Other Should I Become a Mathematician?

[ekrim]

Because before I hit University, I used to love doing maths problems. Not necessarily ones covered in the high school syllabus. The joy of solving a difficult problem that you've been at for a long time! The excitement of arriving at a simple answer to what looked like a comlpex question. The joy of finding connections and the way the mathematics works! I used to love maths, but this first year maths course has really bored me, and now I think majoring in pure maths is not for me.



I agree, that is the way with most of my first year courses.



Do you mean this very thread? If so, I think I have read the first page or two, but I will go back now and read more of the thread.

I didn't become interested until after lower level math. Diff eq, multivariable, etc were filled with uninterested non-majors, and the homework was long and thoughtless. Once I reached upper level math, there are less homework problems that require deeper thought and it feels exciting to dive deeper and deeper into the subject. If at all possible try your best now even if it is boring, because youd regret having a lukewarm background in lower math later on.

 

[teleport]

I don't know if this is of any use, but during my first year second semester, I was very much bored by electricity and magnetism class, even though that was my major concentration back then. This was quite a change for me since I always loved physics before university. As a result, I also didn't study almost at all, and my mark wasn't the best. Now I think there is a similarity with your situation here, because now, whenever they talk about modern physics (what I'm taking now) my eyes open up wide, and I just love going to that class. So, I was afraid initially that I wouldn't like physics, but as you can see, it was probably that specific subject. So try and see if you like linear and abstract algebra. They are as important as the other. But then again, Calc is so important too...

 

[qspeechc]

Wow, talk about doppelganger...I feel exactly the same way about my electricity and magnetism course. I thought I'd take my second major in applied maths or physics, but this physics course has put me off the idea.
I guess the point is to just grind through the first year.

 

[mathwonk]

or to take more honors courses

 

[qspeechc]

? You mean major in more than three things?

 

[teleport]

Well, you could do a challenging, maybe COMP Minor for example. For example, the COMP MINOR in my university requires me to take 8 courses, for a total of two comp classes per year. The neat thing is, that you can do all of them in the summer, making it totally doable. Also, because you are already majoring in two highly respectable subjects (and they probably consider you an "intellectually capable"/hard working student) you may ask them to replace the courses in the Minor with the ones the majors take. As I said, if you take them in the summer, this is attainable (if you like it, and are prepared to put some extra effort). Think of it this way, the opportunity is given to you to be better educated; why not take it if you can and want it? I have made up my mind, and will at least give it a try.

There are so many subjects that are just so damn interesting. Don't fix yourself with the idea that people are just good at something more than the other. That might just be an ilussion. But be true to yourself, and live the moment, and follow what is your passion at the moment. Even mathematicians get bored of math, they take a break, do something else for which they have a passion, only to come back later, ONLY because they like it. So, I would guess that it is useful to try many things, so that later on in the future, you pursue whatever you feel like at the moment.

You like math, not so much calc. You like that girl, but you hate her mom. So what? Who in this world can tell you that if you don't like calc, then you don't like math!? That's absurd! Just do whatever you like. A couple of years ago I sent an email to a mathematician asking him what should I read to make myself better at math becuase I loved it. I was stoned not so much because he did really reply, but becuase he just said this: "Just go to a math store, look for a couple of books; if you find something that looks interesting, and you wish to learn it, just take it". He never mentioned anything about calc, algebra, or whatever! I thought that I understood what he meant, and I think that quote is full of wisdom.

 

[teleport]

Mahtwonk, this might be a stupid question, just out of curiosity, is there an object that could contain a sphere, have more than three dimensions, and have a surface so that for each point in the sphere inside it, and a tangent through it (the pt.), there is at least one tangent of the object that is both perpendicular to the previously mentioned tangent and points towards the center of the sphere? Don't ask me why I want to know this because my excuse will sound crazy :) Thanks.

 

[teleport]

I have been thinking about an object with some sort of rectilinear zigzag shape on the surphace, so there might not be a need for more than 3D. But if that is right, I wonder if there is some other shape.

 

[teleport]

Maybe more interesting if a restriction is that there is one-to-one correspondence between the tangents of the sphere and the tangents that have the properties above. Now I realize that perhaps I should be worrying a little bit more with my broken car than this.

 

[mathwonk]

q: major schmajor. there are usually choices available for math courses, you can choose regualr or honors versions. honors versions are for people who want a challenge and a good teacher and deep coverage. are you saying that at your uni these courses are reserved for majors?

 

[mathwonk]

tele: work backwards, for every point on your sphere, take the tangent and perp that you are describing, and try to construct your containing object with the properties you want.

 

[Werg22]

Are most pure mathematicians and pure math students full of themselves, like the ones I keep on meeting?

 

[teleport]

Oh well, I admit I might be, even though I do not know any other in my class that is. Maybe it has to do with regional math culture then. Perhaps some people should restrict the liberty with which they speak up their own mind, especially when they do not notice what they do, even if not to follow common general social guidelines, as I should. Thanks.

 

[ekrim]

Are most pure mathematicians and pure math students full of themselves, like the ones I keep on meeting?

No, but they will try to instill fear in others to ease their own wavering egos. I.e. saying how easy they thought the test was and how much of a joke the class is, although they go on to get a C-B. At least at my school.

 

[PowerIso]

Are most pure mathematicians and pure math students full of themselves, like the ones I keep on meeting?

I like to say the same about the engineer students, but I know better. For the most part, I just remember them being engineer majors because they were jerks. To the same extent, I realize I know just as many, if not more, engineer majors that are cool people, just I don't associate the niceness to engineering.

Anyway, I can say that pure math students can be cocky, but I think cocky can be confused with confidence. It takes high confidence and esteem to be a pure math student. You'll fail more often than succeed :D

 

[mathwonk]

yeah we're pretty much all insecure jerks, but we're funny, and good looking.

but that doesn't mean you can't be the first self effacing, stylish, confident, kind and generous math guy!

 

[mathwonk]

by the way i was kind of proud of our 60,000 hits and turned on the tv to some stupid rock band wearing johnny cash black, with a website with 60,000,000 hits!

and all they do is wiggle and jump up and down!

hey, i can do that ! I CAN DO THAT !

but i have to turn my brain off first. another glass of bordeaux should do it.

 

[Urkel]

Yeah, mathematicians are cool, classy, "sublime"

who wants to be a mathematician?
I definitely wanted to be a mathematician, my primary school dream
and I would be a mathematician now if the the terror and myth saying that doing maths and science prevents people from getting rich, never succeeded to deceive me
I am now doing graduate study in physics and taking some pure maths courses though, at an age 3 to 4 years older than average age of my fellow classmates, doing undergrad stuff like real and complex analysis, how pathetic!
I have never even completed pure maths linear algebra, as engineering student, what I knew was all only abt matrix
Lucky you are math people and I always say to my science friends "U r lucky"
At least I still have a younger sister whom I will force to do maths till PhD or even further
Hehehe Yes (I can finally make a revenge to pragmatism and anti-idealism)
I'd like to know how society/people in your place view mathematicians/scientists?
idealistic human beings who choose to make their life difficult doing dry thing for the shake of satisfaction of proving theorems or postulatng a new theory in denial of lucrative life of businessman/politician/medic?

 

[Darkiekurdo]

I see mathematicians and physicists as the brightest people in the world. :P

 

[teleport]

What would the world be without the engineers? What would the engineers be without the scientists? Would would the scientists be without mathematicians? What would the mathematicians be without, ahh..., oops don't know.

 

[Darkiekurdo]

I thinks mathematicians need logicians. And vice versa.

 

[teleport]

But you do not see them as one of the brightest then? Doesn't seem consistent nor logical. Unless they had a great start back in the greek days, and became slopy now. But I don't know. Anyways, it is true. I've actually never thought of it. Did the rigorous logic of the mathematics of the greeks develop independently on its own in the mathematics, or were the logic axioms of the time taken and adapted to mathematics?

 

[MathematicalPhysicist]

"logic axioms of the time"

if logic were based on a specific time it wouldn't be logic.

yes you might say now there are non classical logics, but to have them you still first needed the notion of classical logic to begin with.

 

[J77]

It's a dangerous game to start catergorising oneself as either a mathematician, a physicist, or an engineer -- don't narrow your options!

 

[teleport]

loop, but even logic can be flawed to become ilogical. All of that which was considered logical during that period may not have been correct. Hence I could use that expression as I please. I remebered once picking up a book about logic written by, I think Aristotle, and was surprised to not understand a thing. Those guys of more than two millenia ago sure were smart.

 

[teleport]

Oh I see. You meant the use of "logic" by its definition. I meant it as the subject and knowledge (right or wrong) of it. I guess if I didn't hand-wave from the beginning we would both agree to be right from the start. :)

 

[pivoxa15]

Mathwonk, I noticed many upper maths textbooks don't have answers at the back. What does it take to confidently do these exercises knowing there are no answers to look up?

 

[Werg22]

I like to say the same about the engineer students, but I know better. For the most part, I just remember them being engineer majors because they were jerks. To the same extent, I realize I know just as many, if not more, engineer majors that are cool people, just I don't associate the niceness to engineering.

Anyway, I can say that pure math students can be cocky, but I think cocky can be confused with confidence. It takes high confidence and esteem to be a pure math student. You'll fail more often than succeed :D

There's a difference between being cocky and to expect nothing less than people bowing down to you.

 

[PowerIso]

There's a difference between being cocky and to expect nothing less than people bowing down to you.

I think people confuse the two a lot. Especially when you first meet a person.

 

[mathwonk]

pivoxa, when the problem is a proof, you know if you have it or not, so no answers are needed. when it is a calculation, to be sure you have it right, you need two ways to do it so you can compare answers.

 

[teleport]

OMG toss a coin n times and count the number of combinations such that successive heads never appear. What do you get? Fibonaci! Yep, that's sharp. Does anyone know any other kool/crazy/magical thing like this?

 

[Werg22]

I think people confuse the two a lot. Especially when you first meet a person.

The one's I met generally have allot of pretence in their voice and seem almost vexed that you address them.

 

[teleport]

Well the majority of the ones I know in my class are just genuinely funny. My calc prof has a wild sense of humour, but terrifies everyone by asking surprise concept questions in class. I wonder if this is somehow related to the way pure math is. Don't you have the feeling sometimes that pure math is just a very hard infantile game? Combinatorial math reminds me a lot of this for example. What can I say, its just fun.

But math usually takes a lot more effort than many other disciplines so this can take its toll on the person as well. No math people like that around here that I've seen. There are a lot of stupid stereotypes out there. I guess they feel insecure that good looking people can be good in math too. But then again, most just feel insecure in front of good looking people, like if they own the beans...

 

[PowerIso]

The one's I met generally have allot of pretence in their voice and seem almost vexed that you address them.

Well, if that's the case, I suggest you meet new nones :).

Anyway, when do people generally start studying for the Math GRE?

 

[mathwonk]

if you go to a top school, the gre may be less important. but probably nowadays it is wise to take it as a way of comparison with others.

when i was a student, and i realize this is somewhat out of date, as far as i knew no one studied at all for the gre. it was assumed that if you had learned the material in your courses that was sufficient.

i hope i do not come across merely as a wiseguy, but there is more than a little truth to the idea that if you just learn the subject, you will do well on the test over that subject.

hearing myself say these things, i am looking over my shoulder for the guys coming to burn me at the stake, or at least with a straightjacket. so few people believe today that merely learning the material will suffice. everyone has bought into the BS that you need a leg up, and advantage, some special test Kaplan prep, or edge.

this is the kind of thinking that used to be restricted to confidence men and card cheaters.

tests have one purpose, to determine whether you have learned the stuff. not whether you paid some cynical, ignorant hustler $500 to prepare you.

this is so far from being the norm today that i expect some counter messages to follow this immediately, from young people who think they know better than i do, how to succeed. to them, bless you, maybe you do, but please spend a little time thinking about what i said.

after all i have achieved most of what many of you are hoping to obtain.
could it be that my old fashioned advice is not insane after all? try it, it can't hurt you.moral: if you learn the subject, someone will notice and appreciate it, and you WILL get a position.

 

[tronter]

and the means of learning the subject material do not matter (i.e self study)?

 

[J77]

Mathwonk, you won't be burned at the stake for saying the truth.

However, there is the problem that to get into PhD positions in the US, you need the grades from the tests -- at least, that's how I perceive it (am I right?).

As far as I'm concerned, this is completely wrong. Like you say, you don't necessarily have to learn the subject to pass the tests; you can educate yourself to pass a test rather than learn the subject.

Thankfully, it doesn't work like this over here in Europe -- at least, not yet.

I would rather meet the candidate in person and my judgement as to whether or not I'd take them as a student would be based somewhat on their grades (NOT totally) but mainly on their enthusiasm for the research topic and general personality; it's much easier to work with a personality than someone who talks like they're reciting a textbook!

 

[J77]

and the means of learning the subject material do not matter (i.e self study)?

You need to have some grades on paper -- so purely self-study wouldn't work -- but, conversely, you don't need straight A's, a 1st, or 4.0s, afaic (this is the top grade, right?)

 

[pivoxa15]

Mathwonk, can you recall any academics who did poorly in their undergrad studies? If so how poorly? And how did they make it?

 

[mathwonk]

since you ask, i myself had a 1.2 gpa for the first year or so (out of4.0), got kicked out of school, worked in a factory for a year, got back in, did ok and got in grad school.

i never took gre, but as a junior took honors advanced calc, and got B+/A-.
Then as a I senior took one grad course in real analysis, and got an A.

I applied to columbia, brandeis, and a few others, but grades were not that great.
I got into Brandeis, and when i arrived, I was as good as the others, only less well prepared. I lost focus during the vietnam war and left again with only a masters.

'then 4 years later, i began studying again, then just drove over to seattle and took the phd quals at uw.

i passed them and they offered me a slot in the class, but i got a better offer from utah.
so i went to utah, and that's where i finished.

 

[tronter]

well you need a degree in some subject not necessarily math right? Its not necessary to have a math degree to get into grad school for math?

 

[mathwonk]

right. you need to know something and have some ability and impress someone.

i also meant that to do well on tests, the right oreoaration is not test preparation, but real rpeparation.

in high school i never prepared specifically for sat tests (US college scholastic aptitude tests). i took them only once, without ever having seen one before, and got something over 1530/1600.

 

[tronter]

Yeah, for example, if one self studies Analysis by an expert like Dieudonne/Simmons, he would probably be more prepared than one who is taught Analysis from a more contemporary text.

Or if one self studies Algebra by Hungerford/Lang, vs. someone who is taught algebra using Beachy/Blair etc..

I think self study forces you to develop your own perspectives of math rather than following a professor's.

 

[morphism]

Yeah, for example, if one self studies Analysis by an expert like Dieudonne/Simmons, he would probably be more prepared than one who is taught Analysis from a more contemporary text.

Or if one self studies Algebra by Hungerford/Lang, vs. someone who is taught algebra using Beachy/Blair etc..

I think self study forces you to develop your own perspectives of math rather than following a professor's.

Then again if you're taught by someone who knows what they're talking about, they could tell you something you would not find in any textbook, or summarize an entire chapter in one single, brief but illuminating comment!

Of course if you don't study things on your own, they will never sink in.

 

[pivoxa15]

I think that if you can work through a maths book and do everything single excercise then its as good as getting it taught by someone.

Its when you can't do some excercises then you will need someone to teach you so that you can ask them questions. Most people fall into this category so they need to be taught.

 

[mathwonk]

i agree: in order, the best is probably to study from a top book like dieudonne, next best is to be taught by someone good/ but not great who understands it (like me), third is to read a mediocre book like all the ones they use in college nowadays, 4th is to take it in high school from someone who thinks all he needs to teach calc is to have taken it in college.

 

[pivoxa15]

Mathwonk, do you know anyone who are betting at abstract concepts rather than doing concrete examples? i.e most of the time if you tell them to think abstractly they get it right but tell them to think of concrete examples they fail or not as good as when thinking abstractly? Most people would be better at thinking concretely wouldn't you say.

 

[Ki Man]

How much maths would one need to do very basic physics research? Calc II?

 

[mathwonk]

well yes i know people who think very differently. i myself like specific examples, as did perhaps david mumford, whereas people usually say grothendieck thought very abstractly. but mumford told me i believe, that grothendieck also started from concrete examples but very quickly generalized them.

i find it easier to solve problems by thinking of simple cases and then generalizing, rather than thinking generally from the start. but these differences do exist in different people. it is probably no more healthy to force people to think in one way or another, than to try to change a good shooters natural technique.

 

[pivoxa15]

well yes i know people who think very differently. i myself like specific examples, aS did perhaps david mumford, whereas people usually say grothendieck thought very abstractly. but mumford told me i believe, that grothendieck also started from concrete examples but very quickly generalized them.

i find it easier to solve problems by thinking of simple cases and then generalizing, rather than thinking generally from the start. but these differences do exist in different people. it is probably no more healthy to force people to think in one way or another, than to try to change a good shooters natural technique.

I was just about to ask about Grothendieck. If even he starts off with concrete examples then it would be fair to say that no one would start off abstractly?

So would my question be equivalent to asking whether anyone can run before they can walk? Offcourse some can run very soon after they can walk but all start off walking first.