[Method] Learning Math the proper way in college and beyond

I have been researching on how to study math as an undergrad student especially real analysis and I think I finally have the perfect method laid out. Before I begin with the method I wanted to address the problems that I think arise when you follow the youtubers and their scientific study methods :

Problems :

1. Not centered around the proofs : What I feel like is that these people treat math only as a computational subject rather than its real nature(get the pun?). Proofs require not repetition rather curiosity and innovations and their method does not allow for that. 2. math requires practice(even proofs) and you cannot spend all your time around the theory without diving into the questions. 3. Not much scope of playing around with the ideas.

There are several other factors but I will leave it at that.

Here is the method that really works for fostering curiosity and innovation : for classroom setting.

1. go to class(mandatory) and write the theorems and the proofs(also observe how the prof is using one theorem to prove this one and so on and also how one theorem leads to so many lemmas) 2. take notes which are detailed in your point of view because it will help with next step. 3. go back to your room after class and open your notes. 4. go through what has been taught in the class and after each definition and theorem and its proof, close the notebook and rewrite the whole thing and if you get stuck, think of how to simplify it or which theorem should come next and if you are really stuck, look up your notes and understand and then close again and rewrite the whole thing again and again each time this happens. 5. Now the real magic happens : after your done, rewrite the definition, write its converse, contrapositive, negation etc. whatever you can think of and try to reason each out if it is true and if so, prove it and if it is false, find a counterexample. Of course, this step seems like a hefty task but you have to do this and get over with before your next class and if you got some other work like assignment etc. then productively meditate on these ideas in your breaks, lunch time with friends, dinner time, etc all the time you are free(just read deep work and the core idea is to become obsessed with these ideas and become a true maniac.) ask your profs if your ideas are on the right path and if your proofs makes sense. 6. becoming curious : discard your ego, derisive self, negative talks and just become present minded and feedback driven(the power of mathematicians which makes them overpowered) and play around with everything : what happens if I touch this, negate that, prove using binomials or differentials, what happens if I do this or that? and if you fail at any step, just restart without judgement or take a break and talk your ideas with like minded people who are mathematics lover( I am blessed with such a friend and profs). 7. whatever I just wrote also should be applied to assignments, tests and homeworks etc.

You might be thinking why to bother with such a lengthy method and the answer is simple : what you are learning is research not just a computational guy. if you dont master this skill, you will be culled cruely. It will not be education system's fault or govt but yours alone and also the world needs mathematicians after all we are daring enough to push the realm of everything. If you have time to hop on online games, instagram etc. you have enough time to do this too. You might argue that it is for relaxation, I will reply : they are not for relaxation but to distract you with math based algorithm.

In the end, try these ideas as a whole(not a step should be missed) and let me know how did it go.(the results wont show in 1 or 2 days but atleast a week)