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The following are a listing of unpublished  notes I have written on on various mathematical subjects  related to theoretical computer science.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 Strings-of-Strings 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 strings-of-strings and (yet to come) some of its applications in computer science.

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• 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.

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• More to Come!