Mathematical Notes:
The following are a listing of unpublished notes I have written on
on various mathematical subjects related to theoretical computer
science.
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Strings
and StringsofStrings Various notions of the intuitive concept of
a string are employed in computer science. In this note we look at one
that we have found to be especially useful. Namely the notion of a string
of length n over as a set A as a mapping s:{1,...,n}>A. We define the
corresponding category of strings, Str, and examine its properties.
Then, in the second part of the note. we look at the special case where
the set A is itself the set of strings over some other set. We define
the category,
SStr, of stringsofstrings and (yet to come) some
of its applications in computer science.

Notes
on Birkhoff's Theorem Birkhoff's theorem is a famous theorem of algebra
proved by Garret Birkhoff in 1935. It provides a useful characterization
of algebraic varieties, that is, of equationally specifiable classes of
algebras. These notes provide a short review of the basic definitions of
universal algebra, a proof of Birkhoff's theorem, an analysis of the proof
and some examples of classes of algebras that fail to satisfy all
the requirements of the theorem.

More to Come!