SixWingedSeraph

Who

Charles Wells. Currently living in Minnesota, USA.

Background

Professor Emeritus of Mathematics, Case Western Reserve University. I taught there for about 35 years, with sabbatical interruptions at ETH Zürich (in math) and Oxford University (in computing science). I have had a research career in mathematics in finite fields, group theory and category theory. In the last twenty years I have also been interested in the language of mathematics and related issues concerning teaching and communicating abstract ideas.

Web Presence

Gyre&Gimble Blog on the language of math, category theory, and teaching abstract ideas.

AbstractMath.org Website for university-level math students.

CWRU website. Research papers and other info.

Books

Michael Barr and Charles Wells, Toposes,Triples and Theories (revised edition), Reprints in Theory and Application of Categories, 12, 2005.

Michael Barr and Charles Wells, Category Theory for Computing Science, Reprints in Theory and Application of Categories, 221999.

Charles Wells, "A Handbook of Mathematical Discourse", 2003.

Papers

(with L. Carlitz) The number of solutions of a special system of equations over a finite field (1966), Acta Arith. 12, 77-8.

Groups of permutation polynomials, Monatsh. Math. 71 (1967), 248–262.

Generators for groups of permutation polynomials over finite fields, Acta Sci. Math. Szeged 29 (1968), 167–176.

Automorphisms of Group Extensions Transactions of the AMS (1970).

Some applications of the wreath product construction, American Mathematical Monthly 83 (1976), 317-338.

Centralizers of transitive semigroup actions and endomorphisms of trees, Pacific Journal of Mathematics 64 (1976), 165-271.

Extension theories for monoidsSemigroup Forum (1978)

Extension theories for categories(unpublished) (1980)

A Krohn-Rhodes Theorem for categories, Journal of Algebra 64 (1980), 37-45.

A triple in Cat, Proceedings of the Edinburgh Mathematical Society 23 (1980), 261- 268.

The formal description of data types using sketches (with Michael Barr). In M. Main et al, ed., Mathematical Foundations of Programming Language Semantics. Lecture Notes in Computer Science 298. Springer-Verlag (1988).

Wreath product decomposition of categories I and II. Acta Sci. Math. Szeged 52 (1988), 307-319 and 321-324.

A Generalization of the Concept of Sketch Theoretical Computer Science (1990)

A formalism for the specification of essentially-algebraic structures in 2-categories (with A. J. Power). Mathematical Structures in Computer Science 2 (1992), 1-28.

On the limitations of sketches Canadian Math Bulletin (1992)

Sketches: Outline with references February, 1994 printing (unpublished) (1994)

Communicating Mathematics: Useful Ideas from Computer Science American Mathematical Monthly (1995)

(with Atish Bagchi) Varieties of Mathematical Prose PRIMUS (1997)

(with Atish Bagchi) Communicating Logical Reasoning PRIMUS (1998)

(with Atish Bagchi) Graph Based Logic and Sketches arXiv(2008)

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