Should I Become a Mathematician?

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  • Thread starter mathwonk
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  • #1,801
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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.
 
  • #1,802


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.
 
  • #1,803
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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.
 
  • #1,804


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!
 
  • #1,805
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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.
 
  • #1,806
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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?
 
  • #1,807
mathwonk
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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.
 
  • #1,808


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/
 
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  • #1,809


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!
 
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  • #1,810
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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 :biggrin:)
 
  • #1,811
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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 [Broken]
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.
 
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  • #1,812
mathwonk
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something about the "new obscurantism"?
 
  • #1,813
87
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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
 
  • #1,814


I'm curious if anyone knows what sort of gpa and qualifications a middle tier graduate school (in math) would look for?
 
  • #1,815
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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 havent studied too much maths
 
  • #1,816
mathwonk
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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 limits by the greeks stand far above the much later precise statement of that method. the statement came from analyzing the method, not the other way round.
 
  • #1,817
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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?
 
  • #1,818
mathwonk
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forgive me, but i think i have told this tale numerous times here in detail, no?
 
  • #1,819
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forgive me, but i think i have told this tale numerous times here in detail, no?

True. Could you please provide some links?
 
  • #1,820
morphism
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True. Could you please provide some links?
Can't you just do a search yourself?
 
  • #1,821
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Can't you just do a search yourself?

I've tried without success
 
  • #1,822
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hi mathwonk, this is my second year in university and i started to take mathematics as my second major. problem is, i'm not confident about my ability to prove. even simple proofs include some tricks that i think i won't easily come up with at the moment. what would you recommend? i think examining lots of simple proofs will help me at this point but any other advice will also be appreciated. so it would be great if you could point me some good resources where i can find such examples.

thanks
 
  • #1,823
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problem is, i'm not confident about my ability to prove. even simple proofs include some tricks that i think i won't easily come up with at the moment. what would you recommend?

Not all proofs are created equal. Some are so simple or obvious that it's not clear that they should in fact be called proofs. Things like proofs that (x + y)^2 = x^2 + 2xy + y^2. On the other end of the spectrum, there are proofs that seem to require infinite genius to have found. The proof that no rational number's square is two, for instance... the contradiction in the proof is just so damn subtle!

In a single topic in math, you'll notice that many proofs follow a similar pattern or employ a similar "trick". Many mathematicians make their careers off of becoming the first or best at exploiting some kind of mathematical trick. For example, in set theory, Cantor invented the "diagonalization" trick to show relationships between the sizes of sets. The same trick can be used over and over in different ways. You can use it to show that the reals outnumber the rationals. But you can also use it in contexts of computability and formal logic to show that the number of truths and functions outnumber provable truths and computable functions.

By studying proofs, you become more familiar with these tricks. If you study proofs in Point-Set Topology, you'll become much better at proofs in point-set topology. If you come across a theorem which you've never seen, but you recognize topological elements of the problem, you'll have a clue that you should begin looking for ways to reduce the problem to a statement about homeomorphisms, compactness, connectedness, and continuous functions.

As a student, most proofs you'll be expected to exhibit on a test are going to be fairly easy ones. The ones you're most likely to encounter are ones that are very closely related to a definition of some sort. At my school, linear algebra was the course used to introduce students to proofs. Proofs on the test were things like "Prove that the operation 'rotate a vector by 45 degrees' for R^2 is a linear operator" or "prove that a nullspace is a linear space." These kinds of proofs you should be able to do (in any subject) with a small bit of studying.

Sometimes, though, if a major theorem's proof is presented in class, your prof. may want you to reproduce it, or to prove a similar theorem. For example, I had a class where the prof. taught us the proof for the irrationality of the square root of 2, then on the test, asked for the proof for the irrationality of the square root of 3. But if you knew the first (and actually understood how it worked), the second is really easy.

When you're working on a proof which is neither obvious nor has been covered in your class, that's where you're doing real mathematics =-) There is no clear cut path how to solve a proof in general, but as you learn more, you'll pick up lots of useful techniques.
 
  • #1,824
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serkan, from my experience (which is not much more than yours - I've only just done my BSc and am about to embark on a MSc) time and patience are your best friends when it comes to learning how to prove things. It wasn't until my third year courses in analysis and topology that I really began to appreciate the epsilon-delta definition of continuity (in metric spaces). To be honest, I was almost ready to drop out of my first year because I missed so many lectures at the beginning that I had absolutely no clue about abstract definitions and structures like groups, let alone how to prove things about them! Even with this poor performance in my first year, things eventually started to sink in and I graduated with one of the highest marks in my year.
As an aside - the only reason I didn't drop out is because I came across David Burton's book on Elementary Number Theory and it really helped me to appreciate the beauty of the subject (although it took me quite a lot longer to get to grips with analysis!).

My advice for you would be to keep going as you're going, but to take your time when studying proofs. If you need to, ask yourself questions like "why does proof by induction work?" or "why does proof by contradiction work?" and "why is one method of proof used in this circumstance and a different method used in another?" Spend a while contemplating what "necessary and sufficient" means. I would not, however, recommend spending hours agonising over a proof. If you get to a point where you are well and truly stuck, take a break or do some different work. Come back to the problem later and you might be able to see it from a different point of view.

If this post has been too general - or even condescending - I apologise. What I'm saying is you sound like you're doing just fine. If you get to your final year and you find yourself revising for exams and not knowing how to prove things, then you have reason to be concerned. :)
 
  • #1,825
mathwonk
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ok here is my secret: I decided to quit pretending I was smarter than others and to try to see how good I really was: i.e. I decided to see how good I could be by aCTUALLY WORKING AS HARD AS POSSIBLE.

The result? I was nowhere near as good as I fantasized, but much better than I had been.

best wishes to you. you all know what you should be doing. my advice is merely that if you start doing those things, they will work for you.
 
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