Anyone got any handcrafted mnemonics or songs for remembering mathsy things? I remember making this in a physics lesson once;

The Quadratic Equation (to the tune of row, row, row your boat)

Ne-ga-tive of b, plus or take the root
Of b squared minus 4ac
All over 2a

I also made another one for resistivity, which is what we were actually meant to be doing in class (rho, rho, rho your boat) but that is less interesting and I've forgotten it.

Scary fact: I had to look up the chuffing quadratic equation to write this post!

No handcrafted ones, but I found this on MathWorld some time ago:

We present a mnemonic to memorize a constant so exciting that Euler exclaimed: '!' when first it was found, yes, loudly '!'. My students perhaps will compute e, use power or Taylor series, an easy summation formula, obvious, clear, elegant!

By counting the letters in the words of that sentence, you get e to the first 40 decimal places (! counts as 0). It's easier to just memorize the digits though if you ask me. :p

It's not actually a mnemonic as such, but the following "Pizza Theorem" is one way to remember the formula for the volume of a cylinder (also found on MathWorld).

Consider a (cylindrical) pizza of radius and thickness . The volume of the pizza is then given by the expression:

.

Never
Eat
Shredded
Wheat

Mr old maths teachers name was Mr Auger, so to learn CAST in the correct order (we we're easily confused back in A-level)

Auger
Says
Trig's
Cool

Mnemonics Need Extra Memory. Orated, Needless, Idea for Cretins

Somebody had to post the old favourite: the Contraction Mapping Theorem.

If M is a complete metric space
(and non-empty), it's always the case:
if f's a contraction
then under its action
exactly one point stays in place

This is so awsome it is like sex in verse form, says I.

Except that's a limerick and not a mnemonic (and it's probably harder to memorize than the standard statement of the contraction mapping theorem).

All
Silver
Tea
Cups

Cosmin
Smells
Lots

Laughs
Out
Loud

Stop
Posting
Aimless
Messages

Now I know what it feels like to have a meaningful thread spoiled by mindless and confusing spam :(

I used to remember it by
Alex
Sucks
The
????

Cusp?

A mnemonic is anything that makes something easier to remember, be it an acrostic (which most of these are) or a limerick. Personally, I think that I will never in my lifetime forget the contraction mapping theorem as a result of that little limerick

Thing is, they can be corrupted:

If M is a compact metric space
(and non-empty), it's never the case:
if f's a surjection,
but not an injection,
exactly two points stay in place

What the heck does ASTC stand for/mean??? Or are you just creating mnemonics for random letters?

I think (based on Alex's) that S = sine, T = tangent and C = cosine. Not sure what it's for though.

Alex told me the other day, when you go round the trigonometric circle anticlockwise, it's the order in which the trigonometric functions are positive.
ie : All (Sin, Cos and Tan) are positive in the first quadrant, only sin in the second, only tan in the third and only cos in the fourth.

That's not something you'd need a mnemonic to remember though, is it? You can quite easily figure it out whenever you need it even if you don't already know it.

Yeah I never found it useful, I just pictured the pretty graphs in my head.

Yes it's quite obvious, especially with the trigonometric circle and cos = projection on the x axis, sin = projection on the y axis (and then tan = sin/cos)

I guess Alex took the AQA course as well. This was AS level stuff so don't expect it to be either difficult or useful.

We learnt it in year 9 at secondary school, and it was quite useful then. Just because you didn't learn in this way doesn't mean it's not a useful way to think of it.

...When I say useful, I really mean useful for us now. We don't personally need it any more as Xedi pointed out.

Well, it isn't a way to think of it at all, instead it's just remembering it. Much less effective/useful than knowing why it must be so.

Yeah, that was my point as well. Most things which rely on rote and memorisation instead of understanding are generally less useful than those which don't imo.

You have to realise that some people really don't want to, or need to understand all of mathematics. For some people it really doesn't click, and even reducing a fraction to its simplest form is hard. So a quick and easy way of remembering something you find trivial might still be a valid and very helpful thing for them.

Back in first year I remember writing out all the basic analysis and linear algebra definitions and theorems, then copying them over and over until I could churn out any of them on a whim. At that point I really didn't know what they meant, but at least if I was trying to prove something I'd have the algebraic statement of what I was aiming for. Then over the years my brain has been able to fill in the gaps and give me the intuition of these statements too. It's just they way I think about things, and I understand that not everyone thinks like this.

Indeed, it is often a matter of pride to university mathematicians, who have spent two years languishing in a-levels, and taken a comparatively short time to subsume most of its topics, understanding most things as to the right mind they all seem intuitive (with a little work!).

But university maths is highly non-linear (!), and hoping to understand all and everything as it comes up is ambitious at best- sometimes it's far better just to learn by getting a feel for the process, to build the full ideas in your mind later (after all, that's how new maths is actually made...)- paiting the fence a la karate kid.

Working from the top down (what it does) rather than bottom up (what it means) is just as useful, and in some cases better. It is simply a matter of tempering inspiration with rigour and vice versa: the perfect mix gives the best mathematicians.

Of course in the grand scheme of things, it's a matter of taste- but the key is to keep an open mind for which ways of learning work best for you.

But yeah, steven I've never met anyone who used ASTC. It sucks balls. Way better to remember the graphs...

Some subjects, it's perhaps better to not use intuition. Analysis (at the moment) is a case of simply checking whether our definitions are correct to our intuition. In this way intuition can be slightly inhibitive.

Not really, you always need to keep some sort of balance between the two. Even when doing first year analysis, intuition is helpful in realising why certain definitions and theorems make sense, which techniques to use, etc. I think the main reason why people find the first year analysis courses difficult is exactly because they lack the required intuition with which most of the proofs and exercises become almost trivial.

I was quite careful there not to be totally definitive about using intuition. When it comes to writing a proof (given that we have a direction) it's quite important to focus on the algebra. To make sure that we don't accidentally include anything that is obvious, but has not yet been shown.

Still, using a certain intuition of the subject won't make you use "obvious but unproven" statements if you're rigorous about it at the same time, especially if you realise that in mathematics, obvious means "has an obvious proof", in which case it's ok to just say so. That's why I was talking about balance: you can always have both of these, not necerssarily one or the other. Besides, I find that, most of the time, focusing on the mechanical side of the subject ("the algebra") makes for quite long and ugly proofs, which is never desirable.

I do agree absolutely with what you were saying. But I reckon that both in checking and yes, occasionally when writing a proof, wading through the algebra can help create a proof that contains accurate assumptions etc. There IS a certain danger, even when using obvious in the correct way. Most recalled prrofs have the word obvious or clear near the error. Even though the proof appearedd to be obvious, it was horribly wrong.

Well, if you're using "obvious" in the correct way correctly, there's absolutely no danger :P (or at the very least as much danger as there would be by not using it). In the end, both approaches can be exactly as dangerous: being overly concerned with the algebra can quite easily create errors there and make the proof a lot harder to check. Conversely, an elegant proof that relies on ideas rather than manipulation of symbols will generally be a lot easier to check as long as you're being careful about your assumptions and such. One thing that I find too many people ignore (ahem, Alex :P) is that in general we should strive not only for correct proofs but also for elegant ones (one of the many reasons for this being what I was saying above about checking proofs).

Woah, that's the longest mnemonic I've ever seen

No, Tom and Steven's were longer. :P

Mine was actually a mnemonic to remember Steven's post by.

Richard
Of
York
Gave
Battle
In
Vein

Or just listen to Boards Of Canada

I once used, and couldn't shake
R
O
Y
G ave
B irth
I n
V enice

I prefer Roy G Biv

I assume steven means vain, as opposed to fighting in a blood vessel