Studying Is it useful to learn advanced math course by video lectur?

[Alpharup]

Pure math books, in my experience are very hard to read(compared to engineering). An engineering book(in my experience) keeps repeating the same math(high school calculus+some engineering math) again and again. So, after time, the pattern of thinking become more normal. But math books on other hand can become really slow, where you need to understand line-by-line, theorem-by-theorem and proof-by-proof. In this process, a lot of mistakes will be made, a lot of our assumptions will be proven false, a lot of our intuitive imaginations will be just be proven as imaginations. In other words, we make mistakes to learn.
But, I also am seeking video lectures. For engineering, the time spent on watching a lecture and understanding it will be more or less the same as that of reading engineering book itself. But for math, I do certainly find the gap. An hour of lecture may give proper intuition, thinking traps, the direction on what and how to think next and so on...This will be useful because, it saves time from initial understanding of the model by reading alone. Iam not saying that a math grad should watch only videos. What I mean to say is that watching videos will be more time-saving and misunderstandings can be avoided. Iam united in the saying that," Working out problems in math is ultimate guide to mastering it".
But, I do find pitfalls in watching videos. They may help in short-term, but won't they just discourage students from trying? For example, a student may find the concepts of limits intriguing at first but by repeatedly working out on paper, he will definitely avoid misunderstanding sooner or later. He is given an oppurtunity to construct himself, the system. But video leactures, do otherwise. By exposing the student to only "right thinking", "right concepts", "right approach", won't they just spoon-feed the students?
Please help me...

 

[phinds]

It's fairly well known that learning techniques vary considerably from person to person, so it really is more about you in particular than students in general. You need to decide what you are comfortable with.

That said, my approach would be to go through the text somewhat lightly then watch the video, then go through that section of the text with more rigor.

I personally don't think pure-text or pure-video or even a combination of the two could ever really substitute for a lecture where you can ask questions but certainly a video lecture will add a lot for some people.

 

[Simon Bridge]

You cannot learn from simple instruction, you also have to do examples. Practise.
Pure maths can be very formal theorem/proof based - you will want to find a course that does not take that approach.
You will do even better if you can get a tutor or a teacher to help you... a good teacher will be able to tailor a course to you learning style as well as teach you additional learning styles and strategies; but this is also very expensive which is why most people just go to college and kinda time-share the prof.

I learned all my advanced maths through physics - which can mean that I have some sloppiness that annoys mathematicians but the bottom line is: what do you want to know the advanced maths for? That should shape your overall strategy.

 

[ProfuselyQuarky]

You cannot learn from simple instruction, you also have to do examples. Practise.

Agreed! I use video lectures often, but it's all futile without taking out paper and pencil in the process. It's the only way to really learn.

 

[micromass]

Video lectures can be really fun and stuff. But it often gives a false feeling of understanding. I've been on PF for quite a while, and I've seen all kind of students. There are students which rely only on wikipedia, and who rely only on video lectures. Those kind of students somehow never tend to get very far.

I've come to the conclusion that being able to actually read a dry math book is very important. Watching video's is cool, and if you like it then you should continue with it. But do spend some/a lot of time on the theory sections of your textbook.