Do you learn math better through self-study or through taking a formal course?

[andytoh]

I'm sure many of us don't need a teacher to learn a specific math subject, just a good textbook. Self-studying allows us to learn at our own pace, rather than at the pace the teacher sets for the whole class, though the pace we choose for ourselves may not be the correct pace. We can also add/avoid topics of our own choosing, though we might not be making the best choice in so doing. People who self-study also usually don't give themselves assignments or tests (just trusting that they have learned well), which may or may not be a bad thing, depending on whether they truly have learned well or not. Of course self-studying is much more convenient, which thereby saves travel time and so gives us more time to learn.

 

[CRGreathouse]

I self-study very well, and often -- I'm doing two or three textbooks on my own right now. Still, I'd say I learn better in a course; don't underestimate the value of having a professor there to answer questions.

 

[cristo]

It's always better being taught by a person rather than just a textbook. As CRGreathouse says, a lecturer can answer questions that a book cannot!

 

[arildno]

One-to-one study with a great and dedicated teacher is the optimal way of learning the subject.

 

[tronter]

the best textbooks could perhaps be just as good a replacement, like all the books mathwonk as mentioned (as well as asking questions on forums). You get the best of both worlds. After studying a subject, find an online exam or test, and time yourself. See if you do well. This will gauge whether your self study was good. Or just make up your own exam from problems randomly selected from the book or other books.

Of course, the ideal situation, as arildno says, is 1-1 study with a professor. You would probably become an expert in the subject in a very short amount of time. Also you don't have to go in a linear order when studying. Sometimes jumping ahead, and getting the big picture, will allow you to gain a better understanding of earlier concepts that seemed difficult.

But with forums, you get input from both experts (like mathwonk, matt_grime, Chris Hillman, etc.. arldino, all the mentors, etc..) and students. So these different perspectives only aid in your learning experience. So really you would learn the most from a collective group of people like those in this forum.

Sometimes self study will spark creative thoughts/ new ideas. It forces you to come up with your own perspectives of a subject. Thus, you learn the subject at a much deeper level. A formal classroom environment may stifle this. Of course, the opposite could be true.

I recently e-mailed Edward Witten, and asked him what he did. He said that he self-studied most of the physics. But he would still recommend a formal classroom environment. Its an easier track.

Most professional mathematicians learn other fields from their co-authors. So this emphasizes arildno's point about 1-1 study with an expert (or experts) being the most efficient.

 

[vsingh165]

I learn math better through formal courses (not online courses, I'm talking about a real classroom here). And the class size shouldn't be too big, either. It should be a good size (like 20-30 people) where there is a balance between your own studying and the professor/teacher helping you understand things. I believe that is the most efficient way of learning math, especially for high school or college students.

 

[HallsofIvy]

And, with self study, you miss the interaction with other students which is very important.

 

[dodo]

You mean, the beers.

I'm currently following an in-between: as a working grown-up, I found distance-learning a good opportunity. My only complaint is perhaps that I don't know how a B.Sc. by an Open University compares, in pensum extent, to a regular undergraduate degree.

Anyway, if you get any formal degree you'll have to study on your own to keep up to date.