Book Review

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MathSciNet review: 1567019

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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.

**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.**George Pólya,*Mathematical discovery. On understanding, learning, and teaching problem solving. Vol. I*, John Wiley & Sons, Inc., New York-London, 1962. MR**0171671****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**, https://doi.org/10.2307/2303792**8.**D. K. Faddeev and I. S. Sominskii,*Problems in higher algebra*, Translated by J. L. Brenner, W. H. Freeman and Co., San Francisco-London, 1965. MR**0176990****9.**Hugo Hadwiger and Hans Debrunner,*Combinatorial geometry in the plane*, Translated by Victor Klee. With a new chapter and other additional material supplied by the translator, Holt, Rinehart and Winston, New York, 1964. MR**0164279****10.**Konrad Knopp,*Problem book in the theory of functions. Vol. II. Problems in the advanced theory of functions*, Dover Publications, Inc., New York, N. Y., 1953. Translated by F. Bagemihl. MR**0055435****11.**Jan G. Krzyż,*Problems in complex variable theory*, American Elsevier Publishing Co., Inc., New York; PWN—Polish Scientific Publishers, Warsaw, 1971. Translation of the 1962 Polish original; Modern Analytic and Computational Methods in Science and Mathematics, No. 36. MR**0447533****12.**Ya. I. Rivkind,*Problems in mathematical analysis*, Translated by Scripta Technica, Inc, P. Noordhoff, Scientific Publishers, Groningen, 1963. MR**0157880****13.**D. O. Shklarsky, N. N. Chentzov, and I. M. Yaglom,*The USSR Olympiad problem book. Selected problems and theorems of elementary mathematics*, Revised and edited by Irving Sussman; translated by John Maykovich, W. H. Freeman and Co., San Francisco-London, 1962. MR**0157882****14.**W. Sierpiński,*250 problems in elementary number theory*, Modern Analytic and Computational Methods in Science and Mathematics, No. 26, American Elsevier Publishing Co., Inc., New York; PWN Polish Scientific Publishers, Warsaw, 1970. MR**0269580****15.***Contests in higher mathematics (Hungary, 1949–1961)*, In memoriam Miklós Schweitzer. Editorial Board: G. Szász, L. Gehér, I. Kovács and L. Pintér. Manuscript revised by P. Erdös, A. Rényi, B. Sz.-Nagy and P. Turán. Linguistically revised by B. Balkay, Akadémiai Kiadó, Budapest, 1968. MR**0239895****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

DOI: https://doi.org/10.1090/S0002-9904-1978-14405-X