Should I Become a Mathematician?

[mathwonk]

Kracken, someone else has suggested this essay: I have not read it myself.

http://www.maths.manchester.ac.uk/~avb/pdf/WhatIsIt.pdf

 

[TheKracken]

Kracken, someone llse has suggested this essay: I have not read it myself.

http://www.maths.manchester.ac.uk/~avb/pdf/WhatIsIt.pdf

Good essay! It did not really answer any of my questions, but regardless it was still really good. I'm curious, I am currently self studying calculus and I was curious if I would be able to self study topics past calculus without calculus knolege? Let's say stuff after diffrential equations and such.

 

[Dougggggg]

Good essay! It did not really answer any of my questions, but regardless it was still really good. I'm curious, I am currently self studying calculus and I was curious if I would be able to self study topics past calculus without calculus knolege? Let's say stuff after diffrential equations and such.

Not DE, there may be some early level proof courses you could look into. I don't know but imagine that would be a tough one to teach yourself though.

Is anyone going to the Joint Meeting in Boston this year?

 

[mathwonk]

the only sure way to tell what you can understand about a subject is to look at the material and find out. you may not understand it fully, but you might either learn something or learn that you need to know more background. Is is surely impossible to understand much de without calculus, but you can enjoy some of the geometric aspects of vector fields by looking at the pictures or the software animations available.

 

[Li(n)]

What does one have to do to study network theory?

 

[homeomorphic]

What does one have to do to study network theory?

Since no one else is replying, let me take a stab at this, although I am not an expert.

I'll just focus on the side of it that I have explored, which is the pure math perspective. I was very interested in graph theory at one point in time, and maybe I will get back into it, although it seems far removed from what I'm doing now. Really the only prerequisite to start learning it is being comfortable with proofs, although once you get more advanced, other branches of math will become relevant.

You can find Diestel's graph theory book free online. That's the only source I am familiar with.

It's a beautiful subject. Blew my mind. Sometimes, I can't believe I didn't specialize in it, but I ended up at a school where there wasn't much of it going on, and I was so interested in topology and physics, so my attention drifted from it.

 

[mathphyslover]

i am in great dilemma whether to study maths or phys ??

i just love going deep deep deep...in any concept or you can say i just love to no the A-Z of anything i face while studing science.
equally
i love solving problems in mathematics ..

but doing both and keeping pace with school seems to be (i.m.)possible.
or i just love to do research but i am in 11th standard and i can't do that
i have decided to become a theoretical physicist?
nowdays i am tensed about my career ..

i have heard that "learn from yest. , live in present and hope for future."
but how one can hope for future if he don't know what to do in his present...

that's all
{this is my first post and i hope someone will guide me ,
extremely thank you

 

[mathwonk]

try to relax, listen to music, visit natural scenes.

 

[homeomorphic]

i am in great dilemma whether to study maths or phys ??

Which one is easier for you?

I had to make that decision, too, a few years ago before I applied to grad school. Maybe I'm kind of a physicist at heart. I find it hard to have a long-term, sustained interest in math without connections to reality. Physics keeps trying to pull me back in. I find it hard to focus on my thesis sometimes because of the lust to learn more physics all the time (and other math, too). If I do a postdoc, I'm going to try to get into quantum computing or some form of applied topology.

If you have a desire for more contact with reality, like me, maybe physics or applied math would be good. Some people can just work on problems of purely mathematical interest for their whole lives, with some vague hope that it will trickle its way into practical applications one way or another at some point. I don't have that kind of faith or patience. I want to have some reason to believe that the math might be making a contribution to society. Maybe not straight away, but headed in that direction, at least. So, my interest lies in bridging the gap between pure and applied. I'm not opposed to pursuing some things just for math's sake because there are always odds and ends in my understanding of math to be taken care of, but I don't think I can make that the focus of my efforts.

You can try to do both math and physics, but it's difficult. I tried to do both, but when you're in a math department, it can be a challenge not to get sucked way into pure math, and I imagine you could have the opposite problem in a physics department.

 

[mathphyslover]

what you mean by
"" you could have the opposite problem in a physics department.""

 

[mathphyslover]

NOW COMING to career -

i want to know how i can satisfy myself that 'yes , i have potential to become a theoretical physicist'?
what special is present in mind of a theo.physicist
or

i want to know what should be my planning to become a theoretical physicist/
if anyone know any website on theo.phy.

 

[homeomorphic]

what you mean by
"" you could have the opposite problem in a physics department.""

I mean if you like math, there might not be enough math.

 

[MathematicalPhysicist]

How do mathematicians find time to have a girlfriend?

Unless maths doesn't consume most of their time, I guess.

 

[mathwonk]

thats a big problem. math takes so much time and attention. spending too much time with either one, girlfriend or math, can devastate the other relationship. Even as a mature adult I found it impossible about 20 years ago to resuscitate my dormant research life unless I refused to go out drinking with social friends - I needed my brains and will power sharp all the time. But life is full of competing demands, and at some point you have to learn to balance them.

In truth there is not enough time to do even your math job fully. All three aspects of a professor's job, research, teaching, and administration, are potentially infinite time sinks, and you have to truncate them and manage all of them.

Life is the same in general, you have a social self, an intellectual self, a physical self, and a spiritual self, and they all need to be kept healthy. Graduate school however is often a temporary period of imbalance. Thats why it can be a miserable experience.

 

[MathematicalPhysicist]

When did you meet your spouse?
Before, after or during grad school?

 

[atyy]

micromass posted a solution at https://www.physicsforums.com/showpost.php?p=3513336&postcount=1736.

 

[MathematicalPhysicist]

micromass posted a solution at https://www.physicsforums.com/showpost.php?p=3513336&postcount=1736.

The solution assumes I have more than zero, we didn't show existence. :-(

It's funny I remember watching the weakest link at Friday, and there some old guy who says he find his Taiwanian wife from some advertisemnt in the paper...

I guess I can always buy me a spouse. :-D

 

[atyy]

The solution assumes I have more than zero, we didn't show existence. :-(

 

[Nano-Passion]

thats a big problem. math takes so much time and attention. spending too much time with either one, girlfriend or math, can devastate the other relationship. Even as a mature adult I found it impossible about 20 years ago to resuscitate my dormant research life unless I refused to go out drinking with social friends - I needed my brains and will power sharp all the time. But life is full of competing demands, and at some point you have to learn to balance them.

Very wise words, I can relate, its the one thing I often ponder and struggle with. You often have the big-picture of things, have you considered writing a book by any chance?

In truth there is not enough tim to do even your math job fully. All three aspects of a professor's job, research teaching, and administration, are potentially infinite time sinks, and you have to truncate them and manage all of them.

Life is the same in general, you have a social self, an intellectual self, a physical self, and a spiritual self, and they all need to be kept healthy. Graduate school however is often a temporary period of imbalance. Thats why it can be a miserable experience.

I agree with the exception of the spiritual self. Unless you refer to the spiritual self as the subjective experience people attain through their sentient and pondering brains, and not a physical existence of a higher being and a soul ambiguously hidden away within the heart ventricles.

 

[mathwonk]

i mean it in the most comprehensive way. Even if you occasionally wonder about matters beyond your immediate self, i consider that a manifestation of your spiritual self. I do not postulate any mysteries that you must accept. I only mean that at times it seems to me healthy to consider matters more long lasting than our own next meal. Of course just contemplating the beauty of mathematics is something like this.

But I do not ask you to agree. I still think it useful sometimes to get up early and be quiet, or go to a national park and look at a mountain. I used to go to Mt Rainier for a few days in the late summer, to strengthen my resolve to go back to work for another year. It may even be useful to occasionally wonder what we have in common with other human beings.

I was in grad school twice, the first time unsuccessfully. In between the two trips I met my spouse. Then we had to go back to grad school with a child, when my employer was unwilling to keep me on as a teacher without a PhD degree, in spite of the general consensus opinion of my fellows that I knew as much as or more than anyone else there.

This posed a catch 22 for me keeping my job. I.e. without a PhD I could not keep my job, but once I obtained a PhD, I was eligible for so many much better jobs I would not stay where I was.

 

[homeomorphic]

How do mathematicians find time to have a girlfriend?

1) Get a girlfriend who doesn't demand too much of your time.

2) Make mathematical sacrifices. It's not worth it if you become a mathematical automaton with no life outside math.

3) Realize that it is one more reason to use your time wisely.

Which bring me to how to manage your time.

Since I suck at time management, let me just link to Terence Tao:

http://terrytao.wordpress.com/2008/08/07/on-time-management/

I guess the biggest piece of advice I could give to myself is to use my will-power.

Lately, though, I have been using my partially self-imposed excessive workload to distract myself from the fact that I can't get a girlfriend in the first place. I haven't been worried about girls quite as much lately. Tired of failure, I suppose. It just takes so long for the right one to come along, I guess I may as well take advantage of it while I have the extra time on my hands.

 

[morphism]

Another problem is that you will most likely have to move several times for your career. You might have to move for grad school. Once you get your PhD, you'll most likely have to move a couple of times for post docs. And after that you'll probably have to move again for a tenure-track job, and then maybe again after that.

All this instability will make having a long-term relationship more complicated.

 

[homeomorphic]

Another problem is that you will most likely have to move several times for your career. You might have to move for grad school. Once you get your PhD, you'll most likely have to move a couple of times for post docs. And after that you'll probably have to move again for a tenure-track job, and then maybe again after that.

All this instability will make having a long-term relationship more complicated.

It can also make getting the relationship more complicated.

My most common excuse to chicken out on making the moves is the girls that I meet are often grad students who are not in synch with me as far as graduating at the same, as well as later difficulties after that, so I just rationalize it by telling myself it will never work out anyway. When it comes to chickening out, I'll take any excuse I can get.

 

[mathwonk]

none of these difficulties is insuperable. i know mathematicians who work not only in different cities from their spouses but in different countries and even different continents.

 

[epenguin]

How do mathematicians find time to have a girlfriend?

Unless maths doesn't consume most of their time, I guess.

Hardy said he could work on math for only 3 or 4 h a day. Which would have left time for girlfiends - if he had been interested in having one. But Hilbert was, and was a counterexample of the conjecture being made here.

I am not a mathematician but find this impossibility hard to believe. Is it not true mathematicians more than other scientists have time for politics?

Painlevé had time for Madame Curie. What is harder to imagine is her having time for him. Which is the point. Surely experimental scientists have more demanding, longer, less flexible time commitments, demanded by both the experiments themselves and often by the teamwork which is less common for mathematicians. If mathematicians don't have time who does? (And they can even be secretly working while they are out with their girlfriends which experimentalists can't.)

 

[mathwonk]

i assure you that if you think about math while with your girlfriend that she will notice it.

 

[MathematicalPhysicist]

I wrote after my question, "unless maths doesn't consume most of their time".

I didn't say that I'm consumed by maths, I have other interests, but it does seem difficult to find a girl who is nice looking, interested in a similar subject and is unattached already.

I guess I need to compromise...

 

[Mépris]

It can also make getting the relationship more complicated.

My most common excuse to chicken out on making the moves is the girls that I meet are often grad students who are not in synch with me as far as graduating at the same, as well as later difficulties after that, so I just rationalize it by telling myself it will never work out anyway. When it comes to chickening out, I'll take any excuse I can get.

I can relate to/imagine that (in that, this will probably be me (too) in a few years).

You should also consider the possibility of female grad students who share your view while still being open to the occasional "fling". While we're at it, I strongly suspect female undergraduate students could be a possibility as well.

As was once rightly said by some misbegotten fool, "A morning of awkwardness is far better than a night of loneliness" and I'll add to that my opinion that company for a limited amount of time is better than no company at all!

---

Math question this time.

Can any budding mathematician/physicist get away with not being formally acquainted with Euler's "Elements of Algebra" or a similar higher algebra book? I'm already familiar enough with algebra and I can use it well, in my opinion but I may be wrong.

The thing is, I'd rather get started on Spivak or Apostol as soon as I can. On my to-do list, is reviewing some geometry, trig, probability and combinatorics, all of which I should be done with by the end of the next week. Starting Spivak or Apostol at around that time would be lovely as it would help me greatly with my main exams which will be in May/June. (A-Levels - around the same level as freshman maths)

I've actually completed high school but I want better grades at A-Levels, which is why I aim at writing them again in the coming months.

The following is to get an idea of my command of algebra. I can't think of anything else to explain what I know or don't know.

Let a and b be positive integers. Show that 2^1/2 lies between a/b and (a+2b)/(a+b).

I was able to prove that a/b is less than 2^1/2 fairly quickly but I had to refer the the worked example to be able to "see the trick" for the other half of the "puzzle". I'm currently working through problems like that and my review of the other chapters will be from the same book. So, would I be able to "get away" with learning as I do or would I be further complicating things by skipping the reading of this book?

I can also do reasonably well on http://www.cie.org.uk/docs/dynamic/41859.pdf . (note: get some trouble with complex numbers and vectors)

Thoughts on this, gentlemen? (and ladies...if any :-))

 

[mathwonk]

your answer makes no sense to me. a/b can be either greater or smaller than sqrt(2). one can prove that a/b < sqrt(2), if and only if (a+2b)/(a+b) > sqrt(2), however. And there really is no "trick", just obvious rearrangements of fractions (and squaring).

indeed if you cannot prove this yourself without any help, then your algebra skill seems rather weaker than an average high school algebra student's should be, and much weaker than euler's book would teach.

I was about to say go on to spivak, but after this example, I think you need more practice in algebra. Indeed success in standard college calculus is more closely related to skill with algebra than any other thing. Spivak requires also logical ability and creativity, but algebraic manipulation is still crucial.

Oh yes and in many college classes no calculators are allowed. That test looked like the sort of depressing standardized tests they give for AP scores in US, no concepts, no definitions, or proofs, just tedious calculation.

 

[Mépris]

your answer makes no sense to me. a/b can be either greater or smaller than sqrt(2). one can prove that a/b < sqrt(2), if and only if (a+2b)/(a+b) > sqrt(2), however. And there really is no "trick", just obvious rearrangements of fractions (and squaring)

Either I didn't correctly express myself or I really did something wrong.

Here's how I worked it out:

If $$\frac ab < \sqrt2 < \frac{a+2b}{a+b}$$

Then,

$$\frac ab < \frac {a+2b}{a+b}$$

So,

$$a(a+b) < b(a+2b)$$

Thus,

$$a^2 < 2b^2$$

Therefore,

$$\frac ab < \sqrt2$$

---

That was how I figured this out a couple of hours ago. It felt like a great deal to me and I was smiling to myself while half walking, half jumping around the room*. My over excitement was quite short-lived as I couldn't figure out how to proove the second part, i.e, $$\sqrt2 < \frac {a+2b} {a +b}$$.

After looking at the book, I understood that I might have approached the question the wrong way. (this is actually an "example question" w/answer from the book) At the top of page 14 of this book is the solution to the question, which (obviously) is a good way to approach this. Anyway, I hope that I've explained myself clearly enough this time.

I'll ask the question again, if I have no formal algebra knowledge and mainly learned via doing, could I still pull this off? :-)

*Consider that before having done "Example 1 & 2" on that book, the hardest mathematics I had ever been in contact with was that "monkey math exam" I linked to in the previous page. And yes, you're correct, in that this test is essentially an AP equivalent although it covers more material than AP Calculus and Stats. Even then, I'm not sure what good this does, if any at all...