# Distinguishing script letters from regular letters in handwritten mathematics

What is a good handwriting font for mathematics? addresses handwriting on a board. How do you clearly distinguish script letters, such as $\mathcal{ABCDEFG}$, from regular letters $ABCDEFG$ in handwritten mathematics?

Edit: Since posting this question, I have discovered How to write \mathcal letters by hand? on MSE and Andrew Stacey's article: Old Pappus' Book of Mathematical Calligraphy, although his main example is how to write a Fraktur $\mathfrak{g}$.

I always give this piece of advice to my students: only use letters that you can distinguish yourself. (Some people really don't do this unless told so.) When you teach, apply the same more strictly: only use letters that most students can distinguish. This includes avoiding using $v$ and $\nu$ in the same context. If you run out of letters, use something else: overlines, underlines, accents... Or just use different letters for different things.

I make my curly letters more curly than the regular ones, but this distinction is not always easy. If my students (or I myself) seem to have hard time following, I change my notation. Script letters should never be absolutely necessary.

• Your last remark that "script letters should never be absolutely necessary" has prompted me to ask a new question on the advantages of using script letters.
– J W
Sep 20 '14 at 10:32
• Maybe are not necessary, but often highly desirable, e.g. when one has a number of corresponding concepts, like $a$, $A$, $\mathcal{A}$ and $\alpha$ which are all related in the same way as $b$, $B$, $\mathcal{B}$ and $\beta$. Of course, you can use things like $\aleph$ or $A'$, $A_2$, $\check{A}$, but in my experience accents and indexes are not as good as calligraphic letters: after some time the results become messy (after you have to use forward indexes like ${}^i_j{}\tilde{A}^*_l$, you know you should refactor). A good solution to this is to use names like $\cos$, $\mathrm{diam}$, etc. Aug 23 '16 at 6:47

If you have a clear handwriting on board (if you don't, forget about calligraphic letters and use diacritics instead) you can "invent" your own calligraphic set of letters for blackboard. It just has to be clearly distinguishable from your normal one, e.g. like this:

• look at the top left corner of the capital letter
• if it is a corner (B,D,E,F,P,R), make it an arc instead
• if it is a line cap (H,I,J,K,L,T,W,Z), add an arc to it
• if it is an arc (C,G,O,Q,S), make it a corner instead
• if it is skipped (A), make it a corner insteadn
• for X and Y make the line from the top left corner a downward arc
• add a swoosh to the U (or don't use it, because it to easily gets confused with V, Y and the normal variants)
• make both lines of the V inward arcs (or don't use it)

So, except for V and U (and X and Y) the letters are easily distinguishable and the rules are fairly simply.