Suggested notation for the QWERTY keyboard: Writing Mathematics in
email, or in a word-processor which does not provide mathematical symbols:
Prof. Jonathan L.F. King, Mathematics Dept, University of Florida
FOR GRADUATE STUDENTS: At some point, you should learn the
math-typesetting language called "TeX" (Tau, Epsilon, Chi). There are
two common dialects: "plain" TeX and LaTeX (which is particularly well
adapted for writing books). (A third dialect, AMSTeX (sponsored by
the American Mathematical Society), has now become a package that can
be used inside of LaTeX.)
It appears that LaTeX is the best supported, and so that is my
suggestion. Below, I use "TeX" to mean either of TeX/LaTeX.
NOTATION: What follows are conventions from TeX, slightly modified.
(You don't have to use them. You may instead hand-write in symbols,
or you may make up a "Notation sheet" using your own conventions. In
any case, ALL YOUR DIAGRAMS MAY BE HAND-DRAWN!)
Let x_1 mean "x subscript 1" and x^2 mean "x superscript 2".
Eg. 3^2 equals 9.
TeX uses, alas, braces {} for grouping. Thus you would write "x sub
twenty-three" as x_{23} and "R sub (n sub 2)" as R_{n_2}. This is
slightly inconvenient, since we also like to use braces for sets, e.g,
the singleton {3}
and the set {x | 3 < x < 5} .
Fortunately, I expect that I can guess from context if you are using
braces as mathematical symbols, or as TeX grouping-parentheses.
The TeX "escape" character is "\". Thus \gamma means the Greek
letter gamma, and \Gamma means uppercase Gamma. Here are other
symbols:
y \in X means "y is an element of X".
X \ni y (or X \owns y) means "X owns y", i.e, y \in X.
A \subset X "A is a subset of X".
A \subsetneqq X "A is a proper subset of X".
X \supset A "X is a superset of A", "X includes A".
X \supsetneqq A "X is a proper superset of A", "X properly includes A".
\emptyset "The empty set".
\infty The symbol "infinity" , oo.
\int is used to mean "integral". Thus \int_2^{b+1} f(x) dx
means "the integral from 2 to b+1 of f(x) times dx".
Here are some TeX symbols that one can define (these appear in my
macro files) which you may use.
\reals "The set of reals".
\rationals "The set of rationals".
\integers "The set of integers".
\ep An abbr. for the longer \epsilon.
\ii An abbr. for the longer \infty.
\cap or \inter for intersection, e.g, "A \inter B".
\cup or \union for union, e.g, "A \union B".
For the large union/intersection operators, write
\Union_{n=1}^\ii A_n is the union, as n goes from 1 to infinity,
of sets A_n. Similarly,
\Inter_{n=1}^\ii A_n is their intersection.
The names for the large summation and product operators are \sum and
\prod. So
\sum_{n=1}^\ii (1/2^n) = 1 and
\prod_{n=1}^\ii (n/(n+1)) = 0.
I use "A \setdiff B" for the difference set "A minus B", and use
"A \symdiff B" for their symmetric difference.
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