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Other The Should I Become a Mathematician? Thread

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symbolipoint

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VCrakeV discusses and asks:
I want to know if I would enjoy a minor or major. I enjoy Algebra, derivative Calculus, integral Calculus, complex numbers, and concepts of infinity. But matrix Algebra and matrices in general bore me to tears. I also dislike 3D graphing, and 3D visuals in general. A major would also require some computer science, which I find quite a bore.
You would not enjoy any major or minor in Mathematics. Look at the program requirements for a minor concentration at your school and decide if you believe you would or would not want/be interested in earning minor concentration or a degree in Math.
 
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I want to be a mathematician but I am probably too stupid, my favourite things so far have been mostly in discrete mathematics...set theory and logic, loved proofs and mathematical induction when I came across them . I also like vectors and am trying to study analysis on the side, calculus and algebra are my weakest backgrounds, I have very basic knowledge in them and Geometry too, but most of all I have an obsession with numbers and how almost everything else, evaluates to one or can be constructed through them, somehow this always amazes me (dont know why). I only started loving math a few months ago, i ask some very silly questions about it sometimes.. I know it is not a phase.

The question for me is not should, but if I can. @mathwonk great and vast thread..I will be coming here more often.
 
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symbolipoint

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I want to be a mathematician but I am probably too stupid, my favourite things so far have been mostly in discrete mathematics...set theory and logic, loved proofs and mathematical induction when I came across them . I also like vectors and am trying to study analysis on the side, calculus and algebra are my weakest backgrounds, I have very basic knowledge in them and Geometry too, but most of all I have an obsession with numbers and how almost everything else, evaluates to one or can be constructed through them, somehow this always amazes me (dont know why). I only started loving math a few months ago, i ask some very silly questions about it sometimes.. I know it is not a phase.

The question for me is not should, but if I can. @mathwonk great and vast thread..I will be coming here more often.
You mischaracterize yourself and have not spent as much time studying Algebra and Calculus as the other things of your "favorites".
 
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You mischaracterize yourself and have not spent as much time studying Algebra and Calculus as the other things of your "favorites".
I am not smart, and have this silly mental illness. Unfortunately there can only be so many people at the higher end of the intelligence normal distribution, let alone be motivated enough.

math is hard, like all rigourous subjects, a kind of reprogramming of ones soul and identity. I know math is the purest and most used form of knowledge, without it we wouldnt have the framework for sciences and modern life today. So, you can pretty do much A LOT OF things. :D
Thank you for the motivation.
 
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symbolipoint

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I am not smart, and have this silly mental illness. Unfortunately there can only be so many people at the higher end of the intelligence normal distribution, let alone be motivated enough.

math is hard, like all rigourous subjects, a kind of reprogramming of ones soul and identity. I know math is the purest and most used form of knowledge, without it we wouldnt have the framework for sciences and modern life today. So, you can pretty do much A LOT OF things. :D
Thank you for the motivation.
Here is how much of the world may view:

One can struggle to learn Algebra 1,2,3, some one or two Trigonometry courses (even if either repeated or delivered in two different courses), and maybe two or three Calculus course (sequence as Calc 1,2,3), and earn some other degree related to or dependent on Mathematics; and then you could some day apply your possibly limited but very important Algebra and common Geometry skills. Many people will think that YOU ARE SMART. You have used your relatively simple Mathematical skills to solve everyday problems and make good predictions in your work. Other people or at least some of them, will believe you are really smart. Now, how smart are you?
 
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Here is how much of the world may view:

One can struggle to learn Algebra 1,2,3, some one or two Trigonometry courses (even if either repeated or delivered in two different courses), and maybe two or three Calculus course (sequence as Calc 1,2,3), and earn some other degree related to or dependent on Mathematics; and then you could some day apply your possibly limited but very important Algebra and common Geometry skills. Many people will think that YOU ARE SMART. You have used your relatively simple Mathematical skills to solve everyday problems and make good predictions in your work. Other people or at least some of them, will believe you are really smart. Now, how smart are you?
I will attempt a math degree later for sure, tired of being a bottom feeder in the vast field of math.
 

symbolipoint

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I will attempt a math degree later for sure, tired of being a bottom feeder in the vast field of math.
You might feel or find later that Mathematics is not the degree objective for you. You can still pick something that uses Mathematics, and you will apply much of or some of what you learn from Mathematics.
 

mathwonk

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Remark to symbolipoint: the administration changed the title of this thread (without asking me), after thousands of posts had been logged here. So there is no reason most of the the posts should be addressing the current title. Admitted it is similar to the original one, "Who wants to be a mathematician?" but that one was chosen whimsically to mirror a then current tv quiz show, rather than to be specifically pedantically descriptive. I always regretted the loss of some humor and the homogenization of the threads' titles, for no clear reason. I also noted enviously that some physics oriented threads were allowed to keep their original titles.

Anyway, I take no responsibility for the current somewhat dull title nor think it should impose any restrictions on the questions asked here, which are open to all interested in learning about math and learning about learning about math, as far as I am concerned at least.
 
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symbolipoint

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Remark to symbolipoint: the administration changed the title of this thread (without asking me), after thousands of posts had been logged here. So there is no reason most of the the posts should be addressing the current title. Admitted it is similar to the original one, "Who wants to be a mathematician?" but that one was chosen whimsically to mirror a then current tv quiz show, rather than to be specifically pedantically descriptive. I always regretted the loss of some humor and the homogenization of the threads' titles, for no clear reason. I also noted enviously that some physics oriented threads were allowed to keep their original titles.

Anyway, I take no responsibility for the current somewhat dull title nor think it should impose any restrictions on the questions asked here, which are open to all interested in learning about math and learning about learning about math, as far as I am concerned at least.
The new title change is not bad, but I like the original title better for the reasons you described. The two titles really do make the same meaning enough.
 
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So, I started my first contributions to this thread as an undergrad in my 30s. I'm now 40 about to get my master's. At this point I will not be pursuing a PhD, but I'm really ecstatically happy with what I've done. I grew up in a working class suburban family. I am the first in my immediate family to have anything higher than a high school diploma. My high school counselors (back in the 90s) advised me that "people like you don't really go to college" and tried to send me to tech school.

So yeah, a master's is pretty bleeping good.

I had been feeling the "bug" to move on for awhile from being in school. My son was born in February (3 months early - long story) and now the mental shift from "self investment" to family is complete. It is time to move on, but this doesn't mean it's the end of anything.

Some of my acquaintances refer to me as "a mathematician" and I always sort of correct them. But I certainly came out of school with a different brain than what I went in with. Non-mathematical endeavors seem a lot easier now, or, if they are not easier, they are not scary. Actually, after 6 years in school, I am finding talking to people that do not have a math or science background slightly frustrating, but this is something I need to work on. Not their fault.

I still have to finish the qualifier, but I'm actually, perhaps ironically, taking time off from school to study for it. I couldn't do TA+classes+qualifier+new baby and we were running out of money. I actually can't *wait* to be done and move on to something else. What an awesome, challenging time this was.

I hope I pass the thing in January, otherwise I will have to take it in may. I have to enroll in a class to take the qualifier so I'm doing an online biostats course - but that's a whole other post.

-Dave K
 
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VCrakeV discusses and asks:


You would not enjoy any major or minor in Mathematics. Look at the program requirements for a minor concentration at your school and decide if you believe you would or would not want/be interested in earning minor concentration or a degree in Math.
I'm a little perplexed by this response. The poster listed a lot of mathematical subjects he found enjoyable and a few he did not. You certainly don't have to like every subject to enjoy studying math. You study the stuff you like and the stuff you don't like but which you have to study anyway to be well rounded. One may also find tastes change over time, either because of something personal or finding a class or professor that makes the subject click for you.

-Dave K
 

symbolipoint

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I'm a little perplexed by this response. The poster listed a lot of mathematical subjects he found enjoyable and a few he did not. You certainly don't have to like every subject to enjoy studying math. You study the stuff you like and the stuff you don't like but which you have to study anyway to be well rounded. One may also find tastes change over time, either because of something personal or finding a class or professor that makes the subject click for you.

-Dave K
Maybe the portion of his quote that I took would help see how my response would fit:

VCrakeV discusses and asks:

I want to know if I would enjoy a minor or major. I enjoy Algebra, derivative Calculus, integral Calculus, complex numbers, and concepts of infinity. But matrix Algebra and matrices in general bore me to tears. I also dislike 3D graphing, and 3D visuals in general. A major would also require some computer science, which I find quite a bore.
Checking what he said he dislikes helped me decide what to tell him. Not a bad opinion, just MY opinion, and other opinions from other members are still possible.
VCrakeV must decide what he wants to do and what efforts he will make to do it.
 
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Maybe the portion of his quote that I took would help see how my response would fit:

VCrakeV discusses and asks:


Checking what he said he dislikes helped me decide what to tell him. Not a bad opinion, just MY opinion, and other opinions from other members are still possible.
VCrakeV must decide what he wants to do and what efforts he will make to do it.
Point taken. It's just that your statement "you would not enjoy..." seemed kind of definitive to me.

I think it is super important to know that when you choose to accomplish something or learn something there is a big chance you will not enjoy a lot of the process, and that doesn't always mean its not for you. I actually am not big fan of calculus/analysis etc. and at one point as an undergrad I felt that maybe math wasn't for me. I talked to a grad student at the time who told me "nah, there's other kinds of math." Turns out I am just better and more at home with more "discrete" math.

-Dave K
 
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one can develop his 3d spatial skills by:
1. playing with functions in microsoft mathematics (a free software)


2. creating things in wings 3d (another free software):
n3S9F5h.png

I understand the importance, but it doesn't matter if I won't enjoy it. I can always just study whatever math interests me on my own time, in case university programs have too much math I don't like. But might I like such a program?
 
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symbolipoint

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Point taken. It's just that your statement "you would not enjoy..." seemed kind of definitive to me.

I think it is super important to know that when you choose to accomplish something or learn something there is a big chance you will not enjoy a lot of the process, and that doesn't always mean its not for you. I actually am not big fan of calculus/analysis etc. and at one point as an undergrad I felt that maybe math wasn't for me. I talked to a grad student at the time who told me "nah, there's other kinds of math." Turns out I am just better and more at home with more "discrete" math.

-Dave K
Hard to know exactly what to tell the VCrakeV member. If he wants a degree in Math or Phys, then some things he must study no matter how is likes or dislikes. Maybe he will prefer something in Engineering that will use much Mathematics and not need an undergraduate degree-or-more in Mathematics in order to achieve something in Engineering or whatever related.
 
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I want to be a mathematician but I am probably too stupid, my favourite things so far have been mostly in discrete mathematics...set theory and logic, loved proofs and mathematical induction when I came across them . I also like vectors and am trying to study analysis on the side, calculus and algebra are my weakest backgrounds, I have very basic knowledge in them and Geometry too, but most of all I have an obsession with numbers and how almost everything else, evaluates to one or can be constructed through them, somehow this always amazes me (dont know why). I only started loving math a few months ago, i ask some very silly questions about it sometimes.. I know it is not a phase.

The question for me is not should, but if I can. @mathwonk great and vast thread..I will be coming here more often.
We've crossed on a couple of threads, and of course I've clarified that I'm not a mathematician, but I am a fairly slow person who is getting a master's later in life than the average.

I'm not going to tell you that you aren't stupid, because I am fairly stupid and so I'd rather just we talk stupid to stupid.

The thing to decide is not if you are smart enough, but if you are willing to work as hard as you need to and sacrifice as much as you need to in order to overcome any deficiencies you might have (real or perceived). If you aren't one of these "I got advanced placement in 10th grade and won math competitions every year" kids then whatever. I stopped worrying about "smart" during undergrad. There was a point where I believed I'd never even get my bachelor's. I thought it would be the most amazing thing ever if I did. I'd never done anything like it. It would be so amazing and so hard and oh my god.

When I asked myself whether I could get the degree my brain kept insisting that this was probably impossible. When I asked myself if I'd ever be "good at math," the answer came up, "no." Am I really super smart? "no."

So the different question I asked was "Can I study for the tests, do the homework, and pass the courses?"

hmm.

Turns out I was able to do that. One class, one homework set, one test, one subject at a time. Turns out there was no class called "The class where you find out if you are really a mathematician and intelligent or just a fraud." There were just these individual classes that if you took them, they added up to a degree. Weird right?

-Dave K
 

symbolipoint

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dkotschessaa,
Great posting, #3716.

What do you think of the kind of person who studies one course (of Mathematics) at a time, but find he does not pass and needs to repeat every single one of them, such as the typical three-course series of Calculus 1,2,3? The person studies very hard EACH time, does not pass, then REPEATS the course passing successfully. Very slow progress. For this person, the courses, each of them, is just too difficult to pass when going though the semester one time. Learning happens, but the learning did not happen during the first time-through for each of these courses. Worked HARD! Studied long time! Did ALL the homework! Asked for some instructor help! Nobody has the answer to what person is doing wrong; maybe this person just needs MORE TIME to understand and to learn. Could this type of person go back to college or university and study to earn a degree in Mathematics? Probably not, because as he goes through each new course, the same trouble would happen - not pass, need to repeat course, then pass it, and so on. The person will finally know some good Math concepts and skills but getting a undergraduate degree in MATH will just take too long. Is the person stupid? Probably not. Anyone who works through this tough stuff is at least, very hard-working, but something in his head is just not letting him succeed in Mathematics more efficiently. He will very likely find that actually USING some of his learned mathematical concepts and skills in applied fields or situations works well for him; and then other people will say to him, "Wow, you are such a great mathematician", without realizing how much he struggled in his Math courses.
 

IGU

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What do you think of the kind of person who studies one course (of Mathematics) at a time, but find he does not pass and needs to repeat every single one of them....
You didn't ask me, but I'll stick in my opinion anyway (hope you don't mind!).

I think people learn best in different ways, highly dependent on the individual. Such a person as you describe is clearly not learning well from lectures. Indeed lectures are not a particularly good way to learn anything for most people, so this person is not unusual. This person should spend some serious time trying to figure out how it is they learn best. Then they should use that method to learn whatever it is they want to learn. The classes should be taken only after they have learned the material (or at earliest simultaneously), merely to record a grade (and perhaps review). In this way classes will never need to be taken more than once.

Note that at top universities it is often the case that the best students rarely attend lectures. That's because they don't want to waste their time. Part of what makes them the best students is that they learned early what is the best way for them to learn (and it wasn't lectures). The key insight here is that learning methods are almost entirely orthogonal to the content to be learned. What is most important for any student is to figure out what their best learning methods are -- after that everything is much, much easier.
 

symbolipoint

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IGU,
I just wonder, how many of the really successful Mathematics students actually do that/this?:
The classes should be taken only after they have learned the material (or at earliest simultaneously), merely to record a grade (and perhaps review). In this way classes will never need to be taken more than once.
That runs right along with, "having studied the course before".
 

IGU

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I just wonder, how many of the really successful Mathematics students actually do that/this?
From my experience at Caltech (many years ago): many. From what I've read on the TSR forums from Cambridge mathematics students, many there too.
That runs right along with, "having studied the course before".
Sure. It's always best to study material at your leisure in your preferred way. Lectures are a terrible way to encounter material for the first time. It is pretty much inevitable that for difficult mathematical material a student will be looking at it multiple times. Gaining control over that process is one thing that good students do. And often (but not always) it turns out that the lectures are superfluous. Everybody has to find their own way. Certainly for the person under discussion, who needs to take classes twice, a better way must be possible.
 
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dkotschessaa,
Great posting, #3716.

What do you think of the kind of person who studies one course (of Mathematics) at a time, but find he does not pass and needs to repeat every single one of them, such as the typical three-course series of Calculus 1,2,3? The person studies very hard EACH time, does not pass, then REPEATS the course passing successfully. Very slow progress. For this person, the courses, each of them, is just too difficult to pass when going though the semester one time. Learning happens, but the learning did not happen during the first time-through for each of these courses. Worked HARD! Studied long time! Did ALL the homework! Asked for some instructor help! Nobody has the answer to what person is doing wrong; maybe this person just needs MORE TIME to understand and to learn. Could this type of person go back to college or university and study to earn a degree in Mathematics? Probably not, because as he goes through each new course, the same trouble would happen - not pass, need to repeat course, then pass it, and so on. The person will finally know some good Math concepts and skills but getting a undergraduate degree in MATH will just take too long. Is the person stupid? Probably not. Anyone who works through this tough stuff is at least, very hard-working, but something in his head is just not letting him succeed in Mathematics more efficiently. He will very likely find that actually USING some of his learned mathematical concepts and skills in applied fields or situations works well for him; and then other people will say to him, "Wow, you are such a great mathematician", without realizing how much he struggled in his Math courses.
I know you are being hypothetical, but most of the time when I've seen a student fail a class multiple times the problem was in the approach, or they weren't giving it enough time in the *right* way, or they had other classes occupying their grey matter, or some attitude towards mathematics they picked up from somewhere, or some otherwise emotional blockage.

But OK, instead of going down that road I'll let the rest of your scenario play out, because I don't think that was the point.

The following was posted by Field's Medalist Timothy Gowers on Google+ about a year ago:

"What is it like to do maths?

About 99% of the time it's like this. "

GOWERS.JPG



My wife, who supported me through my degree, and who (rightfully) was keen on me not wasting my time, would often ask me how my homework/study was going.

I would often respond with something like, "Well, I didn't get any of the problems done, and I don't feel like I really understand that much yet. But I spent a lot of good time thinking about the concepts."

It took a bit of explaining to assure her that this was actually, in my opinion, productive time. Obviously I had no evidence of this fact unless ultimately I ended up producing something (like a completed homework, or a decent test grade).

So, I think that if you are at least giving a sincere effort to do mathematics, there will always be some benefit, even if you don't seem to have much to show for it. I did terribly in Graduate Algebra, but having gone through the class made other classes and subjects seem a lot easier.

-Dave K
 
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Sure. It's always best to study material at your leisure in your preferred way. Lectures are a terrible way to encounter material for the first time. It is pretty much inevitable that for difficult mathematical material a student will be looking at it multiple times. Gaining control over that process is one thing that good students do. And often (but not always) it turns out that the lectures are superfluous. Everybody has to find their own way. Certainly for the person under discussion, who needs to take classes twice, a better way must be possible.
I attended good lectures where I enjoyed the professor's teaching style and found it elucidating. If the professor was not very good, I would often not attend unless I was stuck at a certain point, then I would go in so that I could hear him discuss it and ask questions about the parts I didn't understand.

-Dave K
 

symbolipoint

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dkotschessaa,

What I described was the pattern of repeated fail/non-passage of ONE COURSE AT A TIME. The finer detail is
  1. Take course
  2. NOT pass course
  3. Repeat course one time
  4. Pass course successfully
  5. Next Course of a sequence of courses --- Repeat at #1 with the incremented course
Meaning, each course passed but always needed to be repeated ONE TIME.
 
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dkotschessaa,

What I described was the pattern of repeated fail/non-passage of ONE COURSE AT A TIME. The finer detail is
  1. Take course
  2. NOT pass course
  3. Repeat course one time
  4. Pass course successfully
  5. Next Course of a sequence of courses --- Repeat at #1 with the incremented course
Meaning, each course passed but always needed to be repeated ONE TIME.
Oh.

In that case, I can't even say. It seems like a pretty unlikely scenario. Most people who fail courses fail one or two and drop out if they fail a whole bunch more. Sometimes they leave and come back much later. Strictly speaking the time it took me to get my bachelors was 18 years, if you count the first time I tried to go to college in 1996. I also repeated pre-calculus and two semesters of calculus, though this was due to time passed rather than failure.

-Dave K
 
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symbolipoint

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Oh.

In that case, I can't even say. It seems like a pretty unlikely scenario. Most people who fail courses fail one or two and drop out if they fail a whole bunch more. Sometimes they leave and come back much later. Strictly speaking the time it took me to get my bachelors was 18 years, if you count the first time I tried to go to college in 1996. I also repeated pre-calculus and two semesters of calculus, though this was due to time passed rather than failure.

-Dave K
Many people will give up when they fail a couple of Math (even Calculus) courses, and then pick or find something much less mathematics-intensive. Then there are some, maybe only a few, who will persist and keeping working at the needed mathematics courses until passing because these people stay dedicated to whatever math-intensive field they have chosen. Not sure which is the smarter way to go. Fail a couple of courses and change direction; or keep at it until passing each of the needed mathematics courses.

Something worth knowing is that if a student really works hard to learn a course the first time, does not pass it, and then repeats the course and again REALLY WORKS HARD the second time too, the course really does become easier to learn and understand.
 

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