Advice on Majoring in Math: A 2nd Year Philosophy Major's Journey

[Plaristotle]

First time posting here. However, this question has been on my mind for a while.

I'm currently a second year philosophy major, but a few months ago (after doing some research and some self-studying) I realized that I would rather be studying math. I'm currently taking Calculus II and Linear Algebra I, and while I understand all of the material, I can't seem to do some of the advanced problems in some of my assignments. I enjoy the material, but sometimes I feel as if, if I can't do every problem (or at least most of them), I shouldn't major in math.

Has anyone else experienced this sort of thing? I guess I'm asking for some advice from anyone else who's been in a similar situation.

Edit: Accidentally pressed "enter" before I finished typing my post... Whoops!

 

[micromass]

You're not giving us much information here...

Why would you want to switch to math??
What did you learn during self-study?? What did you study??
Why would you like math better than philosophy??
Are you good in math??
Why are you hesitating to switch?? (I assume you're hesitating because you're posting a question here)

 

[micromass]

I can't seem to do some of the advanced problems in some of my assignments.

Could you give us an example of something you can't solve??
How long did you think about the problem??

I enjoy the material, but sometimes I feel as if, if I can't do every problem (or at least most of them), I shouldn't major in math.

That's normal, but you'll get over it pretty soon. Math has MANY problems that are difficult. Calculus is supposed to be the easiest math out there, but there are some calculus problems that I can't solve.
Mathematics means a lot of hours thinking about the solution, becoming frustrated and finally finding it (this can take weeks!). If you like thinking about math, then you're all right though...

 

[Plaristotle]

You're not giving us much information here...

Why would you want to switch to math??
What did you learn during self-study?? What did you study??
Why would you like math better than philosophy??
Are you good in math??
Why are you hesitating to switch?? (I assume you're hesitating because you're posting a question here)

Sorry about that. Posted it prematurely. I guess I'll finish the rest of my explanation in this post.

I want to switch because I find it a lot more fascinating than any other subject I've considered studying. I've really always been interested in math but I never considered majoring in it until recently. I didn't do very much self-studying but I did do a lot of reading about various concepts in upper level math. It's hard to explain, really, but I think I would excel a lot more studying math than anything else.

It's hard to define "good," but by my standards, I'd say I am good at it. I did well in Calculus I last year without really putting in much effort. But recently I've been struggling a bit with problems that I know I should get, although some things just aren't clicking with me, I guess. For example, one question on a linear algebra assignment asks to determine what values in a given matrix allow the matrix to be invertible. Not really a difficult problem, but I just can't seem to get it without spending a lot of time thinking about it. I understand all of the concepts in both courses and I do (most of) the practice problems, so I don't know why I'm having as much trouble as I am. I'm really kind of just rambling right now but I guess the reason I posted this thread was to get some perspective from anyone who's been in a similar situation.

 

[Plaristotle]

Could you give us an example of something you can't solve??
How long did you think about the problem??



That's normal, but you'll get over it pretty soon. Math has MANY problems that are difficult. Calculus is supposed to be the easiest math out there, but there are some calculus problems that I can't solve.
Mathematics means a lot of hours thinking about the solution, becoming frustrated and finally finding it (this can take weeks!). If you like thinking about math, then you're all right though...

I do enjoy thinking about it, but sometimes I feel as if I think too much about trivial problems that shouldn't be giving me trouble. It's hard to describe, really. :\ Maybe I'm just afraid that I'm not intelligent enough or something like that.

 

[micromass]

I do enjoy thinking about it, but sometimes I feel as if I think too much about trivial problems that shouldn't be giving me trouble. It's hard to describe, really. :\ Maybe I'm just afraid that I'm not intelligent enough or something like that.

You don't need to be very intelligent to be able to do math. You only need to enjoy it. I guess that right now you're missing a bit of mathematical maturity, which is normal and ok.

And it's ok to think a lot about trivial problems. If I read a math book, then they often say "It follows trivially that...". Then I need to think an hour why this is trivial. Once I found it I think I'm stupid because it really was trivial. (everything is trivial once you know it). But the hour thinking wasn't wasted though: you made yourself more familiar with the material.

Studying math is very unlike non-science courses. Non-science courses must be read a few times and memorized (ok, I'm oversimplifying). But math courses: you need to FIGHT math courses. It's a battle every step of the way. And the battle is far from easy. You can sometimes spend an hour trying to understand one page; this really happens.

I guess I'm saying this to tell you that everybody has troubles with math. But if you persist, then you can conquer the troubles.

If you enjoy learning about math, if you enjoy thinking about abstract problems: then math IS something for you.

 

[Plaristotle]

You don't need to be very intelligent to be able to do math. You only need to enjoy it. I guess that right now you're missing a bit of mathematical maturity, which is normal and ok.

And it's ok to think a lot about trivial problems. If I read a math book, then they often say "It follows trivially that...". Then I need to think an hour why this is trivial. Once I found it I think I'm stupid because it really was trivial. (everything is trivial once you know it). But the hour thinking wasn't wasted though: you made yourself more familiar with the material.

Studying math is very unlike non-science courses. Non-science courses must be read a few times and memorized (ok, I'm oversimplifying). But math courses: you need to FIGHT math courses. It's a battle every step of the way. And the battle is far from easy. You can sometimes spend an hour trying to understand one page; this really happens.

I guess I'm saying this to tell you that everybody has troubles with math. But if you persist, then you can conquer the troubles.

If you enjoy learning about math, if you enjoy thinking about abstract problems: then math IS something for you.

Well, that's reassuring. Thanks for the advice! I'd say I definitely am lacking a lot of mathematical maturity, especially considering that this is the first time I've taken two math courses in one term (which is something I'm definitely not used to at this point). I guess it'll all get better with time and more practice.

Once again, thank you for the advice, and I apologize for the little technical difficulty I had there in my first post (still getting used to these forums, heh).

 

[yenchin]

But math courses: you need to FIGHT math courses. It's a battle every step of the way. And the battle is far from easy. You can sometimes spend an hour trying to understand one page; this really happens.

I guess I'm saying this to tell you that everybody has troubles with math. But if you persist, then you can conquer the troubles.

Indeed. Be a warrior.

 

[chiro]

Indeed. Be a warrior.

My money is on the dragon.

 

[homeomorphic]

Job-wise, I would hate to be a philosophy major. There's a little more hope for math majors.

But what's your plan?

Being a mathematician is not for everyone. You can probably find an okay job with a BS in math. But if you want to go to grad school, it's good to be afraid. Be very afraid. It's not something to be undertaken lightly. I have heard 90% of people who get a PhD in math never do any more original work after their thesis. And maybe around 50% who come to grad school either don't make the cut or decide it's not for them. Most of these people were star students in undergrad.

I would say it's definitely worth pursuing your interest. Math goes very well with a lot of other things. But to make a career out of it--I wouldn't recommend it to most people, unless they are really crazy about it.

 

[deluks917]

I remember it once took me 4 days of hard work to understand a 13 line proof. At around 10 hours a day this came out to 3 hours a line.

 

[Plaristotle]

Job-wise, I would hate to be a philosophy major. There's a little more hope for math majors.

But what's your plan?

Being a mathematician is not for everyone. You can probably find an okay job with a BS in math. But if you want to go to grad school, it's good to be afraid. Be very afraid. It's not something to be undertaken lightly. I have heard 90% of people who get a PhD in math never do any more original work after their thesis. And maybe around 50% who come to grad school either don't make the cut or decide it's not for them. Most of these people were star students in undergrad.

I would say it's definitely worth pursuing your interest. Math goes very well with a lot of other things. But to make a career out of it--I wouldn't recommend it to most people, unless they are really crazy about it.

Ah, to be honest I'm not exactly sure what my plan is. I would definitely like to do more schooling after undergrad; professional school (medicine and pharmacy in particular) has always been my main option. I've taken most of the required courses for both of those so they're always an option, assuming I have the grades by the time I graduate.

I've thought about graduate school a lot and I've looked up requirements and such for various schools, but I really have no idea what to expect from that, especially for a subject like math. The highest level of math I've tried tackling is probably some basic undergraduate-level topology, and that was only a short while ago. I'm finding a few gaps in my knowledge, obviously, but I do find it quite interesting so far. Logic also fascinates me, which I guess kind of ties into being a philosophy major. Mathematical logic seems a lot more interesting though, based on the limited knowledge I have of it. Besides all of that I don't really have much of an idea of third- and fourth-year math beyond having a general idea of what courses I would take. So I have no idea what to expect from graduate school right now (which I guess is normal at this point).

But yeah, in terms of finding a job right out of undergrad, I'd feel a lot more safe with a degree in math than one in philosophy. Which is an advantage to switching, I suppose.

 

[20Tauri]

I'm in sort of a similar situation. I am a creative writing major, but along the way I decided that I really wanted to be doing math. I've been working toward it for a while, but I'm still a bit behind. It does get better as you go on. I remember being confused in Linear Algebra--I did all right, but the proofs were sort of baffling to me, and I needed a lot of help. Proofs get much less scary once you get used to them. It just takes time, practice, and a bit of bull-headedness. Well, and it helps if you have a friend or a professor who will put up with lots of questions while you get the hang of things.

One of my friends is a math and philosophy double major. Is that an option for you? If you're really into logic, you might be interested in someday pursuing the PhD field of mathematical logic, and I can't imagine having a combined math/philosophy background wouldn't be useful for that.

 

[homeomorphic]

Ah, to be honest I'm not exactly sure what my plan is. I would definitely like to do more schooling after undergrad; professional school (medicine and pharmacy in particular) has always been my main option. I've taken most of the required courses for both of those so they're always an option, assuming I have the grades by the time I graduate.

From what I know about medical school, I think if that's your plan, math could be a good option. One of my classmates left math grad school to go to medical school a while back.

I've thought about graduate school a lot and I've looked up requirements and such for various schools, but I really have no idea what to expect from that, especially for a subject like math. The highest level of math I've tried tackling is probably some basic undergraduate-level topology, and that was only a short while ago. I'm finding a few gaps in my knowledge, obviously, but I do find it quite interesting so far. Logic also fascinates me, which I guess kind of ties into being a philosophy major. Mathematical logic seems a lot more interesting though, based on the limited knowledge I have of it. Besides all of that I don't really have much of an idea of third- and fourth-year math beyond having a general idea of what courses I would take. So I have no idea what to expect from graduate school right now (which I guess is normal at this point).

I would say just keep taking more math and see what happens, as long as you are not worried about taking longer to finish the degree. I know a guy who wanted to do logic, but switched to topology after realizing that doing logic research wasn't really like the impression that you get of it from taking a couple introductory classes. One of the dilemmas of becoming a mathematician (or anything, really) is that it can sometimes be hard to get an idea of what it's like to actually work in the field until you are actually doing it. One thing a little bit unexpected for me is the importance of writing in math. One facet of it is being a technical writer, essentially. I knew mathematicians had to write, but I thought it would be more like just an expression that would follow trivially from coming up with enough math ideas. At least for me, I find it to be a substantial barrier to getting work done. Lots of editing and agonizing over just the right way to organize it and the right way to say things. Writing a 1-2 page proof doesn't really give you a feel for more large scale projects.

 

[Plaristotle]

One of my friends is a math and philosophy double major. Is that an option for you? If you're really into logic, you might be interested in someday pursuing the PhD field of mathematical logic, and I can't imagine having a combined math/philosophy background wouldn't be useful for that.

Hmm, I've actually considered just doing a double major in philosophy and math but at my school the degree in philosophy and math is a B.A. and is slightly more focused on philosophy. But I'm going to take a few more courses in philosophy in order to get a minor in it. I might even have enough courses to be eligible for a B.A. in philosophy as well as an honours B.Sc. in math by the time I graduate, so I might end up with two degrees in the end (assuming my school let's me do that). It's definitely an interesting combination.

From what I know about medical school, I think if that's your plan, math could be a good option. One of my classmates left math grad school to go to medical school a while back.

I would say just keep taking more math and see what happens, as long as you are not worried about taking longer to finish the degree. I know a guy who wanted to do logic, but switched to topology after realizing that doing logic research wasn't really like the impression that you get of it from taking a couple introductory classes. One of the dilemmas of becoming a mathematician (or anything, really) is that it can sometimes be hard to get an idea of what it's like to actually work in the field until you are actually doing it. One thing a little bit unexpected for me is the importance of writing in math. One facet of it is being a technical writer, essentially. I knew mathematicians had to write, but I thought it would be more like just an expression that would follow trivially from coming up with enough math ideas. At least for me, I find it to be a substantial barrier to getting work done. Lots of editing and agonizing over just the right way to organize it and the right way to say things. Writing a 1-2 page proof doesn't really give you a feel for more large scale projects.

Interesting... I'm definitely going to take a lot more math and see where I stand after a few years in terms of what my mathematical interests are. By then I should know whether or not graduate school is a reasonable option for me (I'm assuming I'll have a clearer idea of that once I take real analysis and topology and all that stuff).

Thanks for the advice, everyone!