unlike the young students here, I don't expect to solve a major problem - that is like picking the best apple from the top of the tree. But in just the little research I have done, I have started to see so many little apples lying on the ground ready to be picked up.

Wow! I really like your apple analogy. It's very poetic.




And Helical, I used Hughes-Hallet for Calc I, II, and III and I absolutely hated it. Fortunately, I had some really good teachers. I recommend picking up another text to supplement your studies. Try browsing a used bookstore. You'd be surprised what kind of gems you can pick up if you look hard enough.

 

[JasonRox]

It was an opinion.
I did not say that mathematicians were the only people who see things differently. I just said some do.
Between applied and pure mathematics, which was the topic, a pure mathematician is most likely going to understand the concepts more in depth than the person who just uses a formula without questioning what you are really doing. I am not knocking applied math- I would much rather do that any day than proof writing!
I agree, everything is subjective based on our perceptions- that was just my opinion.

That's not true either. Where do you get this from?

A biologists will understand things mathematics will not. I said what I said in a general term. As in, don't try and feel superior or believe something is superior because one is seeing something others do not. There will always be something you don't see and someone else does.

My comment had nothing to do with applied vs. pure either.

 

[merjalaginven]

I did not knock anyone or what they think or how they think it-
I am not disputing an opinion that is mine alone with people that are rude.
I am a grad student and a new mom- Not a philosophy major- you twist my words around- I never said that a 'biologist' wouldn't see things that a mathematician would or whatever trivial example you want to say- all i was implying is that if one has a clearer sense of why you are doing something you are more likely to understand the outcome better.
I came here to read proofs and refresh- not to argue about deductive logic.
If you want to reply to my thoughts please refrain from things such as- well this makes no sense- or what is your point- this is rude. Otherwise feel free to say what you like- just be respectful bc I know I am not hurting anyone here by voicing my opinion-
oh and my comment did have something to do with applied vs pure mathematics- someone brought it up- which one was better to do- so sorry you are so worked over my comment!

 

[mathwonk]

i have not studied hughes hallet's book but she is not even a mathematician as far as i know, so why would anyone use a book by her?

 

[Vid]

It was an opinion.
I did not say that mathematicians were the only people who see things differently. I just said some do.
Between applied and pure mathematics, which was the topic, a pure mathematician is most likely going to understand the concepts more in depth than the person who just uses a formula without questioning what you are really doing. I am not knocking applied math- I would much rather do that any day than proof writing!
I agree, everything is subjective based on our perceptions- that was just my opinion.

What are you saying here? Are you saying that an applied mathematician uses formulas without questioning them because that is definitely not the case.

 

[merjalaginven]

I am not saying that at all- i am not saying ALL of ANYTHING/ANYONE thinks like anything! All i was saying is if you understand WHY you are doing something then you understand the entire concept more thoroughly- omg people get off my case- I was shoutin out to people that take interest in math/science- someone asked - which one should i do- i would do applied over pure but i am just saying i give respect to mathematicians in the past who figured all this stuff out so far- I NOT IMPLYING ANYTHING ELSE- the one you "" was in response to another person- I did not say an applied mathematician- i said a person who uses a formula which could be anyone- i am not knocking anyone.

 

[PowerIso]

I think some of you guys are reading a bit to much into Mer's post.

What she wrote is pretty much common sense. If you understand the root of a subject you will probably understand the subject a lot more. I'm not exactly sure how any of you guys got that she is knocking applied. I study statistics, which is in my opinion, applied math for applied math ;) and I wasn't offended or bother by her post. Relax and take it for what it is.

 

[merjalaginven]

thank you poweriso! I'm just a metal mommy looking to expand my intellect- never knew i could upset so many people without saying anything that profound-see you later fellow philosophers!

 

[Vid]

It's not that I was reading too far into his post. The grammar was rather ambiguous since he started the sentence comparing pure and applied mathematicians then changed to comparing a pure mathematician to some group with a certain property. It's not hard to see why I thought he was saying applied mathematicians have that property. Ironically, if a statement like that would be in a mathematical proof, it would be pretty standard to make that connection.

 

[PowerIso]

You must be reading a different post than I am. I read, pure math is the way to the underground... with no reference to any other field. Anyways, it doesn't matter, let's just say it was one huge misunderstanding!

I have a question though. Does anyone know where I can find good information about algebraic statistics or graduate level material on Combinatorial commutative algebra?

 

[mathwonk]

merjala, you just got an introduction to webworld. whatever you say is read by so many people, that some may take offense. when i started on here blithely saying whatever i thought, i was attacked by people who did not like my mathematician slanted opinions, so i started this thread specifically so no one could do that. I.e. it says right in the title what the purpose is, so no one could blame me for taking the point of view that opinions here were oriented towards people wanting to do math.

unfortunately it is very easy to get off course and attack other peoples opinions when that is not getting us anywhere. this thread may be running its course by now anyway.

certainly the original format of laying out systematic advice for career seekers is almost entirely gone. it has been pointed though that i never covered the crucial areas of publishing, getting grant money, and getting promoted.

 

[merjalaginven]

haha this is funny now- vid- 'HE' IS A 'SHE' and you must write proofs like my last advanced calc teacher-i did not say 'therefor an applied mathematician does not understand as well'. you used your own deductive logic to come to your own conclusion. AHHH my football team lost and then I get an email post talking about grammer.
is anyone here a mathematician or just philosophy and english majors!
thanks for the help iso and wonk- yes i would love to see more talk about resources and ?s like iso's to help fellow people to the site- i will reply when I get more answers for questions such as these. but for now
i am going to just do the readin thing- peace! \m/

 

[merjalaginven]

I want to be a mathematician (sort of), but I don't know if math would still want me. I am more than 15 years removed from undergrad, no major or minor in math/science/engineering. I have taken some math courses for last 3 years, and I am doing research with a Prof this year; I think I have a minor extension of a minor result. But to go into PhD, I would have to quit work (in my good earning years), get through exams (probably not a big deal), get an advisor (may be a big deal) and write a thesis (probably a big deal). Still, I am applying this year.

Unlike the young students here, I don't expect to solve a major problem - that is like picking the best apple from the top of the tree. But in just the little research I have done, I have started to see so many little apples lying on the ground ready to be picked up - like the little problem I am working on. I don't know, meybe this is because my work crosses over with CompSci, and maybe those problems are more accessible.

btw i love this analogy- sometimes those are the most important ones (apple)- compsci is so neat to me- like matrix transformations being applied to comp graphics- little stuff like that is cool to me- and i understand the whole work/being older thing (not saying your old-lol-imsure someone will ""me on that one lol)- I am going back afer just a few years and have forgotten much and i have a new baby- but just do what you want to do- it will better yourself and your family if you are happy and content at where you are in life- you only live once- good luck to you!

 

[muppet]

This is completely off-topic, but Mathwonk sometimes shares insights he has on this thread, so I hope no-one minds my taking a similar liberty...
I FINALLY understand the Euler formula at an intuitive level!
The "point" of a real exponential is that its derivative is proportional to itself, so if f(x)=e^kx then df=kf(x).dx.
If instead, you replace k by i, then your infinitesmal change df is now at right-angles in the complex plane to the change in your real parameter x. And as i has modulus one, you don't change the size of anything- you just push it round sideways :rofl:

(Curses, the smiley goes the wrong way )

 

[Minich]

Arnold:

Ньютон, Эйлер, Гаусс, Пуанкаре, Колмогоров — всего пять жизней отделяют нас от истоков нашей науки.
In english:
Newton, Euler, Gauss, Poincare, Kolmogorov - only 5 lives from the the cradle of our science: mathematics

Can i thank You for mentioning Arnold? He is one of best mathematician in Russia and at the same time excellent writer and genuine russian citizen (i don't know his nationality, it doesn't matter is he russian, german, jew or ukranian,...).
I think it'll be very important to read his exellent article about mathematics, physics, greate mathematicians and mathematical theories,...
But this article is in russian. Because my poor english i can't translate it properly. May be there is russian, who can translate it?
You can find it at:
http://www.mccme.ru/edu/viarn/obscur.htm
http://scepsis.ru/library/id_650.html
and so on

For physicists it may be interesting to read about Berry phase ("submarine phase" ))))), Landau, turbulence, Reinolds number, Klimontovich and Mandelstam, first explaining alfa decay through tunneling (remember Gamow?),...
For mathematician to read about Bourbaki and meaning of mathematics from the point of view of Kolmogorov.
For ordinary people it is interesting article about what do we live for.

----------------------------------------------------------------------
A whole is that which has beginning, middle and end.

 

[mathwonk]

something about the "new obscurantism"?

 

[Minich]

something about the "new obscurantism"?

Not only.
1. About liberal reforms in Russia which will kill not only mathematics in Russia but any pozitive in our education system we have now.
2. What is mathematics and its role in the system of sciencies.
3. What are the main mathematical achievements in the world for last 2-3 centures.
4. The main figures (persons) who made the best in mathematics and main figures, who made the worst (Bourbaki,...).
5. Why such person as Landau can't be regarded in plus in physics and where lead the Landau-like road.
6. How much theories were reopened in modern physics, thou if physicists had proper mathematical education they could knew that their achivements were known several decades or may be hundreds years ago (berry phase, cycles, asimptotic paths,...)...
And so on.
----------------------------------------------------
A likely impossibility is always preferable to an unconvincing possibility. Aristotle

 

[asdfggfdsa]

I'm curious if anyone knows what sort of gpa and qualifications a middle tier graduate school (in math) would look for?

 

[arshavin]

offtopic-

Is weierstrass idea of delta-epsilon definition of limit considered amongst the greatest intellectual achievements?

It seems to me that since all these good things of calculus come from this, it must have taken some genius to choose that definition.

But then I haven't studied too much maths

 

[mathwonk]

i would say this definition is only a small step in a long chain of work going back to the greeks who showed the area of a circle was a number that could be neither less than nor greater than pi R^2 essentially by showing that is was a limit of quantities that differed from pi R^2 by less than any given amount (any epsilon).

so many many people for hundreds and thousands of years gave arguments essentially equivalent to what we have as the epsilon delta definition of limit. i.e. limits were well understood by the masters for a long time before they were stated in the form we have now, and their use of them is roughly equivalent to ours.

i would say the discovery of the method of limits by the greeks stands far above the much later precise statement of that method. the statement came from analyzing the method, not the other way round.

 

[tgt]

Mathswonk, you were saying that you did very badly in your undergraduate years. What was your gpa for those years? Did you not go to graduate school straight away or work instead? After your undergrad disaster, did you repeat undergraduate or go straight into grad school? If the latter how did you catch up with the things you didn't learn properly while in undergrad and the things you've forgotten after undergrad?

 

[mathwonk]

forgive me, but i think i have told this tale numerous times here in detail, no?

 

[tgt]

forgive me, but i think i have told this tale numerous times here in detail, no?

True. Could you please provide some links?

 

[morphism]

True. Could you please provide some links?

Can't you just do a search yourself?