How to take the most of math lectures in college?

This is a common problem, particularly perhaps in mathematics. Lecturers suspect the students expect the lecturer to write everything needed on the board and thus end up writing things on the board that are already (usually much more clearly) written in a textbook. When I was a student I tried to read the material for the lecture (if that was known) before the lecture but I did not bother taking any notes during the lecture (with a few exceptions). I just listened and later photocopied notes from any of the tons of other students who were copying word for word what was said. I used my time reading good textbooks I found (at times I would bring them with me to class as well and read the books while the lecturer was speaking).

I completely agree with you that there is little point in just lecturing by neatly reproducing existing textbook material on the board (though I'm sure some will disagree with me). Today when I lecture I declare a textbook to accompany the course and demand all students bring it with them. I do not reproduce on the board anything from the book, but instead I explain theorem, proofs, work out examples and exercises etc.

I also find that listening to a lecture where the lecture actually uses chalk or whiteboard is very slow and I find it less effective than reading a good book. Listening to a lecture where the lecturer uses slides can often be too fast and is also not highly effective in my view.

Of course the biggest advantage of attending a lecture is the ability to ask questions on the spot and not having to figure out something complicated on your own. I guess my advise would be, if you can get a hold of good lecture notes taken by a classmate so that you know exactly what went on in class and if you manage well on your own reading a book then skip the lectures and spend your time reading the relevant material from (preferably more than one) textbook.

I feel that attending classes is a huge waste of my time. The lecturer just keeps writing formulas on the board and to be honest, I am simply too busy just rewriting all those symbols to really understand what is being taught.

I feel that spending that much time in class just to get an edge in an exam is quite ineffective.

Most reflective people think this at some point. They may be more benefit to lectures than immediately apparent. We learn a lot by copying, Something that's missing from books and notes is just seeing how things are done in real-time by a mathematician: which manipulations are common, which steps get skipped as obvious, which things require more detail than you might otherwise have given them. They also set the pace for your study and give you an overview of what is expected of you. A lot has been written for and against the value of mathematics lectures - have a search online if you like.

the rest are just a bunch of robots attending because they have been told that they have to, or are afraid to miss some important hints for the exam.

I think you need to do your best to break out of this mindset otherwise you may end up isolating yourself and become ill.

It seems to point out that the best way to take advantage of the lectures is to get acquainted with the material first. So is a lecture meant mostly as a complement or substitute for reading the textbook?

You don't necessarily have to look at the material first (if you are lucky enough to have that option though, that's a very useful thing to be able to do!) - I think the most important thing is to read and organize a set of notes afterwards so that you know where you are (in terms of understanding) with respect to the course and have material that fits perfectly with what you would need to look back over if you forgot something.

Do I have to admit that I am too stupid to follow the lectures and write what is on the board at the same time?

I got a big shock when I went to more advanced classes and couldn't understand everything as it was said: I don't think it's normal to follow all the detailed steps of proofs in real-time in your lectures (there may be people that clearly do - don't be discouraged) - any instances where you don't have to time to check details or follow a step is something to read over afterwards. Doing that is a good thing too, because it helps you get a good grip on the material - better than having just sat through a lecture or having just studied notes.

I was in your shoes. During my first semester of calculus I took notes diligently and did well in the class, but I would occasionally look up at a proof and be dazed by what it meant. During my second & third semesters of calculus I had a different instructor with a different teaching style. He didn't just teach the concepts of calculus, he also taught the history of the concept. Who discovered and formalized these ideas and how they came about their discoveries. In these classes I learned to take less notes (the stories surely weren't going to be on any exam). The stories however gave unparallelled context as to how each concept was conceived, what problem space it addressed, and how it was to be applied.

Ever since then, I have never taken notes in math lectures shy of a few important equalities. I find diligently taking notes heavily distracts from understanding the big picture:

• How do these new concepts relate to previously understood concepts?
• What do these new concepts build on top of?
• What makes this new concept unique?

These things are hard to focus on when you brain is busily processing then next line of chalk on the board.

I would attend lectures without any expectation of taking notes. Follow the lecturer's dialog on the subject. Scribble down only those concepts which seem most important. Then go home skim through the book reading in depth only the sections which you did not grasp from the lecture. Attending the lecture will make reading through the book much easier.