(Freshman Seminar 23j: Chess and Mathematics, Spring [2005-]2006)

We shall explain in the seminar how such databases are created; here is one early (1979) explanation in English. [In EG (Roycroft's EndGame monthly), "*C*" means computer-related material, and "GBR class 0103" is Rook vs. Knight -- and in turn GBR stands for Guy, Blandford, and Roycroft, creators of the GBR code for chess endings and diagrams.]

**More game reconstruction puzzles.**
Francois
Labelle's ``Chess Problems by Computer'' contains many remarkable
results and example of game reconstruction puzzles obtained by
exhaustive computer search. There are also many remarkable puzzles
with entirely unique solutions, some of which you can find on the Web
by asking Google for ``proof games". (For an explanation of why they're
called ``proof games'', see the entry on ``Legal position''
in the chess glossary
for the Seminar.

**Chess and combinatorial game theory.**
Here are links to my
first
and
second
articles on chess positions that illustrate and can be explained by
the combinatorial game theory of *Winning Ways* (see below).

**The mathematical knight**:
an article by Richard Stanley and myself
that appeared in the ``Mathematical Recreations'' section of the
*Mathematical Intelligencer*, Vol.25 (2003), #1, pages 22-34.
We'll cover much of this material in the course of our seminar.
You can download the paper as either a
PostScript or a
PDF document;
unfortunately neither format looks perfect on the computer screen,
but at least the .ps should print correctly on a PostScript printer.

D. Hooper, K. Whyld: *The Oxford Companion to Chess*,
2nd ed. (1992) (Hollis #002646059, WID-LC GV1445 .H616 1992);
1st ed. (1984) (Hollis #000254071, WID-LC GV1445 .H616 1984).

This is a wonderful one-volume encyclopedia; particularly good for us are the extensive treatment and well-chosen illustrative examples for chess terminology from Alfil to Zugzwang. I put both editions on reserve because they give different examples for the same terms.E.R. Berlekamp, J.H. Conway, R.K.Guy:

The canonical reference for the ``combinatorial game theory'' invented by the three authors. For the most part we'll use material from the first part of Volume 1.J. Levitt, D. Friedgood:

A pioneering discussion of the esthetics of chess, particularly of chess problems/studies.J. Morse:

Note particularly the last few chapters, which address tasks such as ``What's the longest Mate-in-N problem in which White has only the King and one Pawn?''. Mate-in-2 specialists will also learn a lot from the first dozen or so chapters. Some of the records have been since superseded, but Morse has published periodic updates inT. Krabbé:The Problemist; copies of these updates will also be on reserve at the library.

For the most part this is not directly connected with our Seminar topics, but directed at similar sensibilities. For instance, some actual games in which one player castled after move 40. (For more along these lines, see Krabbé's chess site; for instance, the castling records and many others such as a 269-move game are on this page .)