Other Should I Become a Mathematician?

[MathematicalPhysicist]

i would think that writing a thesis with taking courses and working from 9 to 5 to be a little bit hard on oneself, don't you J77?

 

[mathwonk]

I am very happy to have all these diverse ideas about how to use math in life and career, to balance off my narrow discussions of life in the "ivory tower" and classroom.

Keep em coming! What other careers are appealing?

 

[mathwonk]

to learn what it feels like to be a mathematician, watch "the twilight samurai". [warning: it is rather violent. The point was that it concerns someone of superior ability and integrity but low social status.]

 

[Kummer]

I spend between 8 and 9 hours a day studying mathematics. I do not go outside. I do not watch TV. I do not have much time for anything.

Does that qualify me as a "mathematician"?

 

[JasonRox]

I spend between 8 and 9 hours a day studying mathematics. I do not go outside. I do not watch TV. I do not have much time for anything.

Does that qualify me as a "mathematician"?

All that for one course?

If not, don't compare my one course idea to a 2 course or 3 course schedule.

 

[JasonRox]

Great choice on the financial field but why care about doin' research in your spare time. Use it to grow in the financial areas. There is a lot to learn there is well. In your case, don't waste your time doing some obscure research that will get you noweher. Most "fulltime" PhD's out there are not even able to produce something useful so why bother ?

Really, stick to the financial maths and your life will be much nicer !

marlon

I really enjoyed the Topology and Algebra that I have learned. So, that's why I will do it on my spare time.

If it does consume too much time, I'll just audit courses and do my own thing. I never plan on stopping. I just want to live in poverty doing it. It's not worth it.

 

[Kummer]

All that for one course?

I have Summer break now, no University. I self-study for fun all those hours.

 

[JasonRox]

I have Summer break now, no University. I self-study for fun all those hours.

I guess no offsprings for you.

 

[MathematicalPhysicist]

fanatic, kummer aren't you?
I mean i also in my vacation would learn on my own some stuff, but still i would go sometimes outside my house, especially when in the semester I don't have time to do so.

 

[MathematicalPhysicist]

I guess no offsprings for you.

he can always go the near sperm bank... (-:
but he first needs to go outside the house.

 

[Kummer]

fanatic, kummer aren't you?

Yes, I am. But that is because there are certains areas of math I wish to know which are not taught in the University and there is also a lot of stuff which I want to know. If I do something else with my time then I will not know what I want.

 

[mathwonk]

remember to get some exercise, good food, and sunlight kummer, if only because you can do more math if you stay physically healthy.

 

[MathematicalPhysicist]

Im not sure sunlight in the summer is a good idea.
preferablly you should go in the morning or the evening.

 

[JasonRox]

Im not sure sunlight in the summer is a good idea.
preferablly you should go in the morning or the evening.

Well, he needs to get some Vitamin D that's for sure.

I personally think you need to live a little (like get out of the house). I noticed, on here and elsewhere, people think that hardcore mathematicians have no active social life and all they do is work all day. I would say that's not true at all although there are exceptions like Gauss and Riemann. But look at Galois, Hardy, Littlewood, Halmos, Erdos, Galileo and so on. So where these ideas come from, I don't know but I do know they're far from accurate.

 

[radou]

people think that hardcore mathematicians have no active social life and all they do is work all day. I would say that's not true at all although there are exceptions like Gauss and Riemann.

That's true, and it's what people thing about other scientists too, not just mathematicians.

In general, I don't interact with people who believe in stereotypes.

 

[mathwonk]

the problem is that mathematicians have to be careful when they go out, so as not to be mobbed by women and paparrazzi.

 

[pivoxa15]

Well, he needs to get some Vitamin D that's for sure.

I personally think you need to live a little (like get out of the house). I noticed, on here and elsewhere, people think that hardcore mathematicians have no active social life and all they do is work all day. I would say that's not true at all although there are exceptions like Gauss and Riemann. But look at Galois, Hardy, Littlewood, Halmos, Erdos, Galileo and so on. So where these ideas come from, I don't know but I do know they're far from accurate.

There could be genuine reasons why past great mathematicians interact and socialise so much less then today's mathematicians. In the past traveling would have been expensive and time consuming and education was poor so not many people had the expertise so meeting other mathematicians were harder and not that beneficial. Knowledge didn't spread that quickly as not many were doing it so one can afford to work alone. Moreoever Copy right was a servere issue back then. So it would have been more beneficial for the best to be alone. Hence no need to develop one's social skills in order to succeed at maths.

Today things are much different as fields are more specialised so collaboration is more important and is cheaper to do due to cheap communication costs. However there are still a handful of elites who can and choose to do it alone like Perelman. For the rest its more beneficial to collaborate so more social interactions for mathematicians today.

 

[Werg22]

Well, my take is that the percentage of introverts in the mathematical community far exceeds that of the normal population since introverts tend to spend more time thinking than extroverts and thus have greater affinity for heavily abstract subject such as mathematics.

 

[JasonRox]

Well, my take is that the percentage of introverts in the mathematical community far exceeds that of the normal population since introverts tend to spend more time thinking than extroverts and thus have greater affinity for heavily abstract subject such as mathematics.

The most intelligent student in our math departments are introverted/extroverted or extroverted. Probably one the best things about the department. I would hate to hang out with an introvert.

 

[JasonRox]

There could be genuine reasons why past great mathematicians interact and socialise so much less then today's mathematicians. In the past traveling would have been expensive and time consuming and education was poor so not many people had the expertise so meeting other mathematicians were harder and not that beneficial. Knowledge didn't spread that quickly as not many were doing it so one can afford to work alone. Moreoever Copy right was a servere issue back then. So it would have been more beneficial for the best to be alone. Hence no need to develop one's social skills in order to succeed at maths.

Today things are much different as fields are more specialised so collaboration is more important and is cheaper to do due to cheap communication costs. However there are still a handful of elites who can and choose to do it alone like Perelman. For the rest its more beneficial to collaborate so more social interactions for mathematicians today.

I have no idea what you're talking about because I mentionned mathematicians of the past and today.

Perelman is not choosing to be alone. I believe he's anti-social, so that's not a choice at that point. It's a disorder.

 

[Darkiekurdo]

Do you guys have those moments where you are so demotivated you want to quit with mathematics?

 

[JasonRox]

Do you guys have those moments where you are so demotivated you want to quit with mathematics?

Are you crazy?! No way!

 

[Darkiekurdo]

Never? So if you study mathematics you understand everything immediately?

 

[Kummer]

So if you study mathematics you understand everything immediately?

No. I am had/having a bad experience with modular forms. They are very hard for me.

 

[mathwonk]

i have been demotivated lots of times, thinking i would never grasp something, or never solve something, that i must be in the wrong business. now its more from inactivity. getting back to work after a lull is also hard but usually cures the blues now.

for modular forms, have you tried reading gunning, or serre?

 

[Werg22]

The most intelligent student in our math departments are introverted/extroverted or extroverted. Probably one the best things about the department. I would hate to hang out with an introvert.

And what does you hating to hang out with an introvert have anything to do with his mathematical abilities? Aside from that, I did not exclude exceptions.

 

[Kummer]

for modular forms, have you tried reading gunning, or serre?

It is just I do not have any algebraic geometry skills. It seems to me that I must learn that now, important in number theory.

 

[mathwonk]

not needed for those books is it?

https://www.amazon.com/dp/0691079951/?tag=pfamazon01-20https://www.amazon.com/dp/3540900403/?tag=pfamazon01-20

 

[MathematicalPhysicist]

Perelman is not choosing to be alone. I believe he's anti-social, so that's not a choice at that point. It's a disorder.

just because someone isn't sociable makes it a disorder?

 

[jostpuur]

Do you guys have those moments where you are so demotivated you want to quit with mathematics?

Yes. The university business seems to be dumb and frustrating, and I don't understand why I keep aiming at getting there.

 

[pivoxa15]

Yes. The university business seems to be dumb and frustrating, and I don't understand why I keep aiming at getting there.

Maybe because other instutitions are even more frustrating like private businesses. Moreover only an institution like a university can you do some genuine learning.

 

[pivoxa15]

Mathwonk, I have the serious problem that I pretty much cannot do any of the problems in my pure maths subject unless I take a peak at the solution. Is that a sign that I should quit pure maths? That especially goes for topology. I did poorly in the prereqs as well so that could be the root to my problems.

 

[mathwonk]

it probably means you lack some background. just start further back as you say with perhaps topology. or get an easier book. i don't see why you should quit. we all have the same problem of finding the right entry level treatment of a new topic.

or it may mean you are not learning the material well eneough before trying the problems. or that you need more practice solving such problems. when trying to do a problem that does not yield, just make the problem easier and solve the easier one. then try to work back up.

 

[JasonRox]

I loooovvveee topology.

I can't wait to learn more this Fall.

 

[Jaden]

Mathwonk, do you know a good derivation of the normal distribution. It's used so often everywhere and it bothers me that I have to take something for granted which does not look obvious like 1+1.

 

[Kummer]

Mathwonk, do you know a good derivation of the normal distribution. It's used so often everywhere and it bothers me that I have to take something for granted which does not look obvious like 1+1.

Did you try looking in a standard (mathematical level) probability book.

I say mathematical level one because there are some easier ones used by other majors which need probability theory. In those books the normal distribution is mentioned but not much is developed in theory.

 

[Werg22]

The question is ambiguous. It is of course possible to prove that the integration from minus infinity to infinity of the normal distribution function gives 1. However, as to how to go from "I am looking for a function whose integration from -infinity to infinity is 1 and that is even" to an actual answer, I do not know.

 

[mathwonk]

i did not even know what the question means, but i could ask somebody more knowledgeable, is that the question? prove the integral of something over R is 1? or what? i have not taken probability since 1963, and only got a B+ then. (I think it was discrete probability too.)

 

[pivoxa15]

it probably means you lack some background. just start further back as you say with perhaps topology. or get an easier book. i don't see why you should quit. we all have the same problem of finding the right entry level treatment of a new topic.

or it may eman you are not learning the material well eneough before trying the problems. or that you need mroe practice solving such problems. when trying to doa problem that does not yield, just make the problem easier and solve the easier one. then try to work back up.

But the class is progressing and if I can't do the assignments then that is a problem. The worst thing is that the difficulty is getting to the point where I am actaully trying to avoid the problems which is a 'deadly' sign.

 

[mathwonk]

you may not learn the stuff this time around. that's fine. it'll come later.

or if you are committed to getting it this time, institute a crash plan. When i was flunking diff eq i bought a schaum's outline series in d.e. and began working all the problems until i caught up.

or post some questions on here in the appropriate forum. we'll help you get the ideas. start with one or two here. i love topology. when i was a senior i took kelley's general topology book and read it over the summer and worked the problems. it isn't very hard core or fun topology but it gives you the basic abstract point set stuff.

and i always found Simmons one of the clearest expositors of analysis. Sterling K. Berberian is also excellent.

 

[Jaden]

Can you recommend me a textbook which explains in a more simple way where the normal distribution function comes from ?

 

[mathwonk]

have you read wikipedia?

 

[pivoxa15]

you may not learn the stuff this time around. that's fine. it'll come later.

or if you are committed to getting it this time, institute a crSH PLAN. WHEN i was flunking diff eq i bought a schaums outline series in d.e. and began working all the problems until i caught up.

or post some questions on here in the appropriate forum. we'll help you get the ideas. start with one or two here. i love topology. when i was a senior i took kelleys general topology and read it over the summer and worked the problems. it isn't very hard core or fun topology but it gives you the basic abstract point set stuff.

and i alwAYS FOUND SIMMONS ONE OF THE VERY CLEAREST EXPOSITORS of analysis. sterling k berberian was also excellent.

I flunked point set topology actually and now I am enrolled in a 'proper'? topology course with 'Topics include topological spaces and continuous maps; quotient spaces; homotopy and fundamental groups; surfaces; covering spaces; and an introduction to homology theory'.

So you can see why I am struggling. The contents in the course dosen't seem to be rigorous which dosen't help. Plus my algebra isn't strong either. My brain seem to want to 'turn off' whenever I try to get into a problem which is a big worry.

 

[mathwonk]

well that's a lot of stuff, so just try to learn some of it. covering spaces are nice. for fundamental groups, the best intro is by andrew wallace, in a little book called intro to alg top. unfortunately he wrote more than one book by that title, it seems, but all his books are good. i think this is the one i learned from. he makes it so clear you almost canot fail to follow. and i recall it was still hard to catch onto at first for me.

An introduction to algebraic topology (ISBN: 0486457869)
Andrew H Wallace
Bookseller: Zubal Books
(Cleveland, OH, U.S.A.)
Bookseller Rating:
Price: US$ 6.59
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Quantity: 1 Shipping within U.S.A.:
US$ 7.50
[Rates & Speeds]
Book Description: Pergamon Press 1961, 1961. NOTE: THIS IS THE 1961 HARDCOVER EDITION! 198 pp., hardback, bookplate to front pastedown, minor underlining & notes in pencil to a few pages else v.g. Bookseller Inventory # ZB552817

 

[pivoxa15]

Do you think it might be better to get a better grounding in point set topology first ( I got a 51% on that exam) and then revisit more advanced topology? This would mean quiting the topology course I am doing now.

 

[quasar987]

I did a course with exactly that syllabus last semester pivoxa15.

For one, there obviously wasn't that much time spent on general topology, because of all the other topics to cover, and the rest of the subjects do not have that much to do with point set topology.

In my case also, the professor was rather sloppy in his proofs and statements of thm, because I suppose, he meant for us to understand that problems in topology & algebraic topology are not solved by writing "Let e>0. Then, ... Then,... Then,... QED!". On the opposite, they are solved in your head by visualizing the problem first, and then by moving stuff around in your head until VLAM, you see it. Then, it is only a formality to formalize the solution by writing it down in proper mathematical language.

So for every definition and theorem, you should spend as much time as it take to form a visual idea of what the def./thm. is saying. Use the R^n case for these visualizations; usually, they are adequate for more general spaces too.

But that does not mean I did not take time to transcribe the notes I took in class into a clean, organized, rigourous and massively commented compilation.

Also, remember that you are not restricted to what's written on the black board! Rent as many relevant books as you can (Munkres & Massey come to mind!). Personally, I used only Munkres occasionally and Wikipedia permanently.

 

[pivoxa15]

Just finished the first assignment for topology. It wasn't as bad as I expected. Things are coming back to me and I will continue to be enrolled in this subject. Hopefully one day it will all come to me.

 

[quasar987]

Is there an algebraic geometer around?

I am looking at the page of a professor and he has a list of suggested topics for masters thesis in the field of geometric groups. This is the one that, based on their brief descriptions, interests me the most:

"Algebraic geometry over a free group.
One can define a Zariski topology on F^n taking solution sets of equations as closed sets.
We plan to develop a notion of dimension in F^n."

Would you be able to explain what this is about more precisely?

 

[mathwonk]

he is trying to define dimension in the space F^n by analogy with the definition in k^n where k is a field or maybe algebraically closed field.

in that case a parallel is drawn between prime ideals of k[X1,...,Xn] and irreducible closed sets of k^n, and then the length of chains of these sets, or equivalently ideals, is used to define dimension.

e.g. in a vector space one can define dimension of a subspace as the length of a maximal chain of contained subspaces.

since the free group F has very little commutativity, the analogs are not at all clear to me.

 

[strings235]

mathwonk, I'm currently still a high school student and I've recently finished the two volumes by tom apostol through self-study. I haven't had any significant problems and wonder whether I should continue this by studying ode's, linear/abstract algebra, real analysis, etc, or simply turn to mathematics competitions and stay there until college. I've gotten advice that one shouldn't replace education with competitions, yet finding a university professor for tutoring is difficult because of transportation problems. Would I be able to self-study with success?

Thanks