Other Should I Become a Mathematician?

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Becoming a mathematician requires a deep passion for the subject and a commitment to problem-solving. Key areas of focus include algebra, topology, analysis, and geometry, with recommended readings from notable mathematicians to enhance understanding. Engaging with challenging problems and understanding proofs are essential for developing mathematical skills. A degree in pure mathematics is advised over a math/economics major for those pursuing applied mathematics, as the rigor of pure math prepares one for real-world applications. The journey involves continuous learning and adapting, with an emphasis on practical problem-solving skills.
  • #541
mathwonk said:
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 :smile:

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" :wink:, with four more to go -- including two long-haulers.
 
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  • #542
i enjoyed anonymity for a while, then decided to forego it. thought it might make me more responsible, but it hasn't worked yet.
 
  • #543
perhaps most of us should learn one thing at a time, but then also think about how it relates to other things.
 
  • #544
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!
 
  • #545
mattmns said:
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 :smile:
 
  • #546
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.
 
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  • #547
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.
 
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  • #548
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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  • #549
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  • #550
what in the world was that? and how did it wind up on here?
 
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  • #551
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!
 
  • #552
ask him...
 
  • #553
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.
 
  • #554
proton said:
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.
 
  • #555
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.
 
  • #556
Me... I want to...
 
  • #557
would it be possible to do well in both the intro to proofs and linear alg classes this summer? or would that be overkill?
 
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  • #558
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.
 
  • #559
mathwonk said:
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!
 
  • #560
proton, yes it is possible, provided you find the proofs class easy.

umer i guess you could take a masters degree in math.
 
  • #561
I always get hung up on logical dependencies when I'm studying... takes me so much longer! I blame this on my reading Suppes' "Axiomatic Set Theory" last year. Tonight while reviewing analysis I'm getting wrapped around the axle with ordered rings and the Cauchy-Schwarz Inequality.

Does this happen to anybody else?
 
  • #562
as my prof told one very bright student who was complaining: "well, mathematics IS difficult"
 
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  • #563
Hmmm, well yeah - I do have intentions to do masters and even PhD. in Mathematics. Thanks for your suggestion.

I've been reading the book "Trigonometry" - by Michael Sullivan these days, is that a good book?
 
  • #564
Should a person whose very good in Mathematics do masters degree in Maths?
 
  • #565
BTW, right now - I'm student of Engineering, Telecommunication engineering.
 
  • #566
if you are just now learning trigonometry, it will be awhile before you decide whether phd is your cup of tea.

i was just trying to think of a math activity that was less committed than phd and would both give you an idea and some background of what math is like.
 
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  • #567
Well actually I've been studying Trigonometry for almost 4 years and Calculas for about 3 years (Differentiation and Integration etc.), but as I said previously, I didn't had any interest in Mathematics then so my concepts weren't really good. I have some knowledge about these things - it's just that I'm trying to be VERY GOOD in it, especially Trigonometry is really interesting and easy as compared to other things.

I'm usging the textbook of "Thomas' Calculas" for Integration/Differentiation etc. is that good?
 
  • #568
Umer_Latif said:
Well actually I've been studying Trigonometry for almost 4 years and Calculas for about 3 years (Differentiation and Integration etc.), but as I said previously, I didn't had any interest in Mathematics then so my concepts weren't really good. I have some knowledge about these things - it's just that I'm trying to be VERY GOOD in it, especially Trigonometry is really interesting and easy as compared to other things.

I'm usging the textbook of "Thomas' Calculas" for Integration/Differentiation etc. is that good?
You could at least apply Trigonometry and Calculus to the study of physics and engineering until you decide what you want regarding Mathematics. Realize that studying mathematics is not exactly the same as using it as a tool in other subjects; but you can hopefully enjoy the power mathematics provides as a tool for those other subjects.
 
  • #569
Thanks a lot for the suggestion, symbolpoint.

Yeah, I've been studying applied Mathematics in Engineering - doing world problems in Differentiation, Integration, Applications of Integration and Differentian, problems regarding Polar coordinates etc.etc.

Also been using softwares like Mathematica in Calculas and for Electric Circuit graphing etc. I'm yet in my 3rd semester, I hope I'd study more applications in coming semesters.

BTW, they teach you pure Maths in Masters and PhD. right? But, I never clearly understood the difference between Pure and Applied Maths! ;(
 
  • #570
Umer_Latif said:
BTW, they teach you pure Maths in Masters and PhD. right? But, I never clearly understood the difference between Pure and Applied Maths! ;(
The teaching of pure maths would begin as a core 1st year subject in uni. Here I take pure maths to mean proofs.

These sills will be assumed if you require them at a masters level and beyond; and, here in Europe, they don't "teach" you anything at PhD level -- it's up to you to teach yourself necessary skills/techniques.
 

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