Wayne Aitken

Professor of Mathematics
California State University, San Marcos
waitken@csusm.edu

Research Interests

Algebraic number theory (and other aspects of algebra and number theory),
Foundations of mathematics (and related philosophical and historical issues) especially new approaches to the paradoxes ("algorithmic logic"),
Finite fields (especially sets of values of algebraic mappings),
Arithmetical algebraic geometry (and related areas of geometry and algebraic topology).

Teaching Interests

Number theory (all types),
History of mathematics,
Abstract algebra,
Mathematical logic,
Geometry (including basic algebraic geometry and algebraic topology, as well as the foundations of Euclidean and hyperbolic geometry).

List of recent courses

Publications: Algorithmic Logic

One of my interests is in the foundations of mathematics. On the basis of this work I am currently an affiliated faculty for the Logic and Philosophy of Science (LPS) Department, at the University of California, Irvine.

(with Jeff Barrett)
Computer implication and Curry's paradox
Journal of Philosophical Logic (2004)

(with Jeff Barrett)
Stability and Paradox in Algorithmic Logic
Journal of Philosophical Logic (2006)

(with Jeff Barrett)
Abstraction in algorithmic logic
Journal of Philosophical Logic (2008)

(with Jeff Barrett)
A note on the physical possibility of ordinal computation
The British Journal for the Philosophy of Science (2010)

Publications: Number Theory and Finite Fields

I am a number theorist by training and I continue to have a strong interest in all thing number theoretic.

(with Franz Lemmermeyer)
Counterexamples to the Hasse principle
American Mathematical Monthly (Fall 2011).

(with Farshid Hajir and Christian Maire)
Finitely ramified iterated extensions
International Mathematics Research Notices (2005)

(with Mike Fried and Linda Holt)
Davenport pairs over finite fields
Pacific Journal of Mathematics (2004)

An explicit sign formula for the determinant of cohomology
Communications in Algebra (1999)

Total relative displacement of permutations
Journal of Combinatorial Theory, Series A (1999)

On value sets of polynomials over a finite field
Finite Fields and Their Applications (1998)

(with E Okamoto, G. R. Blakely)
Algebraic properties of permutation polynomials
IEICE Transactions on Fundamentals of Electronics, Communications, and Computer Science (1996)

Book: An arithmetic Riemann-Roch theorem for singular arithmetic surfaces
Memoirs of the American Mathematical Society (1996)

(with E Okamoto, G. R. Blakely, P. F. Stiller)
Simple permutation ciphers using permutation polynomials
International Symposium on Information Theory and Its Applications (1994)

(with E Okamoto, G. R. Blakely, I. Borosh)
Properties of permutation polynomials
The 17th Symposium on Information Theory and Its Applications (1994)

An arithmetic Riemann-Roch theorem for singular arithmetic surfaces
Doctoral Dissertation, Harvard University (Advisor: Barry Mazur)

Lecture Notes and Other Things of Interest

Fermat's Proof
(An essay about a proof that Fermat did manage to fit in his margin)

Legendre's Theorem, Legrange's Descent
(classic results on second order Diophantine equations)

Lagrange (1769), Sur la solution des probl�ms ind�termin�s du second degr�
(Select pages for now)

Linear Algebra (Modified Moore method approach)

Foundation of Geometry

History of Mathematics Handouts

Basic Definitions of Algebra (Reference for second semester algebra)