What would be a good way to memorize theorems about algebra? This post is not constructive, so maybe this rather should be posted on CW, but since there is a 'soft-question' tag, i'm posting it here.
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I believe the best way to memorize theorems is to draw. It was not hard to illustrate theorems by pictures when it is about analysis & topology.
However, i have no idea how to memorize theorems in algebra. Specifically, i'm studying linear algebra right now and it is hard to visualize  theorems. For example, "If $V$ is a finite-dimensional vector space, $T:V\rightarrow V$ is linear, $W$ is a $T$-invariant subspace such that $V=\text{rng}(T)\oplus W$, then $W=\text{ker}(T)$" is a theorem in linear algebra. Well, it is easy to prove this, but it is not that easy to memorize to use this theorem whenever i need this. I cannot visualize this by drawing a big circle named $V$ and two small circles in this big circle, namely $\text{rng}(T)$ and $W$. (Because this diagram tells nothing about their direct sum is $V$. Plus, since i cannot draw a picture illustrating this, i don't understand why it should be.
What would be a good idea to memorize theorems related to algebra?
 A: Step 1 : Prove the Theorem.
Step 2 : Apply the Fibonacci sequence to represent how many days AFTER you will prove the theorem AGAIN.
Step 3 : After every 5 Fibonacci numbers if you cannot remember the theorem, start over the Fibonacci sequence until you remember it for life, otherwise continue the sequence until you feel comfortable remembering it.
A: My two cents: during all my university studies and after that, the best method I've ever had to study and memorize is to teach an imaginary class what I'm trying to grasp...over and over until I could actually teach that piece of stuff to a real class.
This imaginary class poses tough questions, asks for examples and counter-examples, analyzes each tiny aspect of what's been taught, and you as the teacher must be able to address and give satisfactory answers and insights.
Big secret: keep by your side several books on the subject (tablets now are incredibly handy for this), which you'll consult constantly until you're able to give an AAA lecture to your imaginary class on the subject being taught.
Last one big secret: be tough on yourself and demand from yourself excellency while doing this "teaching".
