Question about Math grad school?

[emlekarc]

I really enjoy math and worked hard to get my grades up. I'm a soon to be sophomore right now and I had issues with Calc 1 and got a 2.4 in it. I had a hard time adjusting to college, had to repeat it. Obviously I'm not happy with how I did and am dissapointed in myself. Is Grad School for Math an option or do I have no chance? My overall GPA isn't bad (3.5) and I am working on a double major in Mechanical Engineering and Math.

Also, do grad schools look at how you did in later math courses more heavily than how you did in earlier courses? For example, if I got Bs in the proof based courses, would that look better than the C in Calc and other earlier courses?

 

[homeomorphic]

Is it still an option? Yes, if you improve. But you have to think A's in proof-based courses, not B's.

Do I recommend it? No. I'm not sure I recommend it to anyone, really, particularly someone who has a more marketable second major. Grad school in math = insanity. Do it, if that's what you really want, but don't say I didn't warn you.

 

[MathematicalPhysicist]

Is it still an option? Yes, if you improve. But you have to think A's in proof-based courses, not B's.

Do I recommend it? No. I'm not sure I recommend it to anyone, really, particularly someone who has a more marketable second major. Grad school in math = insanity. Do it, if that's what you really want, but don't say I didn't warn you.

Why to deter the person, maybe he's insane enough to do it and enjoy it... :-D

 

[micromass]

I really enjoy math and worked hard to get my grades up. I'm a soon to be sophomore right now and I had issues with Calc 1 and got a 2.4 in it. I had a hard time adjusting to college, had to repeat it. Obviously I'm not happy with how I did and am dissapointed in myself. Is Grad School for Math an option or do I have no chance? My overall GPA isn't bad (3.5) and I am working on a double major in Mechanical Engineering and Math.

Also, do grad schools look at how you did in later math courses more heavily than how you did in earlier courses? For example, if I got Bs in the proof based courses, would that look better than the C in Calc and other earlier courses?

Surely, if you got a C in calculus, and then get straight A's in stuff like differential topology or advanced functional analysis, then people are not going to care much about your initial C. Grad schools want to see improvements, so screwing up in the beginning is certainly not a complete disaster.

You do need to get a lot of A's in the proof based courses, getting a lot of B's is risky.

Also, you need to ask yourself why you did so bad in calculus? Sure, maybe you weren't ready for college yet. But there might be other reasons. For example, it might be that your study habits are not optimal. Be sure to think this through.

And finally, try to get into research as soon as possible. It might be a bit too soon now, but after sophomore year you should go to some professors and ask whether they got something for you. This will show you whether you will like math grad school (or what aspects you dislike about research) and it will also boost your application.

 

[homeomorphic]

Why to deter the person, maybe he's insane enough to do it and enjoy it... :-D

Few people want to do it, but there are even fewer positions waiting at the end. I think things will improve if less people are interested in grad school in most fields. The market is unbalanced. High demand, low supply. And people are putting a higher utility on grad school than it's worth. I don't think all the competition is really healthy, and I'm not convinced that it's really worth putting that much effort in if you just end up doing something else. I think even if there were half as much competition, it would be plenty. I don't think the best motivation is competition, anyway--I think it's curiosity. Doesn't mean no one should do it, but I think you have to be a really, really extreme case for it to be worth it, so it's worth asking yourself if you are. I thought I was, but I wasn't, and that's an easy mistake to make, even if you've been warned about it.

 

[MathematicalPhysicist]

Few people want to do it, but there are even fewer positions waiting at the end. I think things will improve if less people are interested in grad school in most fields. The market is unbalanced. High demand, low supply. And people are putting a higher utility on grad school than it's worth. I don't think all the competition is really healthy, and I'm not convinced that it's really worth putting that much effort in if you just end up doing something else. I think even if there were half as much competition, it would be plenty. I don't think the best motivation is competition, anyway--I think it's curiosity. Doesn't mean no one should do it, but I think you have to be a really, really extreme case for it to be worth it, so it's worth asking yourself if you are. I thought I was, but I wasn't, and that's an easy mistake to make, even if you've been warned about it.

But in any field there's a fierce competition.

The only thing that I don't like in this field of academia is the publish or perish, I mean you can't really publish something of good quality if you are pushed to do it every year; I mean what are the chances that you'll publish something novel if you publish every year or so?

But I wonder if there are jobs which allow you to keep learning by yourself, and I can't see such jobs outside of academia; all jobs are centred around making more money for the company and studying for the sake of studying doesn't always make an immediate monetary impact.

 

[homeomorphic]

But in any field there's a fierce competition.

That's not really true in all fields. My father is a professor of electrical engineering at a run of the mill university and reports that all of their graduates got jobs last year, even the lousiest students. Well, of course, a lot of those people eventually don't make it as engineers and lose their jobs, but at least they got jobs, initially.

The only thing that I don't like in this field of academia is the publish or perish, I mean you can't really publish something of good quality if you are pushed to do it every year; I mean what are the chances that you'll publish something novel if you publish every year or so?

I totally agree. That's one reason why I didn't even want to stay, even if I could find a place there. Also, as a newcomer, even with a PhD, I felt I was very far from the true frontiers of knowledge where I could really understand what was going on in research (and I think that's pretty much normal), yet the expectation is that I am supposed to start cranking stuff out, anyway. People come in with all the aforementioned straight A's in proof-based classes and think they are hot stuff, but grad school will still give most of them a run for their money.

But I wonder if there are jobs which allow you to keep learning by yourself, and I can't see such jobs outside of academia; all jobs are centred around making more money for the company and studying for the sake of studying doesn't always make an immediate monetary impact.

Academia isn't that different. My father is always complaining about how they have pressure to bring in grant money and stuff and hire people based on how much money they can get. Of course, in math, that's not such a big issue, but still, with the pressure to publish, any freedom in what to study comes at a cost. The thing is, if you are going to do something as hard as math, you don't want people making it even harder by pestering you for publications and giving you massive teaching loads and that sort of thing.

I'd rather be a programmer or something, and have work that is manageable and well-defined, if I am going to be under so much pressure. I definitely didn't feel like I would be free to study what I wanted to any meaningful extent in academia. That's one of the big reasons why I failed in grad school. I took too much time to study what I wanted, at the expense of my research productivity.

Math isn't so bad if you have a strong interest in teaching, as well--otherwise, you basically have to be a superstar.

Being free of both teaching and pressure to publish, I think I might find more time to study the things I really care about in an industry job, in my spare time. I am sure I will be working hard and it will be difficult, but I think it will actually still be easier than as a professor.

Another reason I don't recommend math grad school, though, is that the research-level stuff is incredibly esoteric and a bit removed from reality, in many cases. It's endless and unrelenting and doesn't ever really seem to be going anywhere, to me. I thought I was the biggest math nerd ever, but it was just too much, even for me. I mean, if you have seen 10,000 beautiful proofs already, how much does the 10, 001st really add to that? That's why I say, you have to be a bit of an extreme case in order to enjoy it, in my opinion.

 

[MathematicalPhysicist]

That's not really true in all fields. My father is a professor of electrical engineering at a run of the mill university and reports that all of their graduates got jobs last year, even the lousiest students. Well, of course, a lot of those people eventually don't make it as engineers and lose their jobs, but at least they got jobs, initially.




I totally agree. That's one reason why I didn't even want to stay, even if I could find a place there. Also, as a newcomer, even with a PhD, I felt I was very far from the true frontiers of knowledge where I could really understand what was going on in research (and I think that's pretty much normal), yet the expectation is that I am supposed to start cranking stuff out, anyway. People come in with all the aforementioned straight A's in proof-based classes and think they are hot stuff, but grad school will still give most of them a run for their money.




Academia isn't that different. My father is always complaining about how they have pressure to bring in grant money and stuff and hire people based on how much money they can get. Of course, in math, that's not such a big issue, but still, with the pressure to publish, any freedom in what to study comes at a cost. The thing is, if you are going to do something as hard as math, you don't want people making it even harder by pestering you for publications and giving you massive teaching loads and that sort of thing.

I'd rather be a programmer or something, and have work that is manageable and well-defined, if I am going to be under so much pressure. I definitely didn't feel like I would be free to study what I wanted to any meaningful extent in academia. That's one of the big reasons why I failed in grad school. I took too much time to study what I wanted, at the expense of my research productivity.

Math isn't so bad if you have a strong interest in teaching, as well--otherwise, you basically have to be a superstar.

Being free of both teaching and pressure to publish, I think I might find more time to study the things I really care about in an industry job, in my spare time. I am sure I will be working hard and it will be difficult, but I think it will actually still be easier than as a professor.

Another reason I don't recommend math grad school, though, is that the research-level stuff is incredibly esoteric and a bit removed from reality, in many cases. It's endless and unrelenting and doesn't ever really seem to be going anywhere, to me. I thought I was the biggest math nerd ever, but it was just too much, even for me. I mean, if you have seen 10,000 beautiful proofs already, how much does the 10, 001st really add to that? That's why I say, you have to be a bit of an extreme case in order to enjoy it, in my opinion.

Well as for your last paragraph, you can say the same thing on every job. I mean for a veteran basketball player another dunk is just another day doing his job.
When you become a professional in something, you do it as second nature, and you don't get thrilled by it anymore.

I understand that engineers have better options than math graduates, but they still have to put the hours.

For me, mathematics looks trivial (I mean when you understand the definitions and know basic logic, it does seem as trivial as there is), but reading research articles is quite tricky, because you need to have some faith in the work of others (because this is how research is based, not all research is being scrutinize by others), and this where I have a problem; But I guess this makes my work always unaccomplished, cause I don't have time to read everything and scrutinize the work of every mathematician to the full.

Mind you, some people's work are too trivial to even consider reviewing.

 

[homeomorphic]

Well as for your last paragraph, you can say the same thing on every job. I mean for a veteran basketball player another dunk is just another day doing his job.
When you become a professional in something, you do it as second nature, and you don't get thrilled by it anymore.

I suppose that's a good point, but if it's so esoteric and removed from reality, that's where I need to have external motivation to keep me going once it stops being thrilling. Like building better bridges or saving lives. What's there to keep you waking up in the morning for it? The hypothetical possibility of someone using my work 400 years from now? Personally, I'll take building better bridges or saving lives. Or even making fun games for people to waste their time on, but at least have some fun while doing it.

For me, mathematics looks trivial (I mean when you understand the definitions and know basic logic, it does seem as trivial as there is), but reading research articles is quite tricky, because you need to have some faith in the work of others (because this is how research is based, not all research is being scrutinize by others), and this where I have a problem; But I guess this makes my work always unaccomplished, cause I don't have time to read everything and scrutinize the work of every mathematician to the full.

That's where I got stuck, too. When I realized that I wouldn't have time to understand the work I was building on, I completely lost interest. The only pleasure I get out of it is from understanding it for myself. Taking other people's theorems on faith gives me no pleasure. I don't see it as genuine knowledge. Sometimes, you can understand something intuitively, though, and rely on someone else's proof to take care of the details. I don't mind that so much, if I have some sort of intuition for it. I did that with Sard's theorem in grad school (after attempting to read the proof and not getting much insight from it), but I didn't mind that so much because the consequences of Sard's theorem in differential topology are really pretty intuitive.

Math is very non-trivial. To prove your own theorems, you better have more than just definitions and logic. You have to have some intuition and be able to relate it to the definitions and logic. Even when reading an undergraduate proof, you need more than logic and definitions to have a deep understanding.

I was one of those people with straight A's in all my proof-based classes, by the way (except one B in class that I took in the summer, coming straight out of high school), and yet, I think of myself as astonishingly bad when it comes to research. That ought to tell you something. I don't know, maybe it's topology. Doing basic proofs is trivial for me, too--that doesn't mean I understand Heegard-Floer homology or any of these brutal and endlessly complicated modern theories.

 

[MathematicalPhysicist]

I suppose that's a good point, but if it's so esoteric and removed from reality, that's where I need to have external motivation to keep me going once it stops being thrilling. Like building better bridges or saving lives. What's there to keep you waking up in the morning for it? The hypothetical possibility of someone using my work 400 years from now? Personally, I'll take building better bridges or saving lives. Or even making fun games for people to waste their time on, but at least have some fun while doing it.






That's where I got stuck, too. When I realized that I wouldn't have time to understand the work I was building on, I completely lost interest. The only pleasure I get out of it is from understanding it for myself. Taking other people's theorems on faith gives me no pleasure. I don't see it as genuine knowledge. Sometimes, you can understand something intuitively, though, and rely on someone else's proof to take care of the details. I don't mind that so much, if I have some sort of intuition for it. I did that with Sard's theorem in grad school (after attempting to read the proof and not getting much insight from it), but I didn't mind that so much because the consequences of Sard's theorem in differential topology are really pretty intuitive.

Math is very non-trivial. To prove your own theorems, you better have more than just definitions and logic. You have to have some intuition and be able to relate it to the definitions and logic. Even when reading an undergraduate proof, you need more than logic and definitions to have a deep understanding.

I was one of those people with straight A's in all my proof-based classes, by the way (except one B in class that I took in the summer, coming straight out of high school), and yet, I think of myself as astonishingly bad when it comes to research. That ought to tell you something. I don't know, maybe it's topology. Doing basic proofs is trivial for me, too--that doesn't mean I understand Heegard-Floer homology or any of these brutal and endlessly complicated modern theories.

Well, my philosophy is if your proof can be translated to machine language, and the machine doesn't find flaws in your arguments then you have a kosher proof. The problem is that most research isn't that much formal, so I assume that modern mathematics there maybe a lot of flaws, but nowadays it's hard to find these flaws, cause most researchers don't have time to be focused on research full time.

For example, look at Perleman, he left the USA back to Russia to concentrate on one problem without being concerned with teaching and other academic duties.

BTW, the proof of Heegard-Floer homology may be flawed or not rigorously proven.
Here's an example of a lemma which proof was flawed:
http://en.wikipedia.org/wiki/Dehn's_lemma

Maybe also the proof of Whitehead is flawed (until we can let a machine to decide, we need to rely on humans, and we know that we aren't flawless... :-)).

Also, there's the question what value do we have of a mathematical proof.

For example, suppose in the future someone will find optimal strategies in chess, and they will find as I guess that if we have two perfect opponents the game will always finish in a draw. It won't be that much interesting, it's just counting combinations.

P.S
Intuition for mathematics is gained by exercising, and as we all know exercising becomes dull quite fast.
I think everyone needs to find other stuff to do besides doing mathematics, even if it's your profession.

 

[IGU]

When you become a professional in something, you do it as second nature, and you don't get thrilled by it anymore.

This is just so, so wrong. If you're really good you're always pushing the envelope: solving unsolved problems; building things that couldn't be built before; finding new patterns. In all these endeavors you become better, not only as a practitioner of your art but as a person.

Real professionals realize just how much they could get better and strive to do so. If you are just going through the motions and there's no thrill, then it's time to find something new to do.

 

[homeomorphic]

This is just so, so wrong.

I would say it's partly wrong, but I think there's some magic that happens in math and physics when you first learn it that doesn't really happen again. It's not that you don't continue to enjoy it, but for example, in physics, it seems to me there are only so many of the big surprises that are so impressive at the beginning, like time-dilation and length contraction, the double slit-experiment, and a few more. Once you are a physicist, maybe there are a few weird possibilities that some string theorists are contemplating, but I think you don't get that many truly earth-shattering surprises. I think math can be a little like that, too. It may be still enjoyable, but it's not this whole new world that you've never seen before that it was at the beginning. I still like doing math--I just don't like the research that's being done, and that, along with teaching, is why I quit, not because I don't like math as an activity anymore, as long as I get to play by my own rules.

 

[MathematicalPhysicist]

This is just so, so wrong. If you're really good you're always pushing the envelope: solving unsolved problems; building things that couldn't be built before; finding new patterns. In all these endeavors you become better, not only as a practitioner of your art but as a person.

Real professionals realize just how much they could get better and strive to do so. If you are just going through the motions and there's no thrill, then it's time to find something new to do.

I believe you have a romantic view on academic worklife, or any work for that matter.

Don't worry it will come to you as well, sooner or later.