Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
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.

References [Enhancements On Off] (What's this?)

  • 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. Aviezri S. Fraenkel and Yaacov Yesha, The generalized Sprague-Grundy function and its invariance under certain mappings, J. Combin. Theory Ser. A 43 (1986), no. 2, 165–177. MR 867643,
  • 9. A. S. Fraenkel and Y. Yesha, Complexity of problems in games, graphs and algebraic equations, Discrete Appl. Math. 1 (1979), no. 1-2, 15–30. MR 544387,
  • 10. M. Gardner, Mathematical games, a column in Scientific American.
  • 11. Richard K. Guy, Combinatorial games, Handbook of combinatorics, Vol. 1, 2, Elsevier Sci. B. V., Amsterdam, 1995, pp. 2117–2162. 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
American Mathematical Society