Math 403/603 Foundations of Math
Format for Quiz Problems
Overview. Formal mathematical
writing is the primary means by which mathematical knowledge is
organized, shared, and preserved. New discoveries are often
initially presented orally at conferences and in small groups, but
without a formal written record, this knowledge will quickly be
forgotten. A major goal of this course is to give students
with mathematical writing, which involves some special notational and
formatting conventions. For each quiz problem you are asked
to prepare a careful formal solution following the
guidelines on this page. This sort of writing will be referred to
as Polished Work. The
and formatting conventions should already be familiar: they are almost
always followed in mathematics textbooks.
problem should begin on its own page. The left margin should be
at least 3 inches wide for me to write comments. Also leave white
space between paragraphs for the same purpose. Each polished
problem should begin with a
complete statement of the problem (which will often be a proposition to
prove), as well as a problem and section number (or something similar
for extra problems that do not come from the text). You
organize your work by proving lemmas that you can cite in the main
In this case, each lemma should have a clear statement and proof
from the main question.
either be handwritten or prepared with word processing software.
Word processing has some advantages: revisions and corrections are
easier to produce, and the finished product is easier to read.
But if you are inexperienced using word processing software for
mathematical writing, a hand written approach may be faster, at least
initially. Each student is asked to use software for at least
some of the work in his or her portfolio, so that one outcome of the
course will be a familiarity with this approach to mathematical
writing. More information about word processing software appears
Mathematical writing follows the usual rules of grammar, including the
use of complete sentences, organization into paragraphs, correct
punctuation and capitalization, etc. In addition, there are a few
conventions that are specific to mathematics:
The industry standarrd for writing in
mathematics and several other technical fields is LaTeX, and its
variants. Two share-ware packages for LaTeX are Lyx and Miktex,
and there may be others.
Although I am pretty familiar with LaTeX
, I know very little about these particular packages. Learning to
use some version of LaTeX is probably worthwhile for math majors, and
you may wish to experiment with this type of system. But it is
not required and should not distract you from the primary objectives of
- (Using word processing software) Variables should
be italicized, or for vectors,
set in bold typeface;
- Mathematical equations and inequalities may be
included in symbolic form (although, when read aloud, they should make
sense in the context of the surrounding material);
- Equations, inequalities, and expressions may
either appear in-line within the surrounding text, or may be displayed
on separate lines. Displayed lines should be centered on the page, and
may be numbered for reference. Follow the format of the textbook
- All writing should appear in either normal
paragraph formatting or centered displayed lines of mathematical
symbols, but not a combination. Do not introduce unusual
- Feel free to include tables or figures if
appropriate. These can be formatted as on pages 6 and 100 of the
text, with a label and/or caption. This is usefule when one
problem solution includes more
than one table or figure, and you want a way to refer to a specific
figure. But sometimes no label or caption is needed, and you can
refer to the the figure below or above without any confusion.
- Do not use mathematical symbols as
shorthand. For example, do not insert a ∃ in a sentence
to mean there exists and do
not use arrows as a substitute for words. Logical symbols
generally only permitted as part of symbolic portrayals of formal
logical propositions. The logical symbols
of and subset of
are permitted within
running text though as a general rule, such
should appear only as part of a larger complete mathematical
Thus, it is permitted to write "Suppose n ∊ ℤ" but not "Suppose n ∊ the integers." The 'word' iff is a permitted contraction of if and only if.
Another option is to use MS Word, which includes an equation
editor for formatting complicated mathematical expressions.
In my 2010 version of Word, I start the equation editor by selecting an
option from the insert menu, as shown below.
Something similar should work for newer
versions of word. Once you have the equation editor open, with a
experimentation you will see how to create mathematical
expressions. Feel free to ask me for assistance with
this. If you use word, you can manually italicize variables
and use font properties to create subscripts and exponents that appear in the running text.
For anything more complicated than that, you should use the equation
editor, either in-line or centered on a separate line.
Samples. Here is a sample quiz problem written by hand, with
annotations in red to highlight the format and style. Here is one produced by word processing software,
with annotations in yellow boxes.