Self-Studying Math: Is an Equivalent to a BS Possible?

[TheKracken]

I am currently self studying Calculus I and was curious if it was possible to just self study most or all mathematics on my own without going to college. I would like to learn the equivalent of a BS in pure mathematics, so topics such as topology and such. So is this possible? Practical? And if I decide to do this how should you go about this?

 

[Poopsilon]

Yes it is most definitely possible to learn the equivalent of a BS in pure math on your own, but you'll need discipline. Although if you are interested enough in the material to do such a thing, I can't imagine why you wouldn't want to study it at a university. The only problem I see is that because math becomes so abstract and nuanced at higher levels, being able to hash out the details with a professor or with other students is really helpful, you can do this through the internet to some extent, but not as effectively or as efficiently.

I imagine the situation is similar with physics, but I don't know much about physics.

 

[jtbell]

I am currently self studying Calculus I and was curious if it was possible to just self study most or all mathematics on my own without going to college.

Why? Are you trying to bypass a bachelor's degree and go straight to grad school?

 

[kramer733]

Why? Are you trying to bypass a bachelor's degree and go straight to grad school?

Maybe he wants to not pay university.

 

[deRham]

The biggest problem is that university combines your interest in learning with people who are, like you, interested in studying the subject and possibly making a career of it. Yes, it is possible to do what you are saying in some sense, but ... "mathematics" and "physics" are not fields you can learn all of.

Going to a university can expose you to what the minds of today are interested in working on. It can give you focus and direction. It can give you a record and certification which helps you make a career.

Yes you can self study the BS curriculum, but you have to actively seek out whether you are attaining the necessary level.

 

[deluks917]

I'm sure you could. However there is a limit to how far into the field you will be able to go. If you are not in college you will need a full time job and have little encouragement. I think maybe self-study for 2-3 years part time and see how it goes.

 

[TheKracken]

I don't want to skip college (i'm only 17) but as I will most likely be going to a community college for 2 years I believe I would be able to go much farther in the ciriculum then the class's that are offered there (goes up to a into to DE and LA)

 

[TMFKAN64]

I would like to learn the equivalent of a BS in pure mathematics, so topics such as topology and such. So is this possible?

Yes.

Practical?

No.

OK, a little elaboration... if you are studying to get a little ahead of next semester's classes, or just want to learn more for sheer love of the subject... go ahead, knock yourself out. There is a *lot* you can learn on your own.

But as for practicality... at some point, you'll need to demonstrate that you know what you've studied to someone else, and most of the time people aren't really interested in quizzing you in depth. They'd rather just look at your transcript and know that you've studied certain subjects and passed exams in them. So I don't think studying beyond the short-term on your own is really very practical.

Of course if you are a genius, this doesn't apply to you. But if you are merely very, very smart...

 

[mal4mac]

Take a BS!

Is it the cost of University that's bothering you? Can't you take out a loan? With a BS in mathematics you'll be earning enough to pay off a loan. If you can't get a loan, why not work a few years and save up... in the mean time you can just keep polishing your math in your free time ... doing a full BS amount of work would be a bit much... no need to do that, just read slowly through some textbooks, popular works, biographies... whatever keeps the dream alive without exhausting you.

 

[deRham]

I will most likely be going to a community college for 2 years I believe I would be able to go much farther in the ciriculum then the class's that are offered there (goes up to a into to DE and LA)

Yes you can try self-studying, but as someone said, eventually you need to show you know the material to someone. One way to proceed is to go ahead and self-study, and then take a lot more classes at once, after you get to a 4 year university. If you already know abstract algebra and real analysis, then maybe you can handle taking 6+ math classes at once, while you are getting up to speed. There is also a chance that some undergraduate schools will let you take a placement test to pass out of certain classes.

 

[metiman]

My advice: don't go to community college. Although it's still better than learning on your own. You're only 17. Are you in the US? If so, my advice is to study elsewhere where the cost of education is not so high and where you don't have to waste time studying all kinds of liberal arts courses to get a bachelors degree. Perhaps India. In some countries you can even get a BS in 3 years. At your age going to university is great! I'm in my early 40s and I wish I could go back. It's just such a great learning environment. With peers who are also learning. Studying on your own is no substitute.

I am in the unfortunate situation where I have the money to go to either a foreign university or a US state university, but I have a disability that doesn't allow me to attend day classes. I think that means I am basically on my own. But it sounds like you have a choice. Make the best one. That would be university. Real university. And for as many years as you can afford. Hopefully more than just 4.

 

[TheKracken]

Are you sudgesting that I go to another country (than the U.S) to study mathematics? Also I only speak english...

 

[metiman]

Well, yes. If money is the issue. As far as language, classes are taught in English in India. There are some ridiculously cheap (practically free) universities in South America if you could learn Spanish first. If money is not the issue I would suggest going to a state or private university. I do think it is possible to learn mathematics on your own, but it would be a lot more difficult to do and difficult to really know when you have learned everything that you wanted to learn. OTOH, all those liberal arts courses are a PITA. I believe the US has the highest percentage of liberal arts courses necessary to complete a science degree. I suppose you could just save all the liberal arts courses for last and maybe not even take them. But without the degree it would be difficult to get a job. What do you do with a math degree anyway? Teach?

 

[TheKracken]

The issue isint really the money (though that definatly will be a factor) Its the fact I'm not sure If I will be able to get into any universitys, wether they are state or privet...you see, I did really bad these last years in high school and I doubt that any state university will take me even though I failed class's. I am extreemly good at math and physics and I hope to have double major in mathematics and physics, and from the choose which I would like to continue on with graduate work. But I am just not sure If any university will accept me...

 

[Highway]

The issue isint really the money (though that definatly will be a factor) Its the fact I'm not sure If I will be able to get into any universitys, wether they are state or privet...you see, I did really bad these last years in high school and I doubt that any state university will take me even though I failed class's. I am extreemly good at math and physics and I hope to have double major in mathematics and physics, and from the choose which I would like to continue on with graduate work. But I am just not sure If any university will accept me...

go to community college, do well. transfer to stateu, do well. etc.

 

[metiman]

Ah. So it's just a grades issue. A foreign university won't help with that. It's really not the end of the world. Especially if you only did badly in your non math and science courses. Most math and science nerds will be sympathetic with your plight. If you do well enough on your SATs you might be surprised at some relatively 'normal' universities that will accept you right out of high school. This isn't Japan or India. You won't get into Harvard/MIT/Caltech/Princeton/Berkeley of course, but after a year with a 3.9 GPA taking just math and science courses you could transfer to a more selective university if that's what you want. And for graduate school you could apply to Princeton or Caltech or whatever your favorite school might be. Assuming that you are made of money of course.

Personally I would aim for Berkeley for graduate school. $50k to $60k per year for Caltech, MIT etc is just absurdly expensive. Unless you are super rich. With that in mind I would consider applying to some state school in the UC system. The problem is you really want to have residency and that takes at least a year I think. So the first year you'd have to pay the out of state tuition, which is still dirt cheap compared to private schools.

 

[TheKracken]

If you mean the UC system as in california then Iv'e got that covered as I live in california, What I may have to do is go to a CSU for a year or 2 and transfer into one of the top UC..But even then I'm not sure how a 2.5 average GPA of sophmore and junior year is going to look...I'm thinking CSU chico as they seem to be decently easy to get into...may I ask why community colleges are so frowned upon?

 

[metiman]

Have you taken your SATs yet? Get a perfect score on the math section and you still won't get into Berkeley, but you might get into another school in the UC system. I personally believe the University of California is the best public university system in the country. So you're lucky that you already live in Cali. Is CSU Chico what you are calling 'community college'? If so then no problem. After a couple of years you might even apply for transfer to Berkeley or UCSD or whatever state school you prefer.

Just spend pretty much all of your time now studying math and maybe some physics. If you aren't literally dreaming of equations at night you aren't working hard enough. Grades are one thing. Knowledge and ability are another. And study the SAT itself. Take past tests over and over again until you can get a nearly perfect score in the math portion within the allowed time.

I might also suggest having some specific interests in both mathematics and physics that you can discuss at your interviews. Be passionate about something and be able to articulate why. Keep in mind that a school is really about the professors. Maybe you could find a less selective state school which has a reputation for good instructors.

 

[AlephZero]

you see, I did really bad these last years in high school and I doubt that any state university will take me even though I failed class's. I am extreemly good at math and physics and I hope to have double major in mathematics and physics,

So, what grades did you get in high school math and physics? Do those grades match your self-assessment that you are "extreemly good"?

 

[elfboy]

calculus is easy to learn and nowadays computers can automate any calculus problem

good luck self-studying abstract algebra, you'll need it