Difficulty in learning maths I am an undergraduate student in Mathematics. I am writing here because I think I have a problem in the way I study Math. My grades are pretty good, but I think that I am not able to effectively remember what I studied.
I will try to explain myself better: I passed Calculus and Analysis (I am from Italy, we usually learn those subjects together) with a very good grade, but I struggle to remember some basic stuff to series series or some techniques to solve differential equations. I am able to remember effectively things in short or medium periods of time, but I do not have a way to remember things in longer periods of time (years). I realized this today, during a lesson of Analytic Number Theory for undergraduates: we needed to use the classic series for $\log 2$, the harmonic alternating one, and I was not able to recall it. I have realized that this is a general problem for me in Math, but it is  very clear in Calculus/Analysis.
Do you have any suggestions on how to overcome this problem? How can I study in order to remember better thing in Math (both theorems, their proofs and how to do exercises)?
Thanks
 A: This happens to me also and I'm sure that to many mathematicians too. You cannot remember everything, I generally remember theorems or tricks that I used a lot, or that I have some picture in my mind, or that I have some "conceptual deep understanding".[*]
I realized, when started to learn maths, that I forgot many things after some time. Then I started to do more exercises about the topics that I was studying, and also I started to write these exercises in some way that I could recover easily after some time has passed, so I started to write the solutions of the exercises that I was doing in digital text files.
This helped me a lot to remember some things (generally rare theorems or theorems that I did not used many times) when the time pass.
Also there are topics that you will understand very well and you will "absorb it", and other topics that you dont. In my experience this is usually related with the way the information is presented, there could be an abyss of difference in the way a topic is presented from one textbook to other, so take a look to some different textbooks or recommendations before to decide from what book to study.
I hope this helps. Anyway my background in mathematics is amateur: I study mathematics in my free time, as a hobby. Probably in university is different because there is an imposed timing.

[*] What I try to say by the words "conceptual deep understanding" is that you can explain something really abstract to anyone in simple words (non necessarily mathematicians, and no technical words). Some times this kind of understanding can be achieved, and it is reflected many times in the way some mathematicians present a topic in a textbook.
