Tips for mathematical handwriting (2007)

I make my x's with a backwards c and a c, like Computer Mondern and lots of fonts https://i.ibb.co/8LPsJKsj/image.png - doesn't look much like a chi or a times sign

No one in the target audience is using × for scalar multiplication.

I think it's important to consider audience. If I'm working with the intent that what I write is legible to folks who only have a basic understanding of math, I'll usually use the multiplication symbol (NOT the letter x, but ×, intentionally in the middle). Someone with more advanced knowledge of math, who may be more inclined to think it's an x, because my handwriting is shit, I will typically use the dot operator. But then there's the whole other audience where I need to define what the dot operator does. At that point, I'm probably pulling up something like LaTeX, because, again, my handwriting sucks.

Funnily enough, when I write for the purpose of math, my numbers are more legible than when I just write down a number. For some reason, I code switch in my handwriting. Kinda obnoxious when I'm filling out forms.

In the handwriting I learned, x had hooks on all four ends, while greek chi only on two.

Anyway, I usually use simple cross as x, because it's only very rarely confused with cross product (and you can always parenthesize).

Depending on the context, dot and times may have different meanings.

The article alludes to this when it mentions Calculus 3 (vector calculus):

× is the cross product.

• is the dot product.

In dimensions higher than 1, they are different.

I think the two example images are actually the same. (I've always done an italic X.)

I can't remember the last time I actually wrote a times sign.

i center the x times sign.

Meanwhile I always liked this one, even though it’s not specifically focussed on mathematics: https://foundalis.com/lan/hw/grkhandw.htm

> got derailed when a teacher, in an early grade, said "let x be the unknown"

I don't have the experience to know myself, but I imagine that there are various triggers of early mathematical derailment. It would be interesting to see a list of common causes.

Personally I find it hard to internalise canonical notation. Like f and F in probability theory, which is which again?

I found this little pocket mathematics notation book when I first studying undergrad in this used book store in Boston. it literally carried me through Calc, Linalg, stats, dynamic programming, stochastic processes, game theory, economics, etc.

I ended up copying it by hand along with every exam and test notes over my entire degree into one little moleskine notebook. its a god send any time I have to remember how to do something or learn something new.

There are two other phis with the (non-mathematical) Greek letters earlier, but unfortunately fonts vary in which one they display as \phi or \varphi: φ (U+03CD), ϕ (U+03DC).

I was once taking a real analysis class and there was a very gifted student in my class. She pulled out her notebook one day at a study session and I noticed it was kind of unusual - the pages were very large, and made of a somewhat thicker material, with a slightly rougher texture. Ink also seems to set onto its surface slightly nicer, and it doesn't really bleed through onto the other side either.

She explained to me that it was actually a kind of notebook specifically for artists, and that she much preferred it to the normal plain paper notebooks you typically get.

I bought one myself, and I had to agree with her - it was a much 'nicer' experience to write on it - diagrams could be way less cramped, branch out without hitting the edges. The tactile feedback due to the thickness of the paper was also nice - in a way, it felt like the "mechanical keyboard" of paper notebooks.

Never switched back again after that, and many people I work with have found it curious and nice to work with too.

Part of me feels that there may be more than just a gimmick to this. In the way that it's been shown that pen and paper help for understanding versus typing, I wonder if "the niceness of the pen and paper experience" would have an additional tangible positive effect, too

I used plain for a few years but it has some problems. I now use faint lined paper. Usually Muji notebooks. I leave a blank line between each statement. The lines are handy if you want to make something readable and well aligned which is fairly important. Scans fine.

My kids were forced to use heavily marked blue squared paper. They had problems writing and reading. I pointed this out to their mathematics teacher and said that it may be detrimental and got a diatribe of “what do you know”. Such a bad attitude. I had an answer to this which was embarrassing to him.

I've gone through so many phases on this. But lately, the more writing intensive my math classes get, I've settled on lined paper.

Blank paper is too... Blank! And I'm more prone to write big and messy and waste pages (even though it's all digital)...

I switched to plain white when I was ca 20 years old and never looked back. I need to use plain white since then and I am so used to it that I find lines or grids slightly offensive to me and it throws me off from layouting. You can get used to anything.

Pencil boards can help. An example: https://www.jetpens.com/Hobonichi-Accessory-Pencil-Board-for...

Grid or lined, placed underneath thinner blank paper (heavier paper won't let the lines or grid show through as easily, if at all). Keeps the final presentation neat while giving the structure you may need to keep things aligned.

I agree. However, I have had some good experience using weakly dotted paper for math. Then it is easier to draw graphs by hand.

Here is an example, 4 different dot sizes:

http://trondal.com/p1.pdf http://trondal.com/p2.pdf http://trondal.com/p3.pdf http://trondal.com/p4.pdf

You need to print them to see which one is suitable.

Squares are pointless unless you're drawing graphs, but lines are very handy to have. Without lines my writing moves on an angle and the size of everything becomes inconsistent and usually too large.

You can always do dot grid paper.

> I find these quite interesting and I would be very surprised if these were not the actual common way of writing in cursive learned in school?

With the version I learned in the US in the late 90s, mostly not: https://en.wikipedia.org/wiki/D%27Nealian#/media/File:D'Neal...

The "z" in particular with the crossbar wasn't a thing for any version of writing I learned, and they're missing the leading/trailing tails for most of their versions of the lowercase letters. Even in printing - I learned to write an "l" as a vertical line with a tail to the right, so it's different from 1 or I without a cursive loop.

Funny enough in "digits" section: "Put a loop on the 2 so it doesn’t look like a z" - The looped version is identical to a cursive uppercase "Q".

ISTR the origin of Cyril and Methodius (the two monks that created the precursor to the cyrillic alphabet, can't remember the exact name of that alphabet ATM) cannot be pinpointed as either Greek or Bulgarian because no such documentation has been found. They surely were Byzantine, though.

playing oboe is easy for _most_ Frenchs (inventors of the oboe if you didn't know that)

I never used to cross my zeros until I was spending some time writing a lot of diagrams that had both O (for oxygen) and 0 (for the numeric label). It got very confusing!

I started crossing the Z in college because I was tired of messing things up because I confused a Z for a 2. I only crossed the 0 when Os showed up and it could be confusing. Similarly my 1s would get the hat and feet if I felt like it wasn't clear what it was.

I can't say I ever had trouble with y and 4 looking the same. I use the open 4 but the y has one less angle and it sits lower. If anything a y is more likely to look like a v if you can't see the descender clearly

I always cross my zs in maths to distinguish them from 2s, but in some countries they cross the 2s to distinguish them from zs, so the ambiguities remain.

I started crossing Z, 7, 0 and generally writing in as unambiguous a manner as possible in my math homework because I was afraid of the teacher reading it wrong and taking points off.

To avoid mixing up zeroes with the empty set or phi, simply put a dot inside of them instead of crossing them. Many fonts do that.

\times denotes the cartesian product (to my knowledge) universally. If 3rd-semester calculus is when you introduce a general definition of continuity (I am not from the US, wouldn't know how the programs usually work there) on either metric or topological spaces, the cartesian product starts to appear quite a lot I guess ?

The \times sign is × in latex. To get • you use \cdot.

IIRC at university-level we used the wedge symbol [0] for cross product - not sure how common that is.

https://en.wikipedia.org/wiki/Wedge_(symbol)

The × sign is also used for the Hartesian product, which comes up often when building up Lebesgue integration.