[goal is legibility,
 and distinctive when necessary.]

nutshell
text     board
text     italic print
bold     bbb
fraktur  cursive
calligraphic  calligraphic (but cal rare)

- first, use italic!
(notes from "formatting": Getty-Dubay)

- bold
done as blackboard bold:
double the left stroke (either line, or add a line to C etc.)
Used for: fields, projective and affine space (other?)

what about vectors?
some typeset vectors with bold; use an over-arrow -> at the board
(an over line is an abbreviation), though this is a bit confusing.
More advanced, you can drop the arrow:
u,v,w always mean a vector.

- calligraphic
  Rarely used; roman generally fine.
$\cC^\infty$ (in Rudin), but many prefer $C^\infty$

- fraktur (it's a specific Germanic style)
btw, it actually is alien: $\fr\fx$?
[mostly for Lie algebras and for ideals]

This requires a calligraphic pen to write;
if you want to be proper, you should use a German 
Kurrentschrift or Sütterlinschrift;
I have seen Sütterlin used for $\gl$.

With a normal pen, I use an angular style to emphasize,
as it's usually only for occasional letters,
and my script is legible.
[Very deliberate, angular version of my italic hand.
points:
- all horizontals become upward diagonal, e.g.:
  a, etc.
- flourishes on i, l
  (and b, h, k, r, t; and m,n; and u, y)
  (lower flourish pretty accurate; upper not)
- hook on c, f, r (else a bit lop-sided)
- m, n most successful
- some are a bit tricky:
  v a bit silly,
  | |
  |/   ...works (no flourish or tail; u has both)
  
  s is a bit bare, x and z is already angular (flourishes help)
 ]
(I previously used convex letters, which works ok for
 g and p, but not for l)

You can also just use cursive!
(hey, it's just for emphasis!)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Definitions:
- underline for emphasis, especially *definitions*
I had a teacher who used small caps for definitions,
  (and that's the only use of small caps at the black board that I've seen)
which the typographist in me liked, but I don't find practical.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Other scripts:

- Hebrew

This is very rarely used;
mostly just $\aleph$ in logic.

- Cyrillic
I've seen this used for *one* example: the Shafarevich group
is denoted with a capital sha.

NB: fraktur, Hebrew and Cyrillic are *foreign* scripts.
If you use (traditional) German cursive or Hebrew cursive,
readers will be completely lost.
Cursive aleph is particularly illegible.

"""
some examples are cyrillic variants of GCD (greatest common divisor)
and SCM (smallest common multiple) which are denoted with cyrillic
letters; projection operator in geometry (in russian literature);
people use cyrillic letters in mathematical formulae in some
non-strictly mathematician sciences (e.g. economics); there are some
stable usages of cyrillic letters in physical notations (in russian
texts). but there are also established cases when cyrillic letters are
used internationally in strictly mathematical publications -
e.g. Shafarevich groups in algebraic geometry are often denoted with
capital cyrillic letter sha - not only in russian literature!
"""
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for the love of god, use italics
(you likely will anyway)

pen & chalk:
. Black Board Bold = double left line
(shouldn't be used in texts! Serre's with me on this.)
. fraktur; I make it angular, with LL -> UR strokes [e.g., m, n] (inc.
flourishes: 'i, l')
[this isn't authentic; also did some concave]

ideally, use calligraphic chalk:
turn on side for bold, fraktur
(yes, this is slow, but part of point of chalkboard is to slow you down)

tilt chalk at angle, so thicker stroke

no longer a big issue; much bigger in past
...but mathematicians do lots of writing!
[never seen mathematician using calligraphic pen or brush;
 4-color pen (or I prefer: a few pens) ok, but rarely useful.]

for running text, eventually looks like usual handwriting;
italic is good! (no cursive)

block paragraphs at board bad: use handout for that;
use layout!

NB: on gradually written / to-be-modified things:
warn people, and give space!

*textura* is a bad aesthetic

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Brief notes on math typography style:
- math face and body should agree
  (as should display/headers, obviously)
  Math fonts are rarer, so generally pick that first.
  Some combos:
  - Computer Modern
  - Palatino and Euler (my favorite: Zapf!)
  - Concrete Modern and Euler
  - Lucida
  - Times and Math Roman
- use bold for definitions and headings,
  as people are likely to look 'em up
  Use italics for other emphasis.
  Don't use underline.
- \mathbb is an abomination
  Black-board bold is used at the board b/c bold is hard to draw;
  in type, just use bold!
  (yes, I grant that bbb is kinda cute)
