# Tagged Questions

Questions related to memory devices that help learners recall larger pieces of information, especially in the form of lists like characteristics, steps, stages, parts.

32 views

### How can I remember whether finite or countable cartesian product of countable set is countable

I always forget this result Is cartesian product of countable set countable under finite or countable cartesian products? Is there a good way to remember this? Like a proof sketch where the ...
58 views

### How to remember sum to product and product to sum trigonometric formulas?

They are: I have found nice mnemonics that helped me to remember the reduction formulae and others but I can't find a simple relationship between the formulas above. Can you help?
20 views

### Index notation of tensors and mnemonics

I've been trying to learn to manipulate tensors but I've got probably too comfortable with all the matrices in my Linear Algebra course, that it gets really difficult beyond rank-3 tensors. So, ...
435 views

### Easy way of memorizing or quickly deriving summation formulas

My math professor recently told us that she wants us to be familiar with summation notation. She says we have to have it mastered because we are starting integration next week. She gave us a bunch of ...
13k views

### Easy way of memorizing values of sine, cosine, and tangent

My math professor recently told us that she wanted us to be able to answer $\sin\left(\frac{\pi }{2}\right)$ in our head on the snap. I know I can simply memorize the table for the test by this Friday,...
96 views

### What is the good way to remember the signs of the rotational matrix?

Recall rotational matrix in (x,y) is given by: $R = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix}$ For the life of me I cannot remember if the ...
479 views

### How to remember trig identities?

Suppose I have a trig function $T: \Bbb{R} \rightarrow \Bbb{R}$. I want to be able to derive four basic properties: $$T(x) \cdot T(y)$$ $$T(x) + T(y)$$ $$T(x+y)$$ $$T(cx)$$ where $c$ is some scalar....
285 views

### Remembering that $\sin^2(\theta) = 1/2 - 1/2\cos(2\theta)$?

How do you remember this for integrals? It doesn't seem obvious and I can never remember it when I come across it in integrals.
283 views

367 views

### What makes this mnemonic device work for multiplication?

I stumbled across a mnemonic device related to multiplication, outlined on this wikipedia page. I see that it does work, but I'd like to know why. It works as follows (from the wikipedia page): ...
793 views

### “How I wish I could calculate pi” analogs…

You might know the mnemonic for $\pi$ in the title or even this more elaborated one: Sir, I bear a rhyme excelling In mystic force, and magic spelling Celestial sprites elucidate All my own ...
For a sequence of non-negative measurable functions $f_n$, Fatou's lemma is a statement about the inequality \int \liminf_{n\rightarrow \infty} f_n \mathrm{d}\mu \leq \liminf_{n\rightarrow \infty}(...