Questions tagged [mnemonic]

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

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Is there a handy mnemonic or visual aid for all the basic set theory function relations, such as $f(A\cap B)\subseteq f(A)\cap f(B)$?

Glancing at Appendix A of John Lee's Introduction to Topological Manifolds, I noticed the following list of rules: I'm familiar with rules like these and have no trouble proving them—that's not my ...
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Has anyone heard of the "Of" operator, and if yes then what does it represent?

Where I studied (India), in my school we were taught BODMAS as Brackets, Of, Division, Multi, Add, Sub. With "Of" being the Of operator as in 1/2 Of 4 ie. Literally - 1/2 parts of 4 Can ...
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Mnemonics for memorizing $\overline{g:F(A)\to B}=G(g)\circ \eta_A$ and $\overline {f:A\to G(B)}=\epsilon_B\circ F(f)$

Let $F:\mathscr A\to \mathscr B$ be a left adjoint to $G:\mathscr B\to\mathscr A$. Write overline $(\overline {\circ})$ for the (either direction) of the bijection $$\mathscr B(F(A),B)\simeq \mathscr ...
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20 votes
7 answers
833 views

The formulas of prostapheresis: memorization technique

This question is related purely for my students of an high school and indirectly for me. The formulas below are the formulas of prostapheresis, \begin{cases} \sin\alpha+\sin\beta=2\,\sin \dfrac {\...
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4 votes
1 answer
146 views

Mnemonic to remembering that inverse limits are limits and direct limits are colimits

Sometime ago I had trouble remembering that right adjoints preserve limits (and so left adjoints preserve colimits). But ever since R. Vakil suggested that we use RAPL as a mnemonic to Right Adjoint ...
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1 vote
3 answers
202 views

How do you reverse a percentage change?

Is there any simple way to know how to reverse a percentage? For example if I have 100 and it goes down by 10% I end up with 90. If I then add to it by 10% I end up with 99, not the 100 that you ...
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4 votes
2 answers
259 views

What lies behind the definitions of split monics and epics?

Is there an easy way to memorize the definitions of split monics and split epics, and not to confuse the domains/codomains of the arrows from those definitions? For example, is there a mnemonic rule?...
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Mnemonic for Remembering Epic vs Monic

I am trying to remember which arrows are epic (epimorphisms) and which arrows are monic (monomorphisms), but the terminology is very confusing. What is a hint/mnemonic for remembering which is which? ...
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Is there a reason why we call $\mathrm{Hom}(A, -)$ covariant and $\mathrm{Hom}(-,B)$ contravariant?

I have trouble remembering what it means to apply the covariant or contravariant Hom functor. For example, when I see $\mathrm{Hom}(A, -)$, I always forget if I am going to reverse arrows or not. ...
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What would be the best way to memorize the 10 by 10 multiplication table?

Hear me out before you start downvoting please. I have a learning disability so no matter how hard I try I can’t memorize the table. Please give some tips/hints on how to memorize the table. Thanks in ...
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Mnemonic for cubic discriminant?

I sort of doubt there is a good one out there, but I thought I'd ask. I'm looking for a mnemonic for the general discriminant of the polynomial $ax^3+bx^2+cx+d$, which is $$b^2c^2-4ac^3-4b^3d-27a^...
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8 votes
2 answers
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Am I the only one constantly forgetting the Eisenstein criterion? [closed]

Do you guys have tricks to remember the Eisenstein criterion? I constantly forget it and I am looking for some logic in it to never forget it again.
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6 votes
3 answers
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Mnemonic for Integration by Parts formula?

The Integration by Parts formula may be stated as: $$\int uv' = uv - \int u'v.$$ I wonder if anyone has a clever mnemonic for the above formula. What I often do is to derive it from the Product Rule ...
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How to remember which is lower/upper semicontinuity?

There are several ways in which continuity can be formulated as two conditions - in a way such that one of them is lower semicontinuity and the other one is upper semicontinuity. (See below for ...
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1 vote
1 answer
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Mnemonics for typical integrations

I am supposed to mug up these integrals for my upcoming exams: $$\int\sqrt{a^2-x^2}dx=\frac{x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2}\sin^{-1}\frac xa+C$$ $$\int\sqrt{x^2+a^2}dx=\frac{x}{2}\sqrt{x^2+a^2}+\...
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Memorize inequalities about floor function

Let $n \in \mathbb{Z}$. Prove that: 1.$\lfloor x \rfloor \le n \to x \lt n+1$ 2.$ \lfloor x \rfloor \lt n \to x \lt n$ 3.$ \lfloor x \rfloor \ge n \to x \ge n$ 4.$\lfloor x \rfloor \gt n \to x \ge n+...
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13 votes
5 answers
21k views

How to remember which function is concave and which one is convex?

I always struggle to remember when a function is convex and concave: Do you have a particular trick to help you remember this? My trick is based on the Spanish phrase "No cabe", pronounced ...
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4 votes
2 answers
2k views

Mnemonics for linear algebra

Sometimes formulas in linear algebra are not easy to remember. Some usefulness for the process of remembering can provide application of mnemonics. Do you know some useful mnemonics for this ...
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3 votes
1 answer
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Epsilon-Delta Quasi-Limerick

Is this sufficiently logical to commit to memory? Any suggested edits? If $x$ is within $\delta$ of $c$, so $f$ is in $\varepsilon$ of $T;$ work $f$ minus $T$ to $x$ minus $c$; choose $\delta$ as $\...
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3 votes
4 answers
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Mnemonic for derivative/integral of $\sin x$ and $\cos x$

I'd love to know if anyone has a good mnemonic for answers of the following: $$\frac{\mathrm{d}}{\mathrm{d}x} \, \sin x$$ $$\frac{\mathrm{d}}{\mathrm{d}x} \, \cos x$$ $$\int \sin x \,\mathrm{d}x$$ ...
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1 vote
6 answers
392 views

Sine and Cosine Derivatives

The derivatives of: $$\frac{d}{dx}\sin(x)=\cos(x)$$ $$\frac{d}{dx}\cos(x)=-\sin(x)$$ I currently trying to teach a friend of mine calculus, because he does not know it yet. He keeps forgetting ...
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2 votes
1 answer
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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 ...
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7 votes
4 answers
10k views

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

They are: \begin{align} \cos(a)\cos(b)&=\frac{1}{2}\Big(\cos(a+b)+\cos(a-b)\Big) \\[2ex] \sin(a)\sin(b)&=\frac{1}{2}\Big(\cos(a-b)-\cos(a+b)\Big) \\[2ex] \sin(a)\cos(b)&=\frac{1}{2}\Big(\...
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1 vote
1 answer
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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, ...
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13 votes
2 answers
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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 ...
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58 votes
12 answers
416k 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,...
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3 votes
3 answers
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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 top ...
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14 votes
5 answers
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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....
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2 votes
7 answers
3k 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.
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5 votes
9 answers
908 views

Memorizing the identities $\cos {\pi \over 3}=\sin {\pi \over 6} = {1 \over 2}$

I memorized $\sin {\pi \over 4} = \cos {\pi \over 4}= {1\over \sqrt{2}}$ easily by using the diagonal inside the unit square. I am having great trouble memorizing the identities $\cos {\pi \over 3}=\...
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4 votes
2 answers
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Are there examples of when the ILATE mnemonic for choosing factors when integrating by parts fails?

Is it possible in some cases that using the ILATE rule does not yield an explicit antiderivative but making another choice does yields one? If so, please give examples.
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12 votes
5 answers
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Top 10 math mnemonics

If you study undergraduate medicine, mnemonics are almost indispensable - there is so much factual material to learn. I was never given any mnemonics in my time as a maths undegraduate. But Robert ...
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2 votes
3 answers
562 views

Trigonometric Identities and formulas

There are so many identities like $\sin2θ$, $\cos2θ$, $\tan2θ$, $\sin(θ/2)$, $\cos(θ/2)$ and $\tan(θ/2)$. there are other formulas too like $\cos(α-β)$, $\sin(α-β)$ etc and yes the sum and product ...
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15 votes
5 answers
4k views

Injection vs. Surjection: Mnemonic to remember which is which

What are some mnemonics to help one remember that Injection = One-to-one and Surjection = Onto? The only thing I can think of is 1njection = 1-1.
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5 votes
4 answers
2k views

How to remember a particular class of trig identities.

Please how can I easily remember the following trig identities: $$ \sin(\;\pi-x)=\phantom{-}\sin x\quad \color{red}{\text{ and }}\quad \cos(\;\pi-x)=-\cos x\\ \sin(\;\pi+x)=-\sin x\quad \color{red}{\...
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4 votes
0 answers
524 views

Remembering numbers while performing calculations mentally

Specific question: how can I improve on mentally performing calculations like these : $$(78-59)\times23-8\%\times(270+130)$$ $$[2\text{digit}+-2\text{digit}]\times2\text{digit}+-x\%\text{of}[3\text{...
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3 votes
2 answers
155 views

Mnemonic for centroid of a bounded region

The centroid of a region bounded by two curves is given by: $ \bar{x} = \frac{1}{A}\int_a^b{x\left[f(x)-g(x)\right]dx} $ $ \bar{y} = \frac{1}{A}\int_a^b{\left[\frac{(f(x)+g(x)}{2}(f(x)-g(x))\right]...
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1 vote
1 answer
799 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): ...
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11 votes
8 answers
1k 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 ...
102 votes
9 answers
12k views

What are Some Tricks to Remember Fatou's Lemma?

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}(...
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4 votes
5 answers
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Remembering multiplication of these two numbers: $7 \times 8 = 56$ and $9 \times 6 = 54$

I have almost mastered multiplication table up to 9x9 however, I'm having problems with the following two. 7 x 8 = 56 and 9 x 6 = 54 For some reason my brain thinks that 56 and 54 are somewhat the ...
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