Is time spent going to lectures better spent self studying?

What do you think?

I find it more efficient to get a couple of good books, learn by my own, and if i have questions go to class and ask them.

Yes, maybe a nice lecture is more illuminating than a book, but there's a lot of resources out there. I never got the idea behind being told a proof I can read on my own.

I definitely learn the most when I study and read through things on my own. And I definitely think that the best way to learn is by going through the arguments on your own.

However, there are a couple of good things about going to class that you might consider:

• Even though there are great books out there, I often find that many books are lacking in so much. There are mistakes in books that you might not catch on you own.
• Books can sometimes just be a collection of material and they offer many ways to study the material - i.e. there are many paths through a book. Going to class gives you a coherent presentation.
• Also, on that same note, you might understand the proof as it is written in the book, but you might miss a larger context or miss how the theorem is related to other key questions. A good lecturer will be able to highlight things like that.
• Remember also that if you are taking a class, then the exams might focus on what has been discussed in class and not necessarily focus on how the book has chosen to treat things. This can be a surprise for a student when they go to an exam and find material that is different in some way from the treatment in the text book.
• There is something healthy in meeting people, not just for you own sanity, but as you progress and do research you might find it very helpful to be able to talk to people about math. And I think that a skill like that can be cultivated in a classroom environment.

Just a few thoughts.

Some further remarks to supplement earlier good points: there are two points for me, first, that (of course) there are some aspects of the lecture system inherited from "old times" when possibilities were more restricted, and, second, that one should think in terms of what a lecture can or might provide that a printed source cannot, and vice-versa.

Understandably, the lecture system arose in times when it was far harder to create printed material, especially with mathematical notation and formatting, so it made some sense to have students take notes from a possibly-customized presentation by a lecturer, all the more so if the material were "new" enough so that it didn't exist in print. And in those "bad old days" the time lag for something to be publicly available could easily be two years, etc. Further, apart from mimeos (who here is old enough to remember?) it was impractical to produce cheap copies. Any decent copies could not be produced without the assistance of a publisher, and the latter did not lavish their technical gifts on just anyone. Obviously this situation has changed for the better, although the traditional publication route still confers vastly greater status than direct self-publication, and for some purposes, for some people, this matters. But already a long time ago it was clear that it was a waste of peoples' time to witness even a brilliant mathematician copy from their notes, onto the blackboard, and students copy into their notebooks. The episodes that finally made this clear to me were those in which the room was completely quiet, the professor saying not a word as he carefully, slowly copied onto the board. :)

That last anecdotal riff segues to the other point relevant in my mind, namely, what a lecture can offer that static printed notes cannot, and vice-versa, granting that nowadays there is no serious impediment to creation of at-least-rough notes that students could mark-up during the lecture, whether on printed copies with pen-or-pencil, or on electronic copies on touch-screens on tablet computers.

I would claim that (by now) lectures that attempt to substitute for notes will be inferior to good notes, and that notes that attempt to substitute for a lecture will be inferior to good lectures.

Lectures can be interactive! True, with search-able PDFs, a certain amount of interaction is possible, but the "channel" is more constrained, although more private and less embarrassing, perhaps.

Lectures are samples of the behavior of a live mathematician, in real time, with no "do-overs".

Lectures can include "tone of voice" and facial expressions, which is hard to do in text.

But, yes, text can be edited, revised, indexed, reproduced accurately, which is more complicated, but not impossible, with a live performance.

There are other differences, obviously, too, some of which may matter more to other people. I'd suggest thinking in those terms. E.g., if a specific lecturer is scarcely more than a bad text, that's a severe disrecommendation. Then things devolve into worry over the impression skipping class makes! Ack.

But at the same time many texts are extremely coy (due to stylistic traditions) about underlying ideas, motivations, and so on. And people are (mis-) trained to look at definitions, lemmas, theorems, proofs to see what's going on, while, in the best cases, it is the other discussion, often quite imprecise, that imparts much more information.

Depends on the personality of the auditor/reader, obviously, too. :)