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Book Review

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Book Information:

Authors: G. Pólya and G. Szegö
Title: Problems and theorems in analysis
Additional book information: Die Grundlehren der math. Wissenschaften, Springer-Verlag, Berlin and New York; Vol. I, 1972, xix + 389 pp., Vol. II, 1976, xi + 391 pp., $45.10.

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

  • 1. J. D. Tamarkin, Pólya and Szegö's, Problems in analysis, Bull. Amer. Math. Soc. 34 (1928), 233-234.
  • 2. G. Pólya, How to solve it, 2nd ed., Princeton Science Library, Princeton University Press, Princeton, NJ, 1988. A new aspect of mathematical method. MR 1090087
  • 3. G. Pólya, Mathematics and plausible reasoning. Vol. I, Princeton University Press, Princeton, NJ, 1990. Induction and analogy in mathematics; Reprint of the 1954 original. MR 1109055
  • 4. G. Pólya, Mathematical discovery, Wiley, New York, Vol. 1, 1962, xvii + 216 pp.; Vol. 2, 1965, xxv + 213 pp. MR 171671
  • 5. M. N. Aref and W. Wernick, Problems and solutions in euclidean geometry, Dover, New York, 1968, xiii + 258 pp. [Mostly elementary and routine, but a little interesting material on triangles, circles, and space geometry near the end.]
  • 6. J. D. Dixon, Problems in group theory, Blaisdell, Waltham, Mass., xii + 175 pp. [For supplementing a first serious course in group theory. Maybe 75% exercises, 25% problems.]
  • 7. Otto Dunkel and E. P. Starke, Problems and Solutions: Advanced Problems: Solutions: 3957, Amer. Math. Monthly 49 (1942), no. 1, 64–68. MR 1525335,
  • 8. D. K. Faddeev and I. S. Sominskiĭ, Problems in higher algebra, Freeman, San Francisco, Calif., 1965, ix + 498 pp. [This collection is about 95% painfully routine exercises, but the remaining 5% contains some nice stuff. The solutions leave much room for improvement.] MR 176990
  • 9. H. Hadwiger, H. Debrunner, and V. Klee, Combinatorial geometry in the plane, Holt, New York, 1964, ix + 113 pp. [An outstanding collection of modern problems.] MR 164279
  • 10. K. Knopp, Problem book in the theory of functions II, Dover, New York, 1952, 138 pp. [A good collection of interesting exercises and problems for second and third semester courses in classical function theory. (Vol. I is rather elementary.)] MR 55435
  • 11. J. G. Krzyz, Problems in complex variable theory, American Elsevier, New York, 1971, xix + 283 pp. [For supplementing a regular course. Mostly exercises, but some real problems.] MR 447533
  • 12. Ya. I. Rivkind, Problems in mathematical analysis, Noordhoff, Groningen, ca 1965, v + 98 pp. [Meant to supplement real variable courses; mostly routine on the hard side.] MR 157880
  • 13. D. O. Shklarsky, N. N. Chentzov, and I. M. Yaglom, The USSR Olympiad problem book, Freeman, San Francisco, Calif., 1962, xvi + 452 pp. [An outstanding collection of problems on elementary mathematics.] MR 157882
  • 14. W. Sierpiński, 250 problems in elementary number theory, American Elsevier, New York, 1970, vii + 125 pp. [About half routine, half challenging problems, a few quite challenging.] MR 269580
  • 15. G. Szász et al., Contests in higher mathematics, Hungary 1949-1961, Akadémiai Kiadó, Budapest, 1968, 260 pp. [A collection of highest quality.] MR 239895
  • 16. A. M. Yaglom and I. M. Yaglom, Challenging mathematical problems with elementary solutions, Holden-Day, San Francisco, Calif.; Vol. I: Combinatorial analysis and probability theory, 1964, ix + 231 pp.; Vol. II: Problems from various branches of mathematics, 1967, xi + 214 pp. [A collection of outstanding problems at the U. S. university level.]

Review Information:

Reviewer: Harley Fanders
Journal: Bull. Amer. Math. Soc. 84 (1978), 53-62
American Mathematical Society