> Put a hook on the x to distinguish it from a times sign
This is counterproductive IMO, because it makes it look like a chi. (The article notes the problem.) That seems more likely to cause issues than the possible ambiguity with the “times” symbol (“×”). If you need a multiplication symbol, use the middle dot (“·”) instead.
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 Sweden, with scalars, we used vertically centered dot, but even that is pretty uncommon since most of the time, two letters or a letter and a number are mixed and then it is left it out altogether.
There’s an old joke about “mathematical maturity” meaning being able to write a lowercase zeta, but I took enough classes from professors that would confuse xi and zeta that it probably doesn’t matter that much.
This is a good resource, and pretty much what I tell students in my classes. I take great care to explain how to write symbols, and I also give multiple pronunciations of the Greek letters.
Students with math and physics backgrounds are fine with Greek letters and other mathematical symbols, but the biologists in the class are mystified. They also get terribly confused when I reuse symbols for different purposes.
What I've discovered is that the students who have trouble with mathematical notation and reasoning got derailed when a teacher, in an early grade, said "let x be the unknown". That is a phrase that never comes up in other contexts, and I think it throws them off track. Many find it difficult to get back on-track later, so they memorize and sleep-walk their way through other mathematics classes until the system no longer insists that they take them. A shame, really.
> 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?
> Personally I find it hard to internalise canonical notation. Like f and F in probability theory, which is which again?
Probability theory's notation isn't very canonized. The typical usage, f for PDF and F for CDF, is easy to remember from the calculus notation of uppercase being an integral of the lowercase.
> I imagine that there are various triggers of early mathematical derailment
I have come to believe that the main trigger by far is the attitude of society. Of parents, family, friends, tv stars, heck even many (non math) teachers. "I wasn't good at math haha" is such a standard phrase to hear, and parents telling their kids that they don't need to worry if they "don't get it" as if it's some mystical topic that only a few gifted can unlock. Plus the uncool stigma attached to "math nerds", folks who simply have an open mind to try to "get it", turns out that it isn't actually that hard. At least when talking high school math or some basic college classes.
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
This is famously how Maryam Mirzakhani worked as well. Huge thick A2 sheets where she doodled and did computations; she said she disliked the cramped style of normal notebooks.
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 assume most middle school teachers specify how papers should be organized in binders and labeled with names, dates, etc; but below was my method I developed halfway through college:
Top Margin use: left - name, center - class, right - date
One binder per semester; a divider for each class; handouts, tests, etc were hole-punched and placed with my notes in chronological order.
If my notes didn't make sense as I was copying down what the professor did, I would rewrite my notes later that day while figuring the problem-solving process out and making the notes/arithmetic easier to follow.
This method also applied to non-math-related classes.
Agreed. I did a pure math degree where most of my classes involved copying down 2-3 pages of axioms/proof per lecture, and I settled on mead letter size college ruled spiral notebooks, and yellow note pads for scratch work. Wide ruled led to too much wasted space, graph paper was visually busy and led to awkwardly spaced letters, dot paper just didn't really work. Smaller paper sizes didn't end up holding enough information per page, spiral binding was best for being able to rip out and toss pages, the perforation was nice for the occasional hand in sheet, and I had no need for a nicer quality paper.
Also I always kept Pentel Twist Erase III mechanical pencils with 0.5 mm lead, Hagoromo chalk, and a 4 color set of chunky expo markers in my bag.
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.
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.
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.
I like squares because they allow me to align things vertically.
This is especially useful when maintaining two margins to write in as well as for indenting, blockauotes, or sometimes maintaining parallel lists or columns.
that's right with mechanical pencils written on a proper writing surface with plenty of arm/elbow space with real erasers for completely removing noise from mistakes.
It's incredible to realize how many of the habits mentioned in this post that I've unintentionally picked up while studying applied math. Even after graduation, I still follow a lot of these 'conventions'.
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?
When I was growing up in Bulgaria my first 7 (I would write the 7 crossed by default for example, the Z as well) grades were in a school where we learned German (and Russian as a secondary foreign language) and I remember distinctly handwriting practice in German using more or less the same ways outlined in this article. Is this way of writing cursive not common in the US/UK?
Reading Greek is easy for _most_ Bulgarians (inventors of Cyrillic if you didn't know that) as you can imagine. Them being a geographical neighbor and the close historical ties etc.
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.
Cyril and Methodius didn't create Cyrillic. That's a very common misconception. They created the Glagolitic[1] alphabet which was a precursor script. Cyrillic was developed later by their students and other scholars in the Preslav Literary School[2]. They named it Cyrillic to honour the brothers, but the brothers themselves didn't create Cyrillic.
EDIT: Sorry, I misread what you wrote. It's late and it's been a long day. You weren't saying the brothers created Cyrillic. As for whether they were Greek/Bulgarian I cannot say. I've read different opinions on that throughout the years. Definitely Byzantine, but anything else I cannot say.
Your snark comment is out of place since if you knew something about Cyrillic you'll know that most letters have 1:1 mapping with their Greek counterparts. And since Bulgarian language does use Cyrillic the jump to Greek is quite short. You could argue that there's a bigger difference in pronunciation of letters between English, German and French which all use the Latin alphabet than between Cyrillic and Greek.
Readit News
This is counterproductive IMO, because it makes it look like a chi. (The article notes the problem.) That seems more likely to cause issues than the possible ambiguity with the “times” symbol (“×”). If you need a multiplication symbol, use the middle dot (“·”) instead.
No one in the target audience is using × for scalar multiplication.
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.
Anyway, I usually use simple cross as x, because it's only very rarely confused with cross product (and you can always parenthesize).
× is the cross product.
• is the dot product.
In dimensions higher than 1, they are different.
This made the x problem much smaller.
There’s an old joke about “mathematical maturity” meaning being able to write a lowercase zeta, but I took enough classes from professors that would confuse xi and zeta that it probably doesn’t matter that much.
Students with math and physics backgrounds are fine with Greek letters and other mathematical symbols, but the biologists in the class are mystified. They also get terribly confused when I reuse symbols for different purposes.
What I've discovered is that the students who have trouble with mathematical notation and reasoning got derailed when a teacher, in an early grade, said "let x be the unknown". That is a phrase that never comes up in other contexts, and I think it throws them off track. Many find it difficult to get back on-track later, so they memorize and sleep-walk their way through other mathematics classes until the system no longer insists that they take them. A shame, really.
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?
Probability theory's notation isn't very canonized. The typical usage, f for PDF and F for CDF, is easy to remember from the calculus notation of uppercase being an integral of the lowercase.
I have come to believe that the main trigger by far is the attitude of society. Of parents, family, friends, tv stars, heck even many (non math) teachers. "I wasn't good at math haha" is such a standard phrase to hear, and parents telling their kids that they don't need to worry if they "don't get it" as if it's some mystical topic that only a few gifted can unlock. Plus the uncool stigma attached to "math nerds", folks who simply have an open mind to try to "get it", turns out that it isn't actually that hard. At least when talking high school math or some basic college classes.
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.
Or make it \varrho (ϱ).
> Keep the slash in the phi vertical; keep the slash in the empty-set symbol slanted.
Again, \varphi (U+1D711 which HN doesn’t seem to like) is easier to distinguish.
The author silently chose \varepsilon in their TeX, but chose to ignore the rest of the variants.
My grammar school math teacher used a very large ascender for the alpha, almost into serif-£-sign-without-the-line-through territory.
In Sweden you were expected to use paper with squares but it adds a lot of clutter.
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
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.
https://www.amazon.com/Tops-Engineering-Computation-Punched-...
I assume most middle school teachers specify how papers should be organized in binders and labeled with names, dates, etc; but below was my method I developed halfway through college:
Top Margin use: left - name, center - class, right - date
One binder per semester; a divider for each class; handouts, tests, etc were hole-punched and placed with my notes in chronological order.
If my notes didn't make sense as I was copying down what the professor did, I would rewrite my notes later that day while figuring the problem-solving process out and making the notes/arithmetic easier to follow.
This method also applied to non-math-related classes.
Blank paper is too... Blank! And I'm more prone to write big and messy and waste pages (even though it's all digital)...
Also I always kept Pentel Twist Erase III mechanical pencils with 0.5 mm lead, Hagoromo chalk, and a 4 color set of chunky expo markers in my bag.
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.
Here is an example, 4 different dot sizes:
http://trondal.com/p1.pdfhttp://trondal.com/p2.pdfhttp://trondal.com/p3.pdfhttp://trondal.com/p4.pdf
You need to print them to see which one is suitable.
This is especially useful when maintaining two margins to write in as well as for indenting, blockauotes, or sometimes maintaining parallel lists or columns.
When I was growing up in Bulgaria my first 7 (I would write the 7 crossed by default for example, the Z as well) grades were in a school where we learned German (and Russian as a secondary foreign language) and I remember distinctly handwriting practice in German using more or less the same ways outlined in this article. Is this way of writing cursive not common in the US/UK?
Reading Greek is easy for _most_ Bulgarians (inventors of Cyrillic if you didn't know that) as you can imagine. Them being a geographical neighbor and the close historical ties etc.
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".
[1]: https://en.wikipedia.org/wiki/Glagolitic_script
[2]: https://en.wikipedia.org/wiki/Preslav_Literary_School
EDIT: Sorry, I misread what you wrote. It's late and it's been a long day. You weren't saying the brothers created Cyrillic. As for whether they were Greek/Bulgarian I cannot say. I've read different opinions on that throughout the years. Definitely Byzantine, but anything else I cannot say.
Tips for Mathematical Handwriting (2007) - https://news.ycombinator.com/item?id=32665846 - Aug 2022 (2 comments)
Tips for Mathematical Handwriting (2007) - https://news.ycombinator.com/item?id=22983274 - April 2020 (76 comments)