List of Literature

This is a short list of literature which can be useful to understand the mathematical content of the site, and to be able to query the database freely via SQL statements.

Symbolic Dynamics

Ole Lund Jensen, Symbolic dynamic systems and their invariants, Master Thesis, University of Copenhagen, July 2002.

My Master Thesis documenting the mathematical aspects of this site. It is available as DVI, PDF, and PS file.

 

Douglas Lind and Brian Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, Cambridge, 1995.

A very thorough book on the theory of symbolic dynamic systems, and my primary source on the subject.

 

Ole Lund Jensen and Eik Kristensen, Strong shift equivalence of 2×2 matrices, Fagprojekt, University of Copenhagen, July 2000.

An earlier work Eik Kristensen and I made together concerning many of the same issues, but at a smaller scale. There is also developed database and web site for this project, and the URL is http://www.math.ku.dk/ma/kurser/symbolskdynamik/.

 

R. F. Williams, Classification of subshifts of finite type, Ann. Math. 98 (1973), 120–153; Errata, ibid. 99 (1974), 380–381.

The famous paper, where Williams "showed" that strong shift equivalence and shift equivalence is the same, and the Errata where he admitted, that the proof was not correct and stated the correctness as a conjecture.

 

Kirby A. Baker, Strong shift equivalence of 2×2 matrices of nonnegative integers, Ergodic Theory and Dynamical Systems 3 (1983), no. 4, 501–508.

In this article Baker gives an algorithmic proof, that if two positive integral 2×2 matrices with nonnegative determinant are similar, then they are strong shift equivalent.

General algebra

Michael Artin, Algebra, Prentice Hall, Englewood Cliffs, New Jersey, 1991.

A beginners book on algebra, introducing all major objects such as groups, rings, fields, modules, vector spaces, a.s.o.

 

I. Kaplansky, Infinite Abelian groups, University of Michigan Press, Ann Arbor, 1954.

The title speaks for itself.

Number Fields

Henri Cohen, A course in computational algebraic number theory, Graduate Texts in Mathematics, no. 138, Springer-Verlag, Berlin, Heidelberg, 1993.

This book introduces all the major aspects of number theory, and the main aspect is to give algorithms for computing purposes in practice.

 

Z. I. Borevich and I. R. Sharfarevich, Number Theory, Pure and Applied Mathematics, no. 20, Academic Press, 1966.

A very thorough book about number theory in general.

Programming

C. J. Date, An introduction to database systems, sixth ed., The Systems Programming Series, Addison-Wesley Publishing Company, Inc., 1995.

A general book on databases, which among a lot of other things introduces the general SQL language, and E/R diagrams.

 

MySQL, http://www.mysql.com

The homepage of the free MySQL database server, which documentation pages I have frequently used.

 

H. M. Deitel and P. J. Deitel, C++ how to program, second ed., Prentice Hall, Upper Saddle River, New Jersey, 1998.

A beginners book on how to program in C++