Majoring in Math
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Majoring in Math
I've noticed that people on these boards are helpful and smart, so I'm taking advantage. The following happened today, and I'm hoping it gives some insight into what position I'm in.
Today, as I turned in my Economics final, the professor (PhD from MIT) asked me how hard the test was. I kind of gave an unsure answer, and then he asked me what I was majoring in.
"Mathematics," I said (with a hint of pride).
Recalling my noncommittal answer from seconds before, he creased his eyebrows and said "Really? How are you doing in your math courses?"
"Ok," I said, "I'm not like a natural, or anything, but recently I've been getting interested..."
Now he looked genuinely concerned. "You have be very, very bright to go into higher level mathematics. But if you're just 'interested'..."
I nodded.
"Are you sure you want to go into math?"
"I'm testing the waters a bit."
"Now is the time. But remember, don't swim if the water's too deep for you."
Basically my professor dug up a fear that I had been trying to deny/ignore for some time. What if I'm just too mediocre to have high aspirations in mathematics? I think I subscribe to the 'where there's a will there's a way' mentality, but does this apply to math?
I am taking college level calculus (tomorrow is the final for Integral Calculus in which I would only get an A in with an A on the final) and got a B+ in Differential Calculus. Is the B+ in such an 'easy' (what the math counselor considers it) course even forgivable for someone who wants to go to a top grad school in math?
Please give me counsel.
This desire to go do great things in math might come off as one of those temporary interest things (like an obsession with pokemon). I don't really know whether it is or not, but I do know that I hated math for most of my childhood, and this is one of the reasons I'm worried that my future may not be in math. I kind of want to hear an encouraging story or anecdote or something.
Sorry for the long ramble, I hope some of you can help.
Oh, and thanks a lot!
Today, as I turned in my Economics final, the professor (PhD from MIT) asked me how hard the test was. I kind of gave an unsure answer, and then he asked me what I was majoring in.
"Mathematics," I said (with a hint of pride).
Recalling my noncommittal answer from seconds before, he creased his eyebrows and said "Really? How are you doing in your math courses?"
"Ok," I said, "I'm not like a natural, or anything, but recently I've been getting interested..."
Now he looked genuinely concerned. "You have be very, very bright to go into higher level mathematics. But if you're just 'interested'..."
I nodded.
"Are you sure you want to go into math?"
"I'm testing the waters a bit."
"Now is the time. But remember, don't swim if the water's too deep for you."
Basically my professor dug up a fear that I had been trying to deny/ignore for some time. What if I'm just too mediocre to have high aspirations in mathematics? I think I subscribe to the 'where there's a will there's a way' mentality, but does this apply to math?
I am taking college level calculus (tomorrow is the final for Integral Calculus in which I would only get an A in with an A on the final) and got a B+ in Differential Calculus. Is the B+ in such an 'easy' (what the math counselor considers it) course even forgivable for someone who wants to go to a top grad school in math?
Please give me counsel.
This desire to go do great things in math might come off as one of those temporary interest things (like an obsession with pokemon). I don't really know whether it is or not, but I do know that I hated math for most of my childhood, and this is one of the reasons I'm worried that my future may not be in math. I kind of want to hear an encouraging story or anecdote or something.
Sorry for the long ramble, I hope some of you can help.
Oh, and thanks a lot!
Re: Majoring in Math
I'm in a similar predicament. I'm not the greatest mathematician, but I'm pretty much set on majoring in math.
According to one of my friends, future math majors are the ones who go to PROMYS or qualify for the USAMO (I did neither). According to a graduate professor at the University of Toronto, the "make it or break it" courses are analysis, topology, and abstract algebra and before then it's hard to tell.
So I guess my conclusion is, I don't really know. They say math is something that you either have or don't have. Personally, I'm going to take the chance. If I don't make it, I can always switch to physics or econ.
According to one of my friends, future math majors are the ones who go to PROMYS or qualify for the USAMO (I did neither). According to a graduate professor at the University of Toronto, the "make it or break it" courses are analysis, topology, and abstract algebra and before then it's hard to tell.
So I guess my conclusion is, I don't really know. They say math is something that you either have or don't have. Personally, I'm going to take the chance. If I don't make it, I can always switch to physics or econ.
 Mathmagic
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Re: Majoring in Math
All I'll say is this: I have always been interested in physics, and entered university with the intent of getting a M.Sc. in Physics. After my first year of undergrad, I realized that taking physics in university stressed me out far too much for me to actually enjoy physics anymore. I decided I was better off taking Geophysics, which is less mathintense, but still has enough physics to keep me entertained. I now learn about quantum physics and relativity on my own time as a hobby.
Basically what I'm trying to say is that just because you're interested in a topic, it won't necessarily be in your best interest to spend your money taking courses in it. There are much more costefficient methods of enjoying a subject you have fun learning about.
Basically what I'm trying to say is that just because you're interested in a topic, it won't necessarily be in your best interest to spend your money taking courses in it. There are much more costefficient methods of enjoying a subject you have fun learning about.
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Re: Majoring in Math
Well, I wouldn't worry to much. If you are worried about the calculus material, just take any opportunity you get to tutor people in calculus. The general wisdom among mathematicians is that one never really understands algebra or calculus until one has taught it (a few times). I suggest (if you do enjoy math) is to finish an undergraduate degree in math. People respect a degree in math even if you have Bs or even Cs. If you plan on advanced degrees in math, you will need to wait and see how you do in more advanced courses.
[Edit for full disclosure] I am a Ph.D. candidate in mathematics. Most people I know (currently studying advanced math, including me) took differential and integral calculus in high school, so it is a little unfair to compare experiences.
[Edit for full disclosure] I am a Ph.D. candidate in mathematics. Most people I know (currently studying advanced math, including me) took differential and integral calculus in high school, so it is a little unfair to compare experiences.
Re: Majoring in Math
greenblob wrote:So I guess my conclusion is, I don't really know. They say math is something that you either have or don't have. Personally, I'm going to take the chance. If I don't make it, I can always switch to physics or econ.
mathmagic wrote:All I'll say is this: I have always been interested in physics, and entered university with the intent of getting a M.Sc. in Physics. After my first year of undergrad, I realized that taking physics in university stressed me out far too much for me to actually enjoy physics anymore. I decided I was better off taking Geophysics, which is less mathintense, but still has enough physics to keep me entertained. I now learn about quantum physics and relativity on my own time as a hobby.
Basically what I'm trying to say is that just because you're interested in a topic, it won't necessarily be in your best interest to spend your money taking courses in it. There are much more costefficient methods of enjoying a subject you have fun learning about.
I was leaning towards taking the chance myself... and then maybe doing actuarial sciences if I didn't find pure math to be my area.
yeyui wrote:[Edit for full disclosure] I am a Ph.D. candidate in mathematics. Most people I know (currently studying advanced math, including me) took differential and integral calculus in high school, so it is a little unfair to compare experiences.
If you don't mind me asking, how hard would you say calculus was for you, roughly?
Re: Majoring in Math
To suggest that you have to be "very, very bright" to major in mathematics is absurd. In general, at the undergraduate level, anyone should major in whatever interests him or her. It's always possible to get through the major, so long as you're willing to put in the necessary effort (going to professors' office hours, etc.) when the going gets tough.
However, he's sort of right about graduate school. If you're having trouble with calculus, to be blunt, you won't get into a "top grad school." But, um, so? Very few people do. The "tiers" of grad school are pretty fuzzy to begin with. All that really matters is who you end up working with. Remember that fame is seldom associated with quality of advising. If math is what you want to do, by all means, major in it. I certainly wouldn't let the words of an economics professor (who, like any academic, tends to encourage students to major in his or her own field) dissuade you from following your passion.
However, he's sort of right about graduate school. If you're having trouble with calculus, to be blunt, you won't get into a "top grad school." But, um, so? Very few people do. The "tiers" of grad school are pretty fuzzy to begin with. All that really matters is who you end up working with. Remember that fame is seldom associated with quality of advising. If math is what you want to do, by all means, major in it. I certainly wouldn't let the words of an economics professor (who, like any academic, tends to encourage students to major in his or her own field) dissuade you from following your passion.
Re: Majoring in Math
Do it. I'm a firm believer in doing what you want to do, not what's practical or what you're good at but hate. If you like pure math, you'll find the motivation to persist even when it seems like it's kicking your ass.
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 NathanielJ
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Re: Majoring in Math
Keep at it at least a little while longer, you still haven't even gotten to the "pure math" part of a pure math degree. You'll know whether or not you can handle it once you hit a course like real analysis or set theory (not because those are the hardest classes you'll take, but because they're the first classes that will give you a true taste of upperlevel mathematics). If you can't handle those courses, you'll still have time to switch to something else, and you might as well at least try what you really love.
Re: Majoring in Math
There are plenty of examples of brilliant mathematicians who sucked in college math. Stephen Smale failed nuclear physics and mostly got Bs and Cs in math. What really matters is whether you have a passion for it. Do you do math in your own time? Even if you're having trouble in calculus and computatin, that doesn't mean you'll have the same level of difficulty with other aspects of math. I took a class once with Roger Myerson. His boardwork was horrible, he forgot integrals, messed up just about every calculation, etc. But he also won a Nobel Prize for very mathematical work in game theory.
Another thing to remember is that math as it's researched is far different than math as it's written in textbooks. Textbooks can make all the theorems seem terse, as if a mathematician sat and plucked them out of thin air, saying 'suppose x y and z were true . . ." and you wonder how the hell that popped into their heads. In reality it often works backwards. First comes the general idea, then you go back and find out the assumptions under which it's true.
You mentioned doing 'great things' in math. I think that's mostly up to you. The key is whether you really like sitting down and playing with it.
Besides, it's really easy to go from math to something else, especially if you take time to work in a lab or something.
Another thing to remember is that math as it's researched is far different than math as it's written in textbooks. Textbooks can make all the theorems seem terse, as if a mathematician sat and plucked them out of thin air, saying 'suppose x y and z were true . . ." and you wonder how the hell that popped into their heads. In reality it often works backwards. First comes the general idea, then you go back and find out the assumptions under which it's true.
You mentioned doing 'great things' in math. I think that's mostly up to you. The key is whether you really like sitting down and playing with it.
Besides, it's really easy to go from math to something else, especially if you take time to work in a lab or something.
Re: Majoring in Math
Go as far as you can. When you reach your limit, find something else. It may well be a lot farther out than you fear. And if it isn't, the additional math expertise won't hurt.
About the "math majors are bright" claim, IQ tests do tend to support that. And other tests that are correlated with IQ. For instance when I took the GREs I learned that math majors score higher on the English GRE than English majors do. Of course there is a chicken and egg phenomena here. Do math majors do so well because math stresses areas of the brain that are useful in multipleguess exams? Or are people who have high IQs drawn to math because it is challenging? I don't know, but I suspect a little of both.
ObligatoryDisclaimer: I dropped out of a PhD program in math for economic reasons shortly before I would have finished. So I may have a vested interest in believing that math majors are smart.
About the "math majors are bright" claim, IQ tests do tend to support that. And other tests that are correlated with IQ. For instance when I took the GREs I learned that math majors score higher on the English GRE than English majors do. Of course there is a chicken and egg phenomena here. Do math majors do so well because math stresses areas of the brain that are useful in multipleguess exams? Or are people who have high IQs drawn to math because it is challenging? I don't know, but I suspect a little of both.
ObligatoryDisclaimer: I dropped out of a PhD program in math for economic reasons shortly before I would have finished. So I may have a vested interest in believing that math majors are smart.
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Re: Majoring in Math
Thank you so much for the encouragement. I was half expecting honest people to say that it isn't the field for those who are just 'ok' in it.
I just took my math final which I did decent on, and will probably end up with an A.
I was really discouraged as I walked home because of how hard it was, but reading the replies in this thread brightened my day.
If I quit because I'm mediocre at math... I'll never not be mediocre at math. And never is a scary word...
I just took my math final which I did decent on, and will probably end up with an A.
I was really discouraged as I walked home because of how hard it was, but reading the replies in this thread brightened my day.
If I quit because I'm mediocre at math... I'll never not be mediocre at math. And never is a scary word...
Re: Majoring in Math
Firstyear calc courses give you no taste of what majoring in (pure) math is like. Get to at least an "intro to proof" or number theory class if you want a subtle taste, to see if you are good at it (or even like it at all). Then move onto analysis/algebra/topology, and see if you are still doing well and still like it. Calc should not dissuade you at all, it will become completely different when you get further along.
Re: Majoring in Math
I'm majoring in Mechanical Engineering and Mathematics (because I hate having a social life). I really have to say that the early math classes like differential and integral calculus don't give you any sense for the work you do as a math major. You will get a better sense of the work when you take your first Differential Equations or Linear Algebra course. Even then, that's just scratching the surface. What's important is what interests you. If you enjoy the coursework then you will do better and you'll study harder. Believe me (as someone who has tried about 4 majors on for size), when things get really hard to understand, people who like the subject take on the challenge with pleasure. The others switch majors. So, the question you have to ask yourself is this, how passionate am I about math? If you can appreciate and enjoy Calculus, that's a big start. For the record, I got B's in integral calculus and multivariable calc, and I'm on track for grad school. Don't worry about getting a B in a couple weed out classes.
Re: Majoring in Math
I didn't have any trouble with the calculus I took in high school. This was a full year AP course, 90 minutes a day, five days a week with lots of homework and many many practice tests. It was a LOT of work but left me very prepared for the AP Calculus BC exam. I did struggle some with my undergraduate calculus course (multivariate calculus) though. My first modern algebra course and my first complex analysis courses pretty much kicked my ass. (I got revenge on the complex analysis at the masters level though.)
Re: Majoring in Math
I suspect you can probably get a bachelor's degree in math even if you struggle in calc (although, to be honest, if I had to put money down, I'd say that you wouldn't. But hey, prove me wrong, I'm just some guy on the internet) but I don't think you could go on to grad school.
I also agree with the above poster that actual math doesn't really happen until abstract algebra, analysis and topology.
On a side note, I think it's good to feel like you have something to prove (not mathematically prove, but like, show to people or yourself that you can do it). I feel like I lost that need to prove to other people I was good at math, and that's when I no longer had any drive to do it.
I also agree with the above poster that actual math doesn't really happen until abstract algebra, analysis and topology.
On a side note, I think it's good to feel like you have something to prove (not mathematically prove, but like, show to people or yourself that you can do it). I feel like I lost that need to prove to other people I was good at math, and that's when I no longer had any drive to do it.
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Re: Majoring in Math
I'm getting ready to go "audition" (an oral examination in front of a group of professors; I'll be working proofs for them) at my uni to see whether or not I can test out of some math classes and move on to senior and graduate level math courses, and while I'm on the bright side, I'm absolutely petrified about this oral examination. It's nothing like the calculus or algebra courses. Calculus and algebra are about learning how to use and apply theorems to various problems, but the upperlevel math courses seem to be more focused on a completely different type of learning  learning a new way to think, in a sense. The way of thinking they're trying to teach me is necessary for learning to prove those theorems we were using in calc and algebra, and many more outside of that.
EDIT: Completely forgot! Yes, I suppose I'm in the same boat you are about "oh my gosh, am I really smart enough to do this? What if I completely flunk the audition and make a fool of myself? I've loved math since forever and it'd kill me not to be able to yadda yadda yadda..." And I could go on worrying about my intellectual abilities forever, but I realized that if I just don't quit at it, I can get through whatever the professors throw at me. I believe that much about myself. While I won't say that ability has nothing to do with it, I realized my selfconfidence and my perception of my ability could very well have a strong influence, positive or negative, on what I do. So don't worry about it! You're in/going to college, and we're supposed to be having fun there, enjoying life, and getting some learning done. Also! Your professors are there to help you learn. If you need help, go ask them. Again also! Practice, practice, practice. The more you do of something, the better you get at it.
I think I'm done with my ramblings now.
EDIT: Completely forgot! Yes, I suppose I'm in the same boat you are about "oh my gosh, am I really smart enough to do this? What if I completely flunk the audition and make a fool of myself? I've loved math since forever and it'd kill me not to be able to yadda yadda yadda..." And I could go on worrying about my intellectual abilities forever, but I realized that if I just don't quit at it, I can get through whatever the professors throw at me. I believe that much about myself. While I won't say that ability has nothing to do with it, I realized my selfconfidence and my perception of my ability could very well have a strong influence, positive or negative, on what I do. So don't worry about it! You're in/going to college, and we're supposed to be having fun there, enjoying life, and getting some learning done. Also! Your professors are there to help you learn. If you need help, go ask them. Again also! Practice, practice, practice. The more you do of something, the better you get at it.
I think I'm done with my ramblings now.
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.
Re: Majoring in Math
I suspect you can probably get a bachelor's degree in math even if you struggle in calc (although, to be honest, if I had to put money down, I'd say that you wouldn't. But hey, prove me wrong, I'm just some guy on the internet) but I don't think you could go on to grad school.
I've always found that you can't judge the potential of a person for pure maths by calculus. Relatively, I suck when it comes to calculus (though I'm hoping this is mostly from not touching the subject in 3 years), but excel at pure mathematics. Now I wouldn't say I struggled through freshman calculus, more like I didn't care about math at that time, but those are the only B's I got in math for my undergrad.
Re: Majoring in Math
Individual math courses, especially "easy" math courses are not the best measure for real mathematical ability. I think a more important question to ask is why do you have trouble? Do you have trouble because you get bored? Do you have trouble because you find things are being done in enough detail? Or do you have trouble because math is hard?
Another question to consider is how you respond to logic puzzles and such? Do they ever worm your way into your skull and keep you up at night until you solve them?
The final question I'm bring up is what sorts of things you expect to do with it. There are math bachelors degree programs meant for people looking at graduate school. There are also programs meant more for people who are likely to get into operations research, computer programming and similar.
Another question to consider is how you respond to logic puzzles and such? Do they ever worm your way into your skull and keep you up at night until you solve them?
The final question I'm bring up is what sorts of things you expect to do with it. There are math bachelors degree programs meant for people looking at graduate school. There are also programs meant more for people who are likely to get into operations research, computer programming and similar.
Re: Majoring in Math
In general it's a good idea to never listen to anything an economist says.
 Marbas
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Re: Majoring in Math
I've actually been faced with the same decision. I don't exhibit the most natural aptitude for the subject but I love it. It's what I dump most of my spare time into in fact. This of course, is why I'm going to major in math anyways, despite said lack of aptitude. Damn my 630 on the SAT.
Also, I'm going to parrot what others have said in this thread, calculus is nothing like real math. In fact, one poster on the forum here said something along the lines of: "I suck ass at calculus but am decent at analysis."
Also, I'm going to parrot what others have said in this thread, calculus is nothing like real math. In fact, one poster on the forum here said something along the lines of: "I suck ass at calculus but am decent at analysis."
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Re: Majoring in Math
There's a big difference depending on exactly what you mean by "grad school". There's a big difference between "A master's in math at a mediocre university" and "PhD at Harvard eventually teaching at Princeton", and there's a ton in between. I think the former is easy enough, and the latter difficult enough, so pretty much everyone can find a place where they are challenged but not overwhelmed. Unfortunately, employment is not really the same, and finding a job in academia can be very competitive.
So I'm throwing in another vote for "do it".
I think it's fair to deduce from the given comments that this guy is an economist because the math PhDs at MIT were way smarter than him.
So I'm throwing in another vote for "do it".
bcoblentz wrote:In general it's a good idea to never listen to anything an economist says.
I think it's fair to deduce from the given comments that this guy is an economist because the math PhDs at MIT were way smarter than him.
Re: Majoring in Math
bcoblentz wrote:In general it's a good idea to never listen to anything an economist says.
Sig'd.
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.

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Re: Majoring in Math
I am in a similar situation, and all I can do is echo the advice given by others above. Work hard, practice, and if you enjoy math and are sufficiently good at it that you're not failing out, then stick with it. When I started Uni I expected math majors to be the brightest people on campus. It worried me because while I had been a top student in HS math classes, I thought I'd have to work my ass off just to keep up in Uni classes. I just finished my first semester and took multivariable calc and discrete mathematics at the same time, struggled through the calc class, passed with a c+, but had no problems with discrete math. So, I would say, don't worry much about calc, all the fun stuff is still to come. =)
Re: Majoring in Math
There has already been plenty of good advice offered here, but I'll throw in my own two cents since I'm over the finish line on a similar journey. I was a freshman at 30  just out of the army  thought I'd be an English teacher. I rediscovered math in college algebra, the lowest level of math course offered. Everyone knows the truism that mathematicians who are going to be great are going to be great when they are quite young. Too late for me. But I loved it, and with each step up the ladder I loved it more.
Turns out being great isn't actually the point. I immersed myself in it, got a Master's at a nowhere school, spent a year at Cambridge doing Part III of the Tripos, took damned near forever finishing my PhD back in the states, now teach at a nowhere school.
But I'm doing what I love, I'm helping students do what they love, and I learn new mathematics all the time. I've been well rewarded.
Bottom line: find out what you love to do, and throw yourself at it. Let others do the worrying.
Turns out being great isn't actually the point. I immersed myself in it, got a Master's at a nowhere school, spent a year at Cambridge doing Part III of the Tripos, took damned near forever finishing my PhD back in the states, now teach at a nowhere school.
But I'm doing what I love, I'm helping students do what they love, and I learn new mathematics all the time. I've been well rewarded.
Bottom line: find out what you love to do, and throw yourself at it. Let others do the worrying.
Re: Majoring in Math
Bsidney wrote:Bottom line: find out what you love to do, and throw yourself at it. Let others do the worrying.
Inspiring!
 BeetlesBane
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Re: Majoring in Math
Don't worry too much about calc. It's in the program when it is because that's what the physics and engineering departments want, not because it's that central to math.
Re: Majoring in Math
Maybe what you can do is pick up a copy of Apostol's Calculus Vol 1 and Vol 2 and try to get through the books. It's a whole lot different than the way calc is taught in college; it's a lot more rigorous and will give you a taste of more advanced mathematics. I'm going through them myself right now. I've had 3 semesters of calc and consider myself somewhat gifted in math, but I'm still having trouble because I'm not used to thinking that way. The exercises at the end of the chapters aren't simply "integrate ____, derive ____", he actually has you do proofs of the theorems.
PS: these textbooks are rather pricy, but you should be able to find them at your college library. If not, there are sublegal ways to find it on the internet.
PS: these textbooks are rather pricy, but you should be able to find them at your college library. If not, there are sublegal ways to find it on the internet.

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Re: Majoring in Math
I wanted to weigh in on this so much that I caved in and created an account here.
I just graduated high school a few weeks ago, and I plan to enter college as a math major this fall. I am not, as one person said, one of those kids who went to PROMYS or qualified for the USAMO. I do happen to live very near MIT, and earlier this year I sat through their sophomore differential equations course. Does that mean anything? Am I destined to be a great/good/average/mediocre mathematician because of it? I really don't think so. The idea of starting young somehow guaranteeing that you'll be better than the rest is absurd. If you want an example, I suggest you read Marcus Du Sautoy's book Symmetry. In it he gives a lot of details on his math career, including how he entered college as a language major, and only later switched to math. He ended up at Cambridge for grad school, working close to John Conway.
I think that if you haven't been convinced already, you should at least take the idea of a math major a little further. I think it was wrong of that professor to dash your hopes like that, because I don't believe in this idea of only the best and brightest being good at math. It's a tragic mindset that I bet will discourage a lot of people, and I hope you do not become one of them.
Like I said earlier, I live near MIT. That's given me a chance to meet and talk to some very good mathematicians, and one in particular was with me the whole way through the college process. He told me something that I don't think I'm ever going to forget: he said that while many people go into math because they're good at it, the most important thing is persistence. The ability to keep banging your head on a problem, to not give up, that is what makes a mathematician.
So, don't give up.
I just graduated high school a few weeks ago, and I plan to enter college as a math major this fall. I am not, as one person said, one of those kids who went to PROMYS or qualified for the USAMO. I do happen to live very near MIT, and earlier this year I sat through their sophomore differential equations course. Does that mean anything? Am I destined to be a great/good/average/mediocre mathematician because of it? I really don't think so. The idea of starting young somehow guaranteeing that you'll be better than the rest is absurd. If you want an example, I suggest you read Marcus Du Sautoy's book Symmetry. In it he gives a lot of details on his math career, including how he entered college as a language major, and only later switched to math. He ended up at Cambridge for grad school, working close to John Conway.
I think that if you haven't been convinced already, you should at least take the idea of a math major a little further. I think it was wrong of that professor to dash your hopes like that, because I don't believe in this idea of only the best and brightest being good at math. It's a tragic mindset that I bet will discourage a lot of people, and I hope you do not become one of them.
Like I said earlier, I live near MIT. That's given me a chance to meet and talk to some very good mathematicians, and one in particular was with me the whole way through the college process. He told me something that I don't think I'm ever going to forget: he said that while many people go into math because they're good at it, the most important thing is persistence. The ability to keep banging your head on a problem, to not give up, that is what makes a mathematician.
So, don't give up.
Re: Majoring in Math
I say hang in there too, if you like math. The world needs mathematicians! I can tell you from my own experience that it's possible to convince yourself you're "not good enough" at just about any level of the game. Back in the Jurassic Period, I graduated Harvard w/ highest honors in math, went on to grad school there, and dropped out in my 5th year, partly because I knew there were always going to be so many people better at it than I was. There were other factors involved as wellthere always arebut the point is, if you want to do it, and you can do it, then do it! (I guess I basically didn't want to do it, 'cause I went off in a totally orthogonal direction...)
Re: Majoring in Math
Input greatly appreciated, again.
I've put Symmetry down as my next math book purchase; it does seem an interesting read. Apostol's calculus volumes also seem to be worth investigating, so thanks for that.
hmm... that's curious, especially since you changed in your 5th year. kudos for making it that far all the same!
I (and surely others) hope that the input keeps coming.
I've put Symmetry down as my next math book purchase; it does seem an interesting read. Apostol's calculus volumes also seem to be worth investigating, so thanks for that.
lgonick wrote:(I guess I basically didn't want to do it, 'cause I went off in a totally orthogonal direction...)
hmm... that's curious, especially since you changed in your 5th year. kudos for making it that far all the same!
I (and surely others) hope that the input keeps coming.
Re: Majoring in Math
I just thought I'd mention that one of my professors, whom is currently well respected in his field, flunked out of collage twice before finally finishing and getting his PhD. So earning a few "B"s is certainly nothing that will necessarily prevent one from doing great things in mathematics.
Re: Majoring in Math
I'm
Is it really that bad? I'm planning on doing roughly the same thing.
TelePunk5 wrote:I'm majoring in Mechanical Engineering and Mathematics (because I hate having a social life)
Is it really that bad? I'm planning on doing roughly the same thing.
Of course the game is rigged. Don't let that stop youif you don't play, you can't win.
R.A.H.
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Re: Majoring in Math
someone who wants to go to a top grad school in math?
That is very different than "majoring in math".
Being able to succeed at grad school/research has a lot to do with being able to discipline yourself.
About the "math majors are bright" claim, IQ tests do tend to support that. And other tests that are correlated with IQ.
Heh. On the other hand, taking math courses is a good way to increase the number that IQ tests produce. As is taking IQ courses, or studying IQ courses, or... many other things that are about working on the kind of mental processes that the IQ test tests.
I was half expecting honest people to say that it isn't the field for those who are just 'ok' in it.
You don't have to go into research for a degree in mathematics to be worth it.
..
In a related anicdote, my brother did an undergraduate degree in Physics, found that his fellow students where too smart, and did graduate work in business. Being in the top fractionof 1% mathematically when doing a degree in astrophysics isn't that unusual, but it really blows away business school economics (which isn't highschool level, it just isn't astrophysics level).
...
Finally, suppose you won the worldwide mathematics olympiad. You won a fullride scholarship to go to school. Etc etc.
You can easily not "pull off" becoming a real academic. Either because you decide another 5 years of tenuretrack torture isn't worth it, or you stop being able to motivate yourself, or you decide something else is a better option.
At every level on the academic ladder, well over half of the people fall off. The odds are extremely against you, no matter what your credentials are.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision  BR
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Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.
Re: Majoring in Math
A lot of good stuff in this thread. Here are my thoughts as a physics undergraduate who's taken a few college level math courses:
As many people have said, don't judge all math by calculus. I took Calc I and II in high school and Calc III freshman year (and got a B in each) and took discrete math last semester. Discrete is completely different from calc, and I ended up with a C, and even that was a miracle. I should point out, however, that I did find discrete interesting, and my grade may have had more to do with the strangeness of the material/my lack of study skills/the professor than it did with the difficulty of the course. My point is, you don't need to make a decision with out getting a sampling of a lot of different courses.
Since math underlies so many fields of study, it wouldn't be a problem to switch majors after a year or two if you really don't feel that math is for you. The important thing is whether you are interested in math and can see yourself doing it for the rest of your life. If you don't feel a connection, maybe consider something else, but if you do enjoy it and have an interest, definitely go for it!
As for going into higher level stuff, I remember one of my physics teachers talking about going into higher level astronomy. You don't need to be a genius to do higher level stuff, but you do need to have a passion for it. Once you've taken some higher level stuff, ask yourself whether you would enjoy doing that as your job for the rest of you life.
Anyway, congrats on doing well on your final, hope everything goes well!
As many people have said, don't judge all math by calculus. I took Calc I and II in high school and Calc III freshman year (and got a B in each) and took discrete math last semester. Discrete is completely different from calc, and I ended up with a C, and even that was a miracle. I should point out, however, that I did find discrete interesting, and my grade may have had more to do with the strangeness of the material/my lack of study skills/the professor than it did with the difficulty of the course. My point is, you don't need to make a decision with out getting a sampling of a lot of different courses.
Since math underlies so many fields of study, it wouldn't be a problem to switch majors after a year or two if you really don't feel that math is for you. The important thing is whether you are interested in math and can see yourself doing it for the rest of your life. If you don't feel a connection, maybe consider something else, but if you do enjoy it and have an interest, definitely go for it!
As for going into higher level stuff, I remember one of my physics teachers talking about going into higher level astronomy. You don't need to be a genius to do higher level stuff, but you do need to have a passion for it. Once you've taken some higher level stuff, ask yourself whether you would enjoy doing that as your job for the rest of you life.
Anyway, congrats on doing well on your final, hope everything goes well!
Re: Majoring in Math
I don't mean to hijack the thread by any means, but since the question's in a similar vein, I figured a new thread wouldn't be appropriate.
Long story short, my initial plans to graduate from an unnamed university fell through, so now after community college for a year, I'm going to need a new university to call home for undergrad studies. Anybody have any suggestions as to where I should go for a good math program?
Disclaimer: I know that the quality of a program isn't necessarily dependent on the name of the school, but the passion and devotion of the professors. Which is exactly why I need input from you great people.
Thanks in advance, and again, sorry if this is a thread jack.
Long story short, my initial plans to graduate from an unnamed university fell through, so now after community college for a year, I'm going to need a new university to call home for undergrad studies. Anybody have any suggestions as to where I should go for a good math program?
Disclaimer: I know that the quality of a program isn't necessarily dependent on the name of the school, but the passion and devotion of the professors. Which is exactly why I need input from you great people.
Thanks in advance, and again, sorry if this is a thread jack.

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Re: Majoring in Math
krenzel wrote:Thank you so much for the encouragement. I was half expecting honest people to say that it isn't the field for those who are just 'ok' in it.
I just took my math final which I did decent on, and will probably end up with an A.
I was really discouraged as I walked home because of how hard it was, but reading the replies in this thread brightened my day.
If I quit because I'm mediocre at math... I'll never not be mediocre at math. And never is a scary word...
I humbly suggest the following: Study what you're passionate about. It doesn't matter whether it's hard or not. In fact, everything is hard at university, and the only mandatory prerequisite is passion. Also, how well does this professor know you? Does he know anything about you other than your test score? Weigh his advice (and mine) accordingly.
Re: Majoring in Math
I say you need to do what your heart is telling you. Don't listen to teachers, it's your life to live. In high school I dropped out of math and absolutely hated it. I started college as a Biology major and had to take Calculus....I loved it. Now I'm a math major graduating with honors. Do what makes you happy.
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Re: Majoring in Math
You don't have to be very, very bright to study maths at undergrad. However, most people in 'the West', including some extremely intelligent people, have been very, very badly educated in maths, making them think it is ludicrously difficult or some kind of torture. It tends to be the bright kids who survive this educational abuse well enough to be ready for higher levels of understanding, but it doesn't have to be like that at all.
This is no different to a school in an Englishspeaking country where French is taught very badly, with the result that pupils walk out thinking, 'no normal human could ever hope to speak this crazy language  English is much simpler', then when they visit France they assume all the young children there must be geniuses to speak French so well. Of course, if they found out that some of these French children struggle to learn English, the Anglophone tourists would be totally baffled, and/or imagine French children's brains are wired differently from birth.
(You have to be fairly smart to do a PhD in maths, but you also have to be fairly smart to do a PhD in anything that isn't complete BS. Being committed to what you're doing is a big advantage, but that applies to a very wide range of jobs and certainly any academic career. So maths doesn't deserve to be singled out on either count.)
This is no different to a school in an Englishspeaking country where French is taught very badly, with the result that pupils walk out thinking, 'no normal human could ever hope to speak this crazy language  English is much simpler', then when they visit France they assume all the young children there must be geniuses to speak French so well. Of course, if they found out that some of these French children struggle to learn English, the Anglophone tourists would be totally baffled, and/or imagine French children's brains are wired differently from birth.
(You have to be fairly smart to do a PhD in maths, but you also have to be fairly smart to do a PhD in anything that isn't complete BS. Being committed to what you're doing is a big advantage, but that applies to a very wide range of jobs and certainly any academic career. So maths doesn't deserve to be singled out on either count.)
Re: Majoring in Math
On a related note, are there really no career opportunities for pure mathematicians other than teaching? I mean, I guess you can be a research professor, but no one would hire you for that unless you were extremely qualified (and even then, wouldn't most universities force you to teach?).
I mean, I enjoy tutoring math, but I hate the rigid system that you're forced into when it comes to teaching an actual class. I want to study what I enjoy, but I don't want to then spend the rest of my life doing something I'd rather not be doing.
I mean, I enjoy tutoring math, but I hate the rigid system that you're forced into when it comes to teaching an actual class. I want to study what I enjoy, but I don't want to then spend the rest of my life doing something I'd rather not be doing.
Re: Majoring in Math
greenblob wrote:On a related note, are there really no career opportunities for pure mathematicians other than teaching? I mean, I guess you can be a research professor, but no one would hire you for that unless you were extremely qualified (and even then, wouldn't most universities force you to teach?).
I mean, I enjoy tutoring math, but I hate the rigid system that you're forced into when it comes to teaching an actual class. I want to study what I enjoy, but I don't want to then spend the rest of my life doing something I'd rather not be doing.
I just got a job as a Research Analyst, and I'm finishing up a Master's in pure math. My job has almost nothing to do with pure math, but I can think critically, so they pay me well.
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