Bulletin of the American Mathematical Society

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.

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

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

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.]

Otto Dunkel and E. P. Starke, Problems and Solutions: Advanced Problems: Solutions: 3957, Amer. Math. Monthly 49 (1942), no. 1, 64–68. MR 1525335, DOI 10.2307/2303792

D. K. Faddeev and I. S. Sominskii, Problems in higher algebra, W. H. Freeman and Co., San Francisco-London, 1965. Translated by J. L. Brenner. MR 0176990

Hugo Hadwiger and Hans Debrunner, Combinatorial geometry in the plane, Holt, Rinehart and Winston, New York, 1964. Translated by Victor Klee. With a new chapter and other additional material supplied by the translator. MR 0164279

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

Jan G. Krzyż, Problems in complex variable theory, Modern Analytic and Computational Methods in Science and Mathematics, No. 36, American Elsevier Publishing Co., Inc., New York; PWN—Polish Scientific Publishers, Warsaw, 1971. Translation of the 1962 Polish original. MR 0447533

Ya. I. Rivkind, Problems in mathematical analysis, P. Noordhoff, Scientific Publishers, Groningen, 1963. Translated by Scripta Technica, Inc. MR 0157880

D. O. Shklarsky, N. N. Chentzov, and I. M. Yaglom, The USSR Olympiad problem book. Selected problems and theorems of elementary mathematics, W. H. Freeman and Co., San Francisco-London, 1962. Revised and edited by Irving Sussman; translated by John Maykovich. MR 0157882

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

Contests in higher mathematics (Hungary, 1949–1961), Akadémiai Kiadó, Budapest, 1968. 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. 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.]

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, Princeton Univ. Press, Princeton, N. J., 1945, vii + 224 pp. MR 1090087

3.

G. Pólya, Mathematics and plausible reasoning, Princeton Univ. Press, Princeton, N. J., 1954; Vol. 1: Induction and analogy in mathematics, xvii + 280 pp.; Vol. 2: Patterns of plausible inference, xi + 190 pp. 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.

H. Eves and E. P. Starke, The Otto Dunkel memorial problem book, Amer. Math. Monthly 64 (1957), v + 89 pp. [A selection of "best" Monthly problems, with a high proportion of outstanding material.] 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.]