How do you learn analysis effectively? Do I have to memorize

Pick up a good book like abbott or rudin and do the exercises

As everybody should know the only way of learning math is by doing math. You'll find that you'll spend so much time doing proofs that you should be able to recite the theorems and def in your sleep.

>>7959604
Thanks. I'm working on Rudin's and Tao's book.
However, Tao's book does not have its solutions available. How can I know if I got the correct proofs?
I'm studying by myself so I can't ask anyone in my school.

>>7959612
You can email terry tao himself and see if that gets you anywhere, but just doing the rudin exercises would probably suffice

>>7959616
I will try sending email to him though I don't really think it would work. If it is, his solution could be on google now because the book is kinda old.

>>7959604
>Rudin
its a classic but its crap. Use Bruckner and Bruckner.

>>7959596
Who is that semen demon?

>>7959701
https://www.youtube.com/watch?v=hY8IMjeKHoQ

>>7959612
Rudin AND Tao is not something that you can actually do, as you'll realize once you're past chapter 2. They're wildly different books, and I strongly recommend you drop Rudin before you crash and get discouraged.

In the beginning it's hard to know what constitutes an "acceptable" proof. Try to follow Tao's style, most of the first proofs will be just filling some simple blanks and doing computations. Post some of them here in /sqt/ and let people review them an give you advice.

>>7959596
>Do I have to memorize every single definitions, theorem, lemma, corollary, remarks?
If you have to ask, then yes. Bite the bullet and do it.