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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 Israel just mentioned "iciacids" to help remember the important features when looking at a function plot Function - Main Features? I would certainly have forgotten some of them.

So maybe mnemonics are useful for maths too. Maybe also for tricky proofs? Or for areas knee-deep in definitions, like topology? Does anyone know of a source for math mnemonics? Eg a top 10 type website? Or a kind of successor to sci.math FAQs (although I do not remember any mnemonics there)? Or a book?

Community
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almagest
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    I find "sin = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent" to be a useful mnemonic; there's no other way I could ever remember how to spell the name Sohcahtoa. – bof Sep 11 '14 at 10:22
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    I can't even think of four that I've ever used... – rschwieb Sep 11 '14 at 10:22
  • With a little practice, isn't it rather hard to forget about increasing/decreasing behavior and concavity? The critical and inflection points come naturally as boundaries for those behaviors. Iciacids does not seem like a particularly serious mnemonic. – rschwieb Sep 11 '14 at 10:36
  • there is nothing much rote-learning in maths, everything is pretty easy understanding – RE60K Sep 11 '14 at 16:04
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    @Aditya Lucky you :) The team of world wide number theorists who have still not managed to understand Mochizuki's proof of the abc conjecture should enlist you! But you are right, it is usually the concepts that are hard. – almagest Sep 11 '14 at 19:34
  • In addition to sohcahtoa, in high school I could never keep straight which of $\sin(a\pm b)$ and $\cos(a \pm b)$ expanded to $\sin(a)\cos(b) \pm \cos(a)\sin(b)$ and $\cos(a)\cos(b) \pm \sin(a)\sin(b)$ until I came up with a mnenmonic. If faced with $\sin(a\pm b)$, I recall "s" means "same sign", but in exchange for that niceness we get terms with mixed sines and cosines. If faced with $\cos(a \pm b)$ then the opposite is true. Sort of crude and complicated, but I've always been able to remember these identities since then. –  Sep 11 '14 at 22:13
  • I also wonder whether Littlewood's three principles might count as mnemonics: http://en.wikipedia.org/wiki/Littlewood%27s_three_principles_of_real_analysis –  Sep 11 '14 at 22:21
  • http://mathoverflow.net/a/61478/450 – Georges Elencwajg Sep 12 '14 at 09:55
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    @Bungo My mnemonics for keeping those addition formulas straight were "$\sin(a-a)=0$" and "$\cos(a-a)=1=\cos^2a+\sin^2a$". – bof Oct 05 '14 at 11:01
  • I am not using any mnemonic, this must explain why I am a so poor practitioner. I'd be very grateful to the guy who can give me a bulletproof way to remember how opening/closing correspond to a sequence of dilation/erosion in mathematical morphology. –  May 11 '16 at 21:03
  • Try to find Martin Gardner's column "How to remember numbers by mnemonic devices such as cuff links and red zebras". P.S. A quick google finds a few here. – dxiv Sep 16 '16 at 18:24

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I remember the equality $$\Gamma(\frac{1}{2}) = \pi^{\frac{1}{2}}$$ by writing $$\Gamma( \frac{1}{2}= \Pi^{\frac{1}{2}} $$ or $$\Gamma(^{\frac{1}{2}}= \Pi^{\frac{1}{2}} $$

orangeskid
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Mnemonics are vital to teaching and learning mathematics. They are often unique as many are number-based, and as a mathematics teacher, they are quite powerful tools to help students, colleagues and ourselves the mathematical concepts.

Several studies have been performed on the effectiveness of their use, such as in Effects of Mnemonic and prior knowledge instructional strategies on students' achievement in Mathematics (Akinsola and Odeyemi, 2014), that concluded the most effective form of mnemonic in mathematics are ones that link prior knowledge with new concepts.

Also, as most formula use algebraic terms, these could be used as the first letters to make a sentence, or as a word, as a memory trigger.

There are many resources for mathematical mnemonics online,mostly are for elementary and high school students, such as the Education World website, which has 36 examples on this site, mostly for basic skills; and OnlineMath Learning.com, which includes some trigonometry and algebra. A basic visual mnemonic is included in a presentation for quaternions.

  • Trying to figure out if this is a spoof. Guess I will have to check the refs :) – almagest Oct 05 '14 at 16:23
  • @almagest I assure you, it is not a 'spoof', did some research to put together the answer. –  Oct 05 '14 at 16:24
  • Do not misunderstand. I am a strong supporter of mnemonics. I use them extensively in history, medicine etc. But for some reason maths sticks in my mind more easily. Also, this site seems, on balance somewhat hostile to them. I will read your material carefully when I can get to a desktop. At the moment I am struggling with an iPhone 6+ interface. – almagest Oct 05 '14 at 18:19
  • @almagest I am new at this site, so are not sure what topics are denegrated here. All I can offer is my research skills. –  Oct 06 '14 at 02:11
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I remember the beginning digits of the square root of two by counting the number of letters in each of the following words, and the sentence describes the square root of two, too.

** I have a root of a two whose square is two. **

1 4 1 4 2 1 3 5 6 2 3

Olive Stemforn
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There are a few at Wikipedia:

I've always liked this one on the contraction mapping theorem (also from Wikipedia, though it's no longer on the page):

If $M$'s a complete metric space/(Non-empty) it's always the case/That if $f$'s a contraction/Then under its action/Exactly one point of $M$ stays in place.

In the absence of suitable mnemonics, I highly recommend Anki for memorising stuff in general.

Raoul
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Here is the E E E rule for signs of permutations:

Even number of Even cycles makes an Even permutation.

Yes, the sign is $(-1)^ {\sum_{c \textrm{ cycle}} (|c|-1) }$, but I remember it better with the triple E rule.

orangeskid
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