Book Review

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Book Information:

Author: J. H. Conway

Title: On numbers and games

Additional book information: Academic Press, London, New York, San Francisco, 1976, ix + 238 pp., $26.50.

Author: D. E. Knuth

Title: Surreal numbers

Additional book information: Addison-Wesley, Reading, Massachusetts, 1976, 119 pp.

**1.**A. V. Aho, J. E. Hopcroft and J. D. Ullman,*The design and analysis of computer algorithms*, Addison-Weslcy, Reading, Mass., 1974. MR**413592****2.**E. R. Berlekamp,*The Hackenbush number system for compression of numerical data*. Information and Control 26 (1974), 134-140. MR**354140****3.**E. R. Berlekamp, J. H. Conway and R. K. Guy,*Winning ways*, a book estimated to appear in 1978.**4.**J. H. Conway,*All numbers great and small*, Univ. of Calgary Math. Res. Paper #149, 1972.**5.**J. H. Conway,*All games bright and beautiful*, Amer. Math. Monthly 84 (1977), 417-434. (Essentially the same as Univ. of Calgary Math. Res. Paper #295, 1975, which has the same title.) MR**446534****6.**A. S. Fraenkel and Y. Perl,*Constructions in combinatorial games with cycles*, Colloquia Mathematica Societatis János Bolyai 10: Proc. International Colloquium on Infinite and Finite Sets, Keszthely, Hungary, 1973 (A. Hajnal, R. Rado, V. T. Sós, eds.), Vol. 2, North-Holland, Amsterdam, 1975, pp. 667-699. MR**384171****7.**A. S. Fraenkel and Y. Yesha,*Theory of annihilation games*, Bull. Amer. Math. Soc. 82 (1976), 775-777. MR**449726****8.**A. S. Fraenkel and Y. Yesha,*The generalized Sprague-Grundy function and its invariance under certain mappings*(to appear). MR**867643****9.**A. S. Fraenkel and Y. Yesha,*Complexity of problems in games, graphs and algebraic equations*(to appear). MR**544387****10.**M. Gardner,*Mathematical games*, a column in Scientific American.**11.**R. K. Guy,*Partizan and impartial combinatorial games*, Univ. of Calgary Math. Res. Paper #315, 1976. Shortened version to appear in Proc. Colloq. Internat. C.N.R.S., Paris, 1976. MR**1373699****12.**R. K. Guy and C. A. B. Smith,*The G-values of various games*, Proc. Cambridge Philos. Soc. 52 (1956), 514-526. MR**82408****13.**S.-Y. R. Li,*Sums of Zuchswang games*, J. Combinatorial Theory Ser. A 21 (1976), 52-67. MR**426869****14.**E. M. Reingold, J. Nievergelt and N. Deo,*Combinatorial algorithms: Theory and practice*, Prentice-Hall, Englewood Cliffs, N. J., 1977. MR**471431****15.**C. A. B. Smith,*Graphs and composite games*, J. Combinatorial Theory 1 (1966), 51-81. MR**194362****16.**T. J. Schaefer,*Complexity of decision problems based on finite two-person perfect-information games*, Eighth Annual ACM Symposium on Theory of Computing (Hershey, Pa., 1976), pp. 41-49, Assoc, Comput. Mach., New York, 1976. MR**451853****17.**C. P. Welter,*The theory of a class of games on a sequence of squares, in terms of the advancing operation in a special group*, Nederl. Akad. Wetensch. Proc. Ser. A 57 = Indag. Math. 16 (1954), 194-200. MR**60512**

Review Information:

Reviewer: Aviezri S. Fraenkel

Journal: Bull. Amer. Math. Soc.

**84**(1978), 1328-1336

DOI: https://doi.org/10.1090/S0002-9904-1978-14564-9