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.

**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**, https://doi.org/10.2307/2303792**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

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