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Tips for Mathematical Handwriting (2007)

johnkerl.org

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Re: Tips for Mathematical Handwriting (2007)

#61

Post by wenc »

supernova87a wrote: post #27

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 take your point but there are downsides to restricting oneself to only Roman letters. In a few fields I've been a student of, there's a bias against introducing Greek letters. The downside is one does run out of letters. Eventually one needs Greek letters if one wants to not communicate in an amateurish manner -- either that, or one is forced to use multi-letter variables like "Eff", "Density", which are somewhat unwieldy, especially in complex expressions.

Also some Greek letters have such a strong conventional association with certain quantities that using Roman letters in their place can be more obfuscating, e.g. ρ = density, Δ = change, η = efficiency, θ = parameter, σ = standard deviation, μ = mean, τ = time constant, etc.

Notation is to some extent a function of a community's conventions.

Re: Tips for Mathematical Handwriting (2007)

#62

Post by mynegation »

coopsmgoops wrote: post #14
mynegation wrote: post #6

"Put a loop on the capital O so it doesn’t look like a zero" I do no put loops on O's, but to this day I have a habit of writing a stroke (in forward slash direction) inside zero.

But now it looks like a Theta!

My printed or cursive thetas have horizontal or tilde like bar in the middle.

Re: Tips for Mathematical Handwriting (2007)

#63

Post by sidpatil »

jks wrote: post #41
kmill wrote: post #37

Earlier quoted context omitted.

For my first encounter with lowercase xi, I was sure the professor was taking advantage of his tenure and trying to pass off a scribble as a variable, and that was with my having made a point to familiarize myself with the Greek alphabet the previous semester. Somehow I don't remember him bothering to pronounce it! Then there are the German algebraists who developed ring theory, for whom Greek letters were not suffic…

Apparently set theorists weren't satisfied with Greek, Fraktur or blackboard bold, so they use (at least) aleph and beth from Hebrew.

I wish we used more Cyrillic characters in math, just to keep things varied.

Re: Tips for Mathematical Handwriting (2007)

#64

Post by mnl »

supernova87a wrote: post #27

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…

It's just that at some point you run out of letters, having some 35 glyphs more just comes in handy. Very much so if you have indices for different spaces.

Notation shouldn't be a problem if it's compact enough. Then the bra-ket one is foolproof and not too many physicists study functional analysis proper, so it makes sense to simply follow Dirac there.

Re: Tips for Mathematical Handwriting (2007)

#65

Post by bluenose69 »

In my teaching, I tend to write a lot of Greek letters on the board. Students from physics and mathematics are comfortable with this and can make out my squiggles easily. To make things easier for students coming from biology, I write out the names of the symbols, the first few times I use them. This helps a lot, because they are not just unfamiliar with the symbols, but also the words I use when I talk about them.

Another thing I do is to pronounce symbols in both the Greek and the American ways. That helps them in other classes, because where I teach, the professors are about evenly divided in their pronunciation.

PS. my squiggles are basically identical to those in the article under discussion here.

Re: Tips for Mathematical Handwriting (2007)

#66

Post by Xophmeister »

My cursive “x” looks quite similar to my cursive “n”. In my Real and Abstract Analysis exam, IIRC, I remember writing a limit expression, as n goes to infinity, that involved no “x” variable. The professor read it as an “x”, despite the context, and promptly marked it incorrect. It taught me to make my handwriting unambiguous, but I’m still bitter about this, some 15+ years later :P

Re: Tips for Mathematical Handwriting (2007)

#67

Post by ploika »

lonelappde wrote: post #52
phorkyas82 wrote: post #35

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.

Different things work for different people. The opposite to your approach worked much better for me.

Sitting and thinking would only allow so much to sink in, and then I'd have none of my own notes to work off later. Instead I'd furiously transcribe by hand everything the lecturer said, everything written on the blackboard/slides (very often not the same thing) and add in my own notes on top too.

Understanding would come much later, over a much longer period than an hour-long lecture.

Re: Tips for Mathematical Handwriting (2007)

#68

Post by pbhjpbhj »

_0ffh wrote: post #36
c3534l wrote: post #30

When I went back to school I had to take math again, which wasn't my best subject in school. I was determined to figure out why I could understand the material, yet consistently never quite did as well as I thought I should have on tests. So I kept a journal of every mistake I made so I could categorize them and understand them. Most of the mistakes were very specific handwriting mistakes, but they were very particul…

>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.

Re: Tips for Mathematical Handwriting (2007)

#69

Post by buescher »

supernova87a wrote: post #27

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…

Zeta takes some practice to make legible. Michael Covington's sheet on how to write Greek letters, while oriented towards linguists and language learners, is very clear and aesthetically appealing: http://www.covingtoninnovations.com/pens/#GREEK

Re: Tips for Mathematical Handwriting (2007)

#70

Post by pbhjpbhj »

macintux wrote: post #60
diffeomorphism wrote: post #45

Earlier quoted context omitted.

> but also always horribly written by students/teachers, and made it even more incomprehensible. Honest question: why does the horribly written matter at all? For all intents and purposes the symbol could be a smiley face or a little drawing of a tree. Indeed, in a freshman course you sometimes have at least one worksheet using trees,cars,stars, apples to make this point. As long as the smiley on page 1 and the smile…

Some (maybe most) people find it easier to remember and comprehend things they can vocalize, so using an inscrutable character, even consistently, can cause problems.

Greek letters have simpler vocalisations than "c4" or whatever, though?!

This relates to internal vocalisation, a subject on HN a couple of times recently, as I don't really do that (particularly for equations) then it was never an issue for me. Though at 15 I learnt the Greek alphabet as I was into physics, that probably helped.

People who need to vocalise to read, and don't bother learning (or coming up with) a vocalisation are going to find it very difficult.

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