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Tips for Mathematical Handwriting (2007)

johnkerl.org

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Re: Tips for Mathematical Handwriting (2007)

#71

I'm of mixed feelings about all the Greek letters used in physics, math, etc. Eventually (after years of hard learning how to understand the underlying equations physically) I got over the hurdle of them always instantly making any equation more complicated and hard to understand -- and instead seeing them as just constants that could be basically ignored for most of the procedure (in many settings). I do still feel…

I think it's mostly an artifact of mathematicians using a single letter for variables. (Which one could also argue against.) Certain variables pick up a conventional meaning, and one quickly runs out of letters.

It's pretty common in physics to use subscripts to label variables, like m-sub-e for mass of an electron, say.

Re: Tips for Mathematical Handwriting (2007)

#72

I wish we'd been taught this in high school. One habit I did learn in high school is writing x as two 'c' shapes in a mirror image. This is clearly an x rather than a multiplication symbol. I prefer it to the version listed in the article. I find it hard to distinguish the author's X/χ

X written as )( is the absolute worst. It always looks like two parenthesis when I'm grading student writing and I have no idea how to parse what they write.

Do you grade that lack of distinction and teach the student a better orthography? Obviously x is a single symbol that's joined in the middle, so with proper orthography it would seem to be better than using a × as an x?

What's your subject?

Re: Tips for Mathematical Handwriting (2007)

#73
post #36

Earlier quoted context omitted.

>my solution to the letter O is just to never, ever use them in math That seems reasonable. My solution was to slash my zeros, to the point that it takes conscious effort not to.

How do you visually differentiate nulls from zeroes? That's what stopped me from slashing my zeroes, I've considered dotting them, but it's not relevant for me anymore. I slash my 7s though, and form my 1 like that character, I don't miss off the up-tick. Primarily nowadays I'm writing on a tablet and need to be very precise to make it readable.

>How do you visually differentiate nulls from zeroes?

My zero is a continuous line, starting top right and angling sharply left-down after a ~360° oval. That nicely makes it writable in one fluid motion.

My null/empty set is a somewhat smaller circle and a separate slash starting and ending visibly outside the circle.

Re: Tips for Mathematical Handwriting (2007)

#74

I'm of mixed feelings about all the Greek letters used in physics, math, etc. Eventually (after years of hard learning how to understand the underlying equations physically) I got over the hurdle of them always instantly making any equation more complicated and hard to understand -- and instead seeing them as just constants that could be basically ignored for most of the procedure (in many settings). I do still feel…

I had one professor in university who called lowercase xi “squiggle” and wouldn’t make much effort to draw it properly. He would talk about, for example, “d squiggle d t,” and so on.

The advantage of a xi is that it looks nothing like an x so coordinate transformations (xi = f(x), tau = f(t)), are easier to keep track of.

Re: Tips for Mathematical Handwriting (2007)

#75
post #40

I'm of mixed feelings about all the Greek letters used in physics, math, etc. Eventually (after years of hard learning how to understand the underlying equations physically) I got over the hurdle of them always instantly making any equation more complicated and hard to understand -- and instead seeing them as just constants that could be basically ignored for most of the procedure (in many settings). I do still feel…

To write the lowercase xi and zeta, I imagine that I am looping around the horizontal bars in the corresponding uppercase letters, and they tend to come out approximately right. I remember a Greek-born colleague writing the uppercase Omega as just an underlined letter O. I suppose that shape is probably the idea behind the flourishes in the typeset Omega.

I found it disproportionately mindblowing realizing omega and omicron are literally "big o" and "little o."

Re: Tips for Mathematical Handwriting (2007)

#76

Reminds me of my first analysis professor. He managed to explain the proofs while writing them with chalk on the blackboard, all equations nice an clean like the Latex in our scripts - while we struggled to keep up with his pace, was impossible for us to copy it all. He came across a bit dry, overstructured, exact, but also kind and humble - maybe like you imagine a German mathematician.

Don't waste time in lecture taking notes. Pay attention and think. Save your rote copying for homework time.

> "Pay attention and think"

Not everyone can.

As someone who left numerous classes early, because confusion & anxiety over the lecture caused vomiting or diarrhea, I promise you I would have given everything to just be able to "pay attention and think."

Re: Tips for Mathematical Handwriting (2007)

#77
I have somewhat strong opinions on this. I uploaded a similar set of symbols here: https://imgur.com/a/gKJ3KO2

I’ve added notes in red, some baselines in blue and some lines at x-height in yellow.

I want to point out a few things:

1. OP misses out the need for script and blackboard bold letters and various symbols. You want them to not be confused with letters. In particular U and set union, epsilon and set membership, and oplus and capital theta.

I think OP’s eta looks wrong. Too much like an m.

One trick to use is that letters can have ascenders and descenders. Numbers can too but I don’t use that. I also incorrectly write a rho as a letter with an ascender and no descender to help to distinguish it from a p. I also try to impart a big curve at the top so you won’t think there could be the top of a straight line hidden in there.

I draw the top of a tau just below x-height while the bar on a t is somewhat above it. This and the rest of the t being higher helps to disambiguate.

Never use an o (“oh”) or omicron and probably not upsilon either (I missed out capital upsilon because OP did too and I didn’t notice). An exception is big/little O notation but I don’t really like it.

I don’t like OP’s q. It looks too much like a double bowled g. I prefer a tick to a loop.

I tend to not have issues with 2 vs z but I do with nu vs v. I kinda dislike using nu because of it. In print I have trouble with v vs u.

I often use variant letters for some Greek letters (in particular my epsilon is what TEX calls varepsilon because it is more like handwriting and less like a print font. Similarly for theta kappa, and phi. I don’t use varpi which looks too much like an omega, cardigan which is only really to go on the end of a word in Greek, varrho because I don’t like it, and I don’t write capital omega the modern Greek way (a horizontal line with a circle above it).

Other tricky symbols are: Angle brackets vs lt/gr. Usually context suffices. Angle brackets vs parens: just don’t rely on this distinction.

Or vs v can and union vs U can usually be solved by context and spacing (you have a bigger space between a term and an operator than between factors or arguments in a term)

A final note is that I tend to write mathematics more upright than my normal handwriting. This helps distinguish inline mathematics from the rest of a sentence.

I looked through some random old notes to see if I could still read my writing and I can. The only thing I struggled with was the script C for conjugate classes because I was missing the context and struggling to guess what ccl stood for. At first I thought it was a script G.

Having written this, I realise I omitted forall, exists, nabla/del, integral sign, partial sign, therefore dots, infinity, approxequal and hbar.

A final note is that spoken names matter to o. “Twiddle” is a much better name than “tilde” because it is more naturally made into a verb. You can say “define the relation twiddle on the naturals such that a twiddles b if ...” and then you can easily use that verb when talking through a proof of eg transitivity.

Re: Tips for Mathematical Handwriting (2007)

#78
post #28
post #16

Earlier quoted context omitted.

at some point in math you'll never use x for times/multiplication -- you'll always use a dot, unless you're specifically doing a cross product. And that is a good stage to reach. (I still have trouble using x for multiplication though.)

> you'll always use a dot No, often you will use nothing - simple juxtaposition.

Which leads to simple mistakes: http://zerooutoffive.blogspot.com/2008/10/1n-sin-x_21.html

Re: Tips for Mathematical Handwriting (2007)

#79
I can tell the design is ad-hoc. There is a science to manual writing, the author appears to be unaware of it (I guess by virtue of being born into an English speaking nation which afaict never saw fit to follow other ones who had already developed relevant standards in the 1960s). I see a couple improvements so that the proposal falls more in line with those standards:

1 should have an upstroke.

0 should have a loop, dot or stroke, not O.

q descender should have a stroke, not a loop.

9 should have a round bottom.

g descender should have a loop.

Latin letters should be written in script form, not block letter form, notably: ℰ, 𝒢, ℐ, 𝒥, ℒ, 𝒴, not E, G, I, J, L, Y.

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