Is it possible to learn math on your own?

[valentin132]

Hi guys I'm wondering if it's possible to learn math on my own. I'm talking about high level math such as calculus differential equations and other math subjects. What do you guys think?

 

[snipez90]

Yes.

There are probably a few caveats though.

Ideally, you should be comfortable solving problems at the level from say, the http://www.artofproblemsolving.com/...&cid=44&sid=5b997d7a43d277ca8a81a7519b119754". The contest has a good coverage of precalculus topics and, more importantly, it is perhaps the most basic example of problem-solving at the high school level. If you can't solve the first 15 problems correctly, which should be enough to make it to the next level of competition (the AIME), you should seriously consider revisiting the basics.

Also, if you think you might major in math or physics in college, start by reading a textbook on http://en.wikipedia.org/wiki/Mathematical_analysis" .

 

[valentin132]

Do you have any recommendations on any real analysis books?

 

[gb7nash]

Teaching yourself really depends on the person. I know some people that are accustomed to teaching themselves concepts and some people that struggle with it. Sometimes it's just good to have an instructor talking about concepts and examples.

If you don't mind saying, what's your math background? The only reason I ask is because you'll need to learn how to crawl before you walk. It's good to get a decent understanding of calculus (and other topics) before you even try to attempt to understand real analysis. If you're not accustomed to writing math proofs, understanding the material will be even more difficult to understand, as it is laden with theory.

To answer your question though, google "Baby Rudin". It's a really good real analysis book.

 

[valentin132]

gb7nash- I am barely getting into calculus right now. In fact, I am studying Thompsons book, Calculus Made Easy.

 

[gb7nash]

gb7nash- I am barely getting into calculus right now. In fact, I am studying Thompsons book, Calculus Made Easy.

That's a good place to start!

 

[Unit]

Do you have any recommendations on any real analysis books?

I find "An Introduction to Analysis" by William R. Wade to be excellent. Like gb7nash said, you might want to familiarize yourself with calculus concepts first. For that, I recommend Michael Spivak's "Calculus" over James Stewart's "Calculus: Early Transcendentals".

 

[lugita15]

James Stewart's "Calculus: Early Transcendentals".

I'm not sure why you're specifically recommending the Early Transcendentals edition. The only difference between the two editions is when transcendental functions like ln(x) are covered - whether it's done as part of differential calculus, or whether ln(x) is defined in terms of integrals later on.

 

[mathwonk]

try a college library to see which calculus books speak to you. I would guess a very small subset of self studiers would choose baby rudin, one of my candidates for the least user friendly math book in the galaxy.

try euler's elements of algebra, euclid's elements, gauss's disquisitiones arithmeticae, cruse and granberg's lectures on freshman calculus, or an old $1 edition of Thomas' calculus, say from the 60's.

 

[chiro]

Hi guys I'm wondering if it's possible to learn math on my own. I'm talking about high level math such as calculus differential equations and other math subjects. What do you guys think?

Hey valentin132 and welcome to the forums.

It is possible and there are a lot of resources out there nowadays compared to even a few decades ago with the internet, forums, blogs in addition to conservative resources such as textbooks.

I will tell you though, it's a lot harder to do it completely on your own in comparison to doing at a place like university. It's not that people that go to university aren't motivated (they are usually very motivated), but social dynamics has a big impact. At university you are with other people that (usually) want to learn and this creates a good environment for the students.

Also if you don't get something, it usually takes about half a minute with a lecturer to iron out any misunderstandings.

Another thing is that the lecturers give you problems that usually are good at getting you to learn the "nooks and crannies" of the subject that just isn't available time-wise to teach in class. The fact that the lecturer gives the exercises means that the students don't have to worry about what they have to learn: they are guided and just work under the instruction of the teacher which makes learning a lot more focused and less prone to erroneous judgement and anxiety.

So even though university students do a lot of work themselves in their own time, the lecturing aspect is still very beneficial both for motivated students.

I guess if you're that kind of person, you could do it, and if you can all the best to you. It's just that in my experience many people (myself included), find it hard to go completely solo, for some reasons that I have mentioned above, at least for initially understanding things in an affective manner.