If you find a mistake, omission, etc., please let me know by e-mail.

• Zermelo's theorem, and generalizations to many other games (what exactly is Zermelo using about Chess)?
• what can ``slight advantage'' or ``strong move'' etc. mean in light of Zermelo's theorem?
• Exhaustive ``retrograde'' analysis (an example of ``dynamical programming'') to determine perfect play; variations: computer databases (with 4, 5, 6, or most recently 7 units on the board, per Moore's Law), corresponding squares (Ebersz), other games (Connect Four: completely solved; checkers: getting closer...)

September 25: Introduction to chessboard combinatorics

• The bipartite Knight (knight cocliques and tours, etc.)
• That eight Queens Problem, and other maximal (co)clique questions
• Domination numbers
• Enumeration of maximal cocliques and minimal dominating configurations in some other cases

October 9 (Columbus Day): Introduction to enumerative chess problems and some of the mathematics and computational techniques they lead to

• Binomial coefficients; a series problem with Binomial(14,5)=2002 solutions; sum over k of Binomial(n,k) and Binomial(n,k)² (Interlude on ``proof games'' a.k.a. helpgames)
• A position with Fibo[N] solutions in N moves (Interlude on sextupled pawns etc.)
• Catalan numbers; the Bonsdorff-Väisäinen serieshelpmate in 14 with C₇=429 solutions; R.Stanley's extension to a serieshelpmate in 34 with C₁₇=129644790 solutions
• Updates: Size and enumeration of maximal Bishop co-cliques and minimal Bishop domination on square boards, and of Kings on even-odd boards; minimality of the 12-Knight domination on 8x8 board.

October 16: Introduction to various genres of chess problems and notions of soundness, and how to adapt the ``Zermelo'' approach to obtain them. Also: follow-up on enumeration problems (how many walks of length N on a path of length k?); the Grasshopper; Bettmann's selfmate Babsontask; some other problem variants (series-movers, reflex, maximummer).

October 23: Computational complexity and other asymptotic issues
(also: problem twins etc.)

October 30: Combinatorial game theory; transfer matrices and some enumerative applications

November 6: Root-of-unity tricks for counting paths on cycles, and the connection with earlier transfer-matrix stuff;
the knight hypercube;
Richard Stanley's guest lecture on series-helpmate queue problems

November 13: Some preliminary progress reports on final projects;
The use of definite integrals to count linear extensions of finite posets (used in Stanley's talk);
Kasteleyn's permanent-determinant method for enumerating domino tilings of a rectangle
(interlude: the sign of a permutation, and Loyd's 15 puzzle)

November 20: More progress reports;
An illustration of Erdös-style probabilistic argument: exponential lower bound on the Ramsey number R(n,n);
Problem exotica: three- and fourfold combinative separation, Schrödinger's Cat mates in 2 (a.k.a. partial retrograd analysis), Buchanan's ``Dead Reckoning'' and recent proof game, mutant castling, Circe;
Trying to make a long one-sided proof game;
Pfun with Pfaffians (introduced by enumerating matchings in graphs that are planar but not necessarily bipartite) and exterior algebra

November 27: More progress reports;
A classic cross-check problem and a recent Tamerlane's Cage problem (directmates in 2 and 4 respectively);
Transfer matrices, cont'd: rational generating functions (interlude: the power-series form of the binomial theorem, e.g. Binomial(-1,n) = (-1)ⁿ)

Dec.4: More progress reports;
A few conditional chess problems: Rook may not move except to mate, K + Q + capped pawn vs. K, mate with K+Q without moving K;
Interlude: the opposition, and Putnam problem B4;
Linear programming

Dec.11: More progress reports;
Interludes on 163 and friends, on Fritz and the finer points of the triple-repetition rule, on progressive chess, on addition chains, and on the physical limits of computing.

Dec.18: More progress reports;
Also: two classic retroanalytic miniatures, and the return time of finite Markov chains.

Jan.8: Final reports