Should I Become a Mathematician?

[JasonRox]

From your wide observations, what kind of wife is best suited to an academic mathematician? i.e another mathematician, school teacher, etc. OR is it too wide ranging to say?

Um... that's like asking the average guy the same question.

You want a wife that you'd love. If she's not suited for your career, don't marry her. A girl you love suits within your life in every way.

I'd want a nice good looking girl who loves playing in the bedroom. I need to clear my mind once in awhile.

 

[mathwonk]

well I admit the standard russian math journals are regularly translated into english so maybe it is not too crucial to know russian for math. but every now and then I find a russian preprint or paper that is not translated and it helps that i read russian. this does not happen too often though.

i do have several russian math friends though and i enjoy at least being able to say hello.

there are a lot of outstanding russian mathematicians and their contributions are legion: novikov, arnol'd, postnikov, shafarevich, tjurin, shokurov, alexeev,
nikulin, margoulis, dolgachev, moishezon, pontrjagin, tichonov, urysohn, sobolev, lobachevsky, malcev, kac, kazhdan, efimov, markov, givental, voronoy, delaunay, lefschetz, kurosh, gromov, iskovkikh,...

 

[mattmns]

Here is a silly question for you mathwonk How do you pronounce Spivak?

 

[pivoxa15]

I wonder why there are so many outstanding Russian mathematicians. It seems like the fields medalist list are dominated by them and Americans. However the Americans tend to come from many different ethinic backgrounds.

Is it because they are biologically more adapted to abstract things like maths and chess or is it because of their communist ruling for most of the recent past so there isn't many things to do or not many distractions.

 

[matt grime]

More strange opinions there, pivoxa. I would suggest you might consider that in Russia (in the past), eduaction was just more highly valued than elsewhere, and especially mathematics. Similar things have happened throughout the world in a variety of arenas.

The Aussies put a lot of emphasis on sports now, as they saw it an arena where they could compete with the rest of the world. Consequently in the 80s they spent a lot of cash on the infrastructure to create cricketing, rugby league and swimming teams that are te envy of the world. Another case, albeit an odd one, is scrabble. Some of the best scrabble players in the world (in English) are from Taiwan (or do I mean the Philippines) even though they can't speak English - it is taught in schools for some reason.

The Russians invested heavily in mathematics. Now they don't spend that much on it and consequently a lot of the best Russians are no longer in Russia.

 

[MathematicalPhysicist]

I'd want a nice good looking girl who loves playing in the bedroom. I need to clear my mind once in awhile.

exactly!
(-:

 

[mathwonk]

I pronounce Spivak as Spih - vak, i.e. not Spee - vak.And it is interesting that although the Soviets did invest heavily in math and science and valued it greatly, the communist government often tried to prevent their jewish citizens from benefiting from these math opportunites.

In spite of many obstacles in their path, nonetheless many Jewish soviets still became mathematicians and outstanding ones.

I do not know in general which of those I named are Jewish, but I know Moishezon was, since Boris was a friend of mine. Also Kazhdan, since I knew him slightly.

I also omitted to name perhaps the most famous recent Russian mathematician, Grigory Perelman.

 

[MathematicalPhysicist]

the better question is how spivak pronounce his last name?

 

[mathwonk]

well, i apologize for being vague, but since he is a friend of mine you may assume my pronunciation is one he has heard a few times without objecting, and that i have also heard many other people pronounce it as i do over the past 40 years.

i cannot recall hearing him pronounce his own name in a long time since he knows I know what it is.

 

[MathematicalPhysicist]

so it's spy-vak, i thought it was spee-vak.

 

[mathwonk]

spih not spy or spee, but i think it is allowed to say it other ways.

 

[Werg22]

Mathwonk, what do you suggest for self studiers? Learn one branch at a time or learn them all together?

 

[mathwonk]

if you are like me i can only learn one thing at a time, at best. and not one branch, one fact!

 

[Werg22]

Hummm, often I find myself amputated when it comes to some subjects in mathematics (for example, I know very little about linear algebra) because I've put all my energy into number theory and analysis. Wouldn't it be better, for example, to learn the foundations of several branches before pressing on the mastery of one?

 

[Data]

Hummm, often I find myself amputated when it comes to some subjects in mathematics (for example, I know very little about linear algebra) because I've put all my energy into number theory and analysis. Wouldn't it be better, for example, to learn the foundations of several branches before pressing on the mastery of one?

You're still in high school; study whatever catches your fancy! You will get a much more general background when you start a university program in math (or math-physics). For now, if you think you'd like to learn something about linear algebra, go ahead and pick up a textbook.

Personally, I'm taking advantage of the small gaps between my exams to start learning a few topics that I haven't had a chance to pick up yet. For example, I've just read all of the elementary material on measure theory that I can find online; Tomorrow, I have half a dozen books to pick up at the library!

 

[J77]

feel like summarizing what you said about non linear optics? even if it way over my head, someone will enjoy it.

If I started, I fear I would lose anonymity somewhat -- which I prefer on bbs

I would defintely reiterate your advice of conferences -- sharing your ideas with others (in an informal way rather than peer-review) and getting criticism really helps you to spur you on.

I've done four so far this "season" , with four more to go -- including two long-haulers.

 

[mathwonk]

i enjoyed anonymity for a while, then decided to forego it. thought it might make me more responsible, but it hasn't worked yet.

 

[mathwonk]

perhaps most of us should learn one thing at a time, but then also think about how it relates to other things.

 

[mattmns]

How important is a basic differential equations class (not theory, but a computational class that engineers and physics majors would take) for grad school admissions (PhD in Pure math)? I have been looking at different programs and it seems many schools want you to have taken basic differential equations.

Personally, I have never taken the class, and it looks to be a boring class that I really don't care to take. I am basically done with all the requirements for my degree in pure math, so I could take the class if I absolutely needed to, but I would prefer to take a class on topology or a second course in abstract algebra, or some other upper level theoretical math class.

Your thoughts? Thanks!

 

[J77]

How important is a basic differential equations class (not theory, but a computational class that engineers and physics majors would take) for grad school admissions (PhD in Pure math)? I have been looking at different programs and it seems many schools want you to have taken basic differential equations.

Personally, I have never taken the class, and it looks to be a boring class that I really don't care to take. I am basically done with all the requirements for my degree in pure math, so I could take the class if I absolutely needed to, but I would prefer to take a class on topology or a second course in abstract algebra, or some other upper level theoretical math class.

Your thoughts? Thanks!

DE is a hard one.

I think most student's views would be that it's only about learning methods and applying them by rote. However, I believe this to be a bit naive... or moreover, students don't understand that a great many mathematical fields are about applying techniques -- the complication of the technique just means the subject requires longer to master.

Basic DE classes form the backbone of many physical applications -- including, for many, the first obvious use of calculus.

Furthermore, they form the backbone of everything higher -- which some would label as pure math -- eg. in the pursuit of solutions of PDEs.

I think the "pure" guys on here may like to get rid of simple DE courses -- and start on, say, waves and their instabiities.

However, I like the basic DE courses because they give students a sense of application for, eg., calculus and linear algebra.

Even if they may be easy -- imo, they are worth it

 

[mathwonk]

well DE is important. some intro de courses are really boring, but some are not. the book by devaney blanchard et al, is kind of fun, altho i criticized it.

and arnol'd's book is wonderful, and interesting too. i also recommend martin braun's book for interesting applications as well as computations.

for a classic book that explains everything basic as well as advanced in a traditional way, try pollard and tenenbaum.

or take whatever you find fun.

 

[mathwonk]

sorry i did not notice the question on number of conferences i attend. in 2001 i suffered an injury and was unable to travel easily for several years.

up until then i had attended roughly 23 mostly international conferences as an invited speaker since 1977, about 10 more as a participant (not a speaker), and given about 40 more invited or contributed seminar or colloquium talks at various places here and abroad, as well as three invited courses of a total of 25-40 lectures abroad.

in the last 5 years or so i have received 2 international conference invitatiions and several invitations to give seminars which i have not been able to accept. this UGA birthday conference is thus the first one i have been to in a while.

it reminded me how wonderful and stimulating conferences are and now i am very tempted to go to a couple more in europe in june. the problem is that as a senior participant and not an invited speaker, airfare and hotels are quite high now, especially in euros.
our travel budget is essentially nil right now, which reminds me to suggest you investigate such things when choosing a university job.

since conferences are so useful, a travel budget is one of the most important ways for a govt or university to suppoort research.

so i guess for the first 25 years or so i averaged abut one major conference a year. the only time i did not feel the need to go to them was when i was at harvard. the atmosphere there was so stimualting, especially talking to David Mumford, that it was actually better than an international conference.

in fact when i did leave Harvard to go to an international conference, i found that the speakers were behind the curve of what was gong on right in the department at Harvard. In fact one of the talks concerned a result I myself had worked out and reported on to a Harvard colleague some 18 months earlier. So you could be more up to date by asking questions from people standing around the coffee room at Harvard than going to a big conference of experts.

at that time (1979-1981) Mumford, Griffiths, and Hironaka were all at Harvard, making it the center of the algebraic geometry universe. and everyone who did anything notable in the area would either send a copy to people at harvard for their review and approval, or would actually come up to speak about it there first.

as to conferences, there is a difference between being a participant and being a speaker. i find being a speaker even more stimulating usually because you are motivated to think very hard about your work, and you get to present it to a usually appreciative audience. it can be a real high.

As a speaker you also get the chance to advertise yourself and your work, and it helps people get to know you, which helps you get jobs, invitations, and grants.

being a participant, i.e. mostly listening, is more of a job, since it is hard to really grasp the talks in depth. the good side is it keeps you up to date in a way reading cannot do as quickly. it also acquaints you with the young people in the field, allows you to assess how strong and personable they are, and this is crucial in planning your own hiring.

if the talks are really good, you may learn something that inspires research of your own. I heard a talk by Mumford once that did just that, and the work that grew out of it with my colleague Robert Varley is one of the things I am most proud of.

As it happens I also said something in my talk that Mumford turned into a nice piece of work himself, extending some other work he had recently done. it was real thrill to have mumford call me over at lunch the next day, and show me his result. i still have the handwritten version of the proof he gave me.

by the way David Mumford is being honored on his 70th birthday at a 2 day conference June 1-2, at Brown, for his work in both algebraic geometry and artificial intelligence and perception. It should be a nice occasion, and if you are able to be in Providence then, it would be a wonderful way to begin your conference attending career.

 

[mathwonk]

back to DE. This is an enormously important subject that everyone needs to know about. all questions here about vector fields and diferential forms and de rham cohomology, are actually questions about differential equations.

i.e. a vector field IS a differential equation, and vice versa. this is the way it is taught in arnol'd, and from a more elementary viewpoint also in blanchard, devaney et al.

learn it that way and it will be both interesting and useful.

i was speaking about ode. partial diff eq is equally important but harder, less well understood as a theory hence concerns a study of more special equations.

but these special equations are among the most fundamental objects in mathematics: the laplace equation, the heat equation, and the wave equation, to mention only the most classical ones. So it may be that people just study one important pde at a time. I myself feel I know essentially nothing about pdes, but have long used the several variable complex heat equation, since it is satisfied, as perhaps Riemann first showed, by the theta function in the theory of abelian varieties. As far as I know, the heat equation was first used in the study of the famous Schottky problem in algebraic geometry in the now classic paper of A. Andreotti and A. Mayer, or possibly earlier in the case of genus 4 by Mayer.

 

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[mathwonk]

what in the world was that? and how did it wind up on here?

 

[mattmns]

Thanks for the advice, my adviser also agrees, and I think I can easily fit in DE in the spring, and still take some other math classes.

One more question. It seems like letters of recommendation are extremely important for grad school. Should I take an independent study with a professor that I would like to get a letter from instead of taking another upper level math class (with professors that I have not had before)?

To be specific, I would probably being doing the independent study on Linear Algebra, reading either Axler's, or Hoffman & Kunze's, book. And the class I would not be taking would be either Topology (using Munkre's book), or Probability (using Casella & Berger), both of which are senior undergrad / first year grad classes.

The professor I would take the independent study with has already written a letter for me (for some REU's, one of which I got accepted to), but I have taken him for only two classes, both of which were pretty easy classes (graph theory, and discrete structures), which is why I think taking an independent study in something more difficulty would greatly strengthen my letter. Am I wrong, does it really not matter? Any ideas would be appreciated, thanks!

 

[mathwonk]

ask him...

 

[proton]

hey mathwonk and others,

I'm currently a physics major considering either a double major or minor in applied math. I'm not sure I'll really have a passion for math because I both loved and hated my lower div linear algebra class that used some proofs. We used an extremely outdated textbook and my professor rushed thru the lectures and plus it was in the summer, so I didn't understand the subject when I took it. But I enjoyed the challenge of proving mathematical results. I also enjoyed the subject when I reviewed/self-studied everything I learned in that class a few months later. I'm transferring to a university from a community college this fall but I can take a summer math class. I'm thinking about taking either a upper-div Linear algebra class or a Intro to proofs/abstract math class. The proofs class isn't a graduation requirement, but it is strongly recommended by the school. But am I really going to learn a lot from that class? Would I be better off self-studying/practicing proofs instead? Which one would be the better choice? I'd appreciate any advice.

 

[pivoxa15]

I'm not sure I'll really have a passion for math because I both loved and hated my lower div linear algebra class that used some proofs.

I had this same delima and experience after I took first year linear algebra. But I went on with pure maths and am enjoying more of it the more I do and understand. I realize that when I hate it, its because I don't understand it.

 

[mathwonk]

the proofs class seems recommended by the school, and by me.

it is sort of a language class to help you understnd the way mathematics is discussed, in lectures and in books.

 

[Mathematicus]

Me... I want to...

 

[proton]

would it be possible to do well in both the intro to proofs and linear alg classes this summer? or would that be overkill?

 

[Umer_Latif]

Hi everybody!

It's sgreat to see such a nice forum on Mathematics and Physics.

Actually I want to share my problem with you people. The problem is that I've starting loving Mathematics pretty late i.e in the fourth semester of my University. (I'm an Engineering student) - Before that, I always used to HATE Mathematics. Maths was the worse subject for me. So, the problem is that my basics of Maths are pretty weak. Now, I'm getting more and more interested in Mathematics and I've starting loving it very mcuh.

Please tell me what should I do? How can I increase my Mathematical skills? Please give me some suggestions.

Regards.

 

[J77]

as to conferences, there is a difference between being a participant and being a speaker. i find being a speaker even more stimulating usually because you are moptivated to think very ahrd about your work, and you get to rpesent it to a usually appreciative audience. it can bea real high.

As a speaker you also get the chance to advertise yourself and your work, and it helps people know you, which helps you get jobs, invitations, and grants.

being a participant, i.e. mostly listening, is more of a job, since it is hard to really grasp the talks in depth. the good side is it keeps you up to date in a way reading cannot do as quickly. it also acquaints you with the young people in the field, allows you to assess how strong and personable they are, and this is crucial in planning your own hiring.

I think it a waste to go to a conference and not give a talk -- both for time and money.

If talks are limited, one should at least take a poster along -- these poster-type/coffee sessions seem to becoming increasingly popular.

Adding to your post -- speaking in front of a large crowd, and the old guys in your field, also gives you a lot of confidence both in yourself and in your work.

And communication is a massive part of academic life!

 

[mathwonk]

proton, yes it is possible, provided you find the proofs class easy.

umer i guess you could take a masters degree in math.