Other Should I Become a Mathematician?

[tinylights]

Hi, I wanted to introduce myself. :)

I have recently discovered that math is my calling, and am studying it at a small 2-year college before transferring out next Fall to pursue my BS. I'm taking Calc 1 right now with a Stewart textbook (though due to the earnest recommendations for it all over this site I have ordered Spivak's Calculus as well) and am doing well, though there is a definite change in difficulty level between Pre-Calculus math and Calculus. It's actually quite exciting to me because I remember finding myself so bored in other classes when I could easily predict where my teachers were going with every idea, and the course I am in now is a lot closer to my pace.

Out of curiosity, does anyone know what the best colleges/universities in Florida are for a solid math education? I live nearby UCF so it is my most likely option, but I want to consider others so as to avoid my grad school speaking at me in a new language. And I've heard of a lot of people having issues with UCF's massive enrollment, primarily that of never getting a chance to connect with your professors.

Secondly, I've looked at a lot of grad school programs and they recommend acquiring reading fluency of mathematical texts in French, German or Russian. Which one(s) are most useful to learn, in your experience?

 

[mathwonk]

I "read" French, German, and Russian, well enough to pass a grad school math proficiency test, but only French well enough to actually read a math paper fairly easily.

As far as Russian goes, so few English speakers read it that most big Russian journals are routinely translated into English.

I staggered through a few sections of Riemann's papers in German but even those are at last available in English.

I always thought I could read Serre's clear papers in French, but boy the English version of Algebraic groups and class fields is much easier to get something out of.So while it is recommended to learn these languages, at least french, and less so german, most of us get by quite well in english, occasionally having to struggle through an original language with a dictionary. but even to do that you need to know the basics of the language.

i.e. learn what languages you can, but be aware that you will be able to read almost everything written fairly recently in english. original languages are needed especially for reading some important works from the 19th century and early 20th cent.

e.g. with my weak german, i still have not read the great paper on linear series on algebraic curves, treated purely algebraically, including an early algebraic proof of the riemann roch theorem, by brill and noether.

it was kind of entertaining trying to struggle through a russian textbook on vector spaces (vyektornye prostranstva) when i kept running across the same words (ochevidno shto and silno) over and over, which turned out to mean "obviously" and "clearly"!

 

[symbolipoint]

MATHWONK,

you described your career progress a few times, but not remembering exactly, could you tell us: Did you study anything (Mathematics) while you were a meat-lugger, not in school? Or did you just work your labor job without studying your subject?

 

[mathwonk]

thats a little like asking country joe mcdonald what he remembers about the 60's, and he answers "nothing".

this is not a thread for discussing politics, but that was a great distraction. those were years when we were fighting in vietnam. it was hard to focus on just preparing for a narrow scientific career. the one advance i made in those years was by assisting/grading in honors calculus, i had to read spivak's calculus book, and learned a lot of calc i should have known much earlier.

 

[converting1]

has here been any older mathematicians (30+) who've made any impact on mathematics (if so who)? Reading up on mathematicians it seems as though everyone makes great work in their early twenties then just die down

 

[micromass]

has here been any older mathematicians (30+) who've made any impact on mathematics (if so who)? Reading up on mathematicians it seems as though everyone makes great work in their early twenties then just die down

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list

 

[converting1]

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list

Guess it's never too late then! Thought I had little time left seeing as I'm 17,

thanks

 

[homeomorphic]

has here been any older mathematicians (30+) who've made any impact on mathematics (if so who)?

30 isn't that old. Actually, very few mathematicians today even get to the point where they can make any significant contributions UNTIL they are about that age. The average PhD age is like 27 or 28, and my impression is that postdocs were this extra thing that they had to stick in because a PhD isn't really enough to become a mathematician anymore. So, by the time you are done just getting started, you're that old.

 

[eliya]

30 isn't that old to start or to finish. A lot of mathematicians ``made impact" beyond their 30's. Andrew Wiles, for instance, missed the Fields Medal by a few months.

As a general rule though, don't think about making an impact. Every mathematician who's active and writing papers is changing mathematics, of course, to different extents. To paraphrase Robion Kirby, don't worry about the significance of your mathematical results, worry about being the best mathematician you can be, and the rest will follow.

 

[chiro]

Take a look at George Polya, who started late relative to a lot of others (consider also that mathematics has exploded since 100 years ago) and didn't start studying mathematics:

http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/polya-george.pdf

Born in 1987, got the doctorate in 1912 so got the doctorate at the age of 25 (but please put that into context for mathematics especially probability at that time, and I am not denigrating Polya when I make these statements).

 

[mathwonk]

whether or not you will do important math is not determined by your age, surname, gender, or anything else. It is based on your desire. go for it.

 

[dkotschessaa]

Just turned 36. Still an undergrad. Not giving up. :)

 

[Mariogs379]

@mathwonk,

regardless of what I do re: staying in NYC vs. Brandeis program, I'm going to take some math in the spring semester. Seems like it makes sense, for continuity's sake, to take real analysis II.

Was also thinking Algebra I. Thoughts?

 

[giorgiv19]

Well, I have read some of the posts about textbook recommendations and want to offer an insight of my own:
Normal calculus textbooks? Don't bother. Don't read them, they do more damage, than good. The best thing to do is pick up a Russian Analysis textbook, like Fihtengolz, Zorich or Kydriatsev. They all come in 3 volumes.
Also no textbook is good without exercises. For this the best one by far is Demidoviche's "A Collection of Problems in Analysis".
The other essential thing for mathematics is linear algebra and analytic geometry. Serge Lange has very good book in linear algebra.
But the most important thing is not just studying at a university. You should look for open seminars. These seminars will give you much greater knowledge, than any course ever would.

 

[mathwonk]

thank you for these views which differ from many usually found here, and supplement them nicely!

 

[NegativeDept]

By the way, to my knowledge, the only mathematicians posting regularly on this site are Matt Grime and me. Please correct me on this point, since nothing this general is ever true.

I raise my hand with magnitude $r \in (0,\tfrac{1}{2}]$. I'm a physics PhD student with a math undergrad degree. My thesis is on quantum decoherence, but it consists entirely of equations, simulations, theorems, and other people's data. When asked, I identify as either "applied mathematician" or "theoretical physicist."

Arnol'd, who is a MUCH better mathematician than me, says math is "a branch of physics, that branch where experiments are cheap." At this late date in my career I am trying to learn from him, and have begun pursuing this hint. I have greatly enjoyed teaching differential equations this year in particular, and have found that the silly structure theorems I learned in linear algebra, have as their real use an application to solving linear systems of ode's. I intend to revise my linear algebra notes now to point this out.

I agree! I just wrote a linear-systems-of-ODEs numerical software package which uses silly theorems of linear algebra to beat the hell out of RK4. (The catch: linear systems only. If you're interested, look up "Magnus expansion.") I'm sure my advisor, who has published huge amounts of Arnol'd-related stuff, would also applaud your effort. I suspect we're both working on one of his big long-term goals: show scientists and engineers that Sophus Lie's view of ODEs can be really practical and useful.

 

[Hercuflea]

Is it possible to receive an applied math Ph.D, but do your dissertation in some other area of science or engineering? I am asking because I want to get a solid foundation on some mathematics courses (functional analysis, advanced and numerical linear algebra, ODE's, PDE's, hilbert spaces, several complex variables) at the graduate level, but I would not really have a chance to take all of these courses if I did an engineering Ph.D. However It seems like it would be the best of both worlds if I could go for an applied math Ph.D. and do my dissertation in nuclear fusion which is ultimately my intended research interest, whilst being able to get the solid mathematical background.

Do you know if this is a common thing to do in applied math programs?

 

[QuantumP7]

I just got What Is Mathematics: An Elementary Approach to Ideas and Methods, Second Edition. It's by Richard Courant, Herbert Robbins and revised by Ian Stewart. I'm REALLY looking forward to solidifying my knowledge of the really basic parts of mathematics. Hopefully, it'll answer some questions I have about the fundamental concepts.

 

[Cod]

I just got What Is Mathematics: An Elementary Approach to Ideas and Methods, Second Edition. It's by Richard Courant, Herbert Robbins and revised by Ian Stewart. I'm REALLY looking forward to solidifying my knowledge of the really basic parts of mathematics. Hopefully, it'll answer some questions I have about the fundamental concepts.

A great book you just got. The beauty of it is, its not a book that must be used in order. You can skip around as you see fit in order to meet your goals.

 

[QuantumP7]

A great book you just got. The beauty of it is, its not a book that must be used in order. You can skip around as you see fit in order to meet your goals.

Thanks! I'm really loving this book so far!

 

[analyzer]

Hello, everyone. I am from Ecuador, and plan to study math at Escuela Politécnica Nacional, one of the most prestigious universities in my country. Perhaps it is the best one in math (the one that does the most research in the area, and the one with the more PhDs teaching.)

The program places emphasis on applied math. There are two concentrations: modeling and scientific computing, and statistics and operations research. The following are the links to the department's curricula.

Modeling and scientific computing: http://www.epn.edu.ec/attachments/article/77/MALLA%20CURRICULAR%20ING%20MATEMATICA-MENCION%20MODELIZACION.pdf

Statistics and operations research: http://www.epn.edu.ec/attachments/article/77/MALLA%20CURRICULAR%20ING%20MATEMATICA-MENCION%20ESTADISTICA.pdf

My question is whether I can pursue graduate studies in pure math with any of both curricula.

Also, I have to mention that there are two other universities in my city which offer programs in math. One is too expensive for my parents (I do not meet the requirements for scholarships). Anyway, I post the link to its math department curriculum:

http://www.usfq.edu.ec/programas_academicos/colegios/politecnico/carreras/Paginas/matematicas.aspx

Do you think it is better preparation for a PhD in pure math?

The other university's program is the following:

http://www.uce.edu.ec/documents/22800/143833/Malla%20Curricular?version=1.0&t=1351174886263

 

[analyzer]

Sorry. The expensive university's math curriculum is actually at the following link:

http://www.usfq.edu.ec/programas_ac...ments/mallas_academicas/malla_matematicas.pdf

 

[SirIsaac]

"i loved comenetz's book, and wrote the initial rave review of that book. unfortunately i gave away my review copy as a prize to a good student. I attach my (edited) review, no longer available on the publisher's website: (see below)
unfortunately for the buyer, the price has increased from under $40 to over $125. Perhaps that is one reason my review has been removed, since it originally contained a grateful comment about the price."

Correction: mathwonk's review is now at
http://www.worldscientific.com/page/4920-review01
and the paperback edition is $67 at Amazon

 

[converting1]

after doing maths straight for around ~5 hours I find I tend to make a lot of mistakes and usually need a break. What do you guys usually do for a break? I can't find anything to do that isn't too distracting, I don't really play video games nor watch television and work out 5 times a week already. I tried to read but again, it just is too distracting. So what should I do for a break? Or a better question, what can I do so I won't need to have a break?

 

[ovael]

“All human evil comes from a single cause, man's inability to sit still in a room.”
-Blaise Pascal

You could also lie down if you have a bed or sofa available. Perhaps even take a nap. Or take a little walk outside.

 

[mathwonk]

i usually walk around the block and then get back at it. short exercise breaks like that are quite helpful, and better than no breaks at all.

 

[n10Newton]

Mathwonk can you give yours Mathematics Department Undergraduate Course Syllabus.and Books used in each semester. There is syllabus given by you but that is of 2006.

 

[N5soulkishin]

this is an awesome thread what are the job prospects for mathematicians for theoretical mathematics?

 

[mathwonk]

n10Newton,, does this help?

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

 

[mathwonk]

N5soulkishin, even in pure math, learn as much as possible about computers, beginning with how to type your own papers in TeX. Job prospects are better the more you know about computers in my opinion. Today everyone needs to maintain a/or many web pages, possibly even prepare lectures in computer format, and type papers in technical formatting. Those who actually understand how to manage accounts in the cloud for others can earn far more in the business service world.