Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Tips for Mathematical Handwriting (2007)

johnkerl.org

Post reply on HN
Print view View original

41–50 of 79 posts

Re: Tips for Mathematical Handwriting (2007)

#41

Post by jks »

kmill wrote: post #37
filmor wrote: post #33

Earlier quoted context omitted.

I don't get the issue. It's just notation. You could "feel" the same way about the integral sign or fractions or about underused letters in your own alphabet. When the greek letters are used, they usually give you a clear indication that they are "something different" from the things written. It's much either to understand that alpha, beta, gamma, delta are some counterpart to a, b, c, d than if you had to use i, j,…

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.

Re: Tips for Mathematical Handwriting (2007)

#42

Post by anonytrary »

h-cobordism wrote: post #25
anonytrary wrote: post #12

Loop your l's, and cross your sevens and your z's to avoid confusing them with ones and twos. Exaggerate the differences between your i's and your j's by looping your j's. Curve the base of your t's to avoid confusing them with f's. Math is a lot harder to do when you cannot distinguish your variables from each other and numbers.

And also make sure to distinguish between your pi's and your n's! I can't count the number of times I've mixed the two up while finding Fourier coefficients.

This is why I exaggerate the pi's top cross (like a capital T with two legs). A lot of people write pi in a way such that the top cross has no dangling edges[0]. I always try to exaggerate the unique features of symbols. One can avoid a lot of these problems by first exhausting the least overlapping symbols.

[0] See left variant: https://pm1.narvii.com/6331/cb50e106b141735ad714b934eb18ea55...

Re: Tips for Mathematical Handwriting (2007)

#43

Post by adiabatty »

throwawaysea wrote: post #18

Do we need everyone to memorize these guidelines or do we need an alphabet that is designed to be naturally distinguishable despite stylistic differences? I feel like with cursive and handwriting focus going out of style, it isn’t practical to expect convention to be followed more strictly than it already is(n’t).

Since my penmanship isn't all that great, I use quite a few of these guidelines when I'm writing out math problems. At any rate, you can ignore a lot of them if, like most people, all you need is A-Za-z0-9πθ+.

Re: Tips for Mathematical Handwriting (2007)

#44

Post by huffmsa »

My biggest gripe in school and now isn't legibility, but wondering if the professor / author is using his Greek letters as some magic, universal constants or just throwing them in as variables because it's "convention". Spend more time hunting down context and the "With {} as {}" section than understanding the equation.

Re: Tips for Mathematical Handwriting (2007)

#45

Post by diffeomorphism »

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…

> 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 smiley on page 3 look the same you are fine.

Same for mu, nu, kappa, rho. They could just be written as C1,C2,C3,C4, but it makes it much easier to read when you use the Greek letters, because you can be reasonably certain that for example rho has something to do with a density (while C4 tells you nothing).

Re: Tips for Mathematical Handwriting (2007)

#46

Post by MaxBarraclough »

filmor wrote: post #33
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 don't get the issue. It's just notation. You could "feel" the same way about the integral sign or fractions or about underused letters in your own alphabet. When the greek letters are used, they usually give you a clear indication that they are "something different" from the things written. It's much either to understand that alpha, beta, gamma, delta are some counterpart to a, b, c, d than if you had to use i, j,…

Just notation? I don't see that it's a trivial matter, any more than good writing is trivial. I'm reminded of a recent HackerNews thread on Why is Maxwell's theory so hard to understand?

https://news.ycombinator.com/item?id=22812969

Re: Tips for Mathematical Handwriting (2007)

#47

Post by vitus »

gjvnq wrote: post #32
rahimnathwani wrote: post #3

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

In my school we always used a middle dot (· U+00B7) for multiplication since 6th grade.

That works great until the note that \times returns for cross product, curl, and cartesian product.

(And in both cross product and curl, if you substitute a \cdot, then that's an entirely different operation!)

Re: Tips for Mathematical Handwriting (2007)

#48

Post by patrickthebold »

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 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.

Re: Tips for Mathematical Handwriting (2007)

#50

Post by lonelappde »

mbeex wrote: post #28
kaitai wrote: 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.

At which point it becomes ambiguous with function application.
Post reply on HN