Problems and Theorems in Analysis. Volume II: Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry (Classics in Mathematics) (v. 2) [Paperback]

George Polya (Author), Gabor Szegö (Author), C.E. Billigheimer (Translator)

Book Description

ISBN-10: 3540636862 | ISBN-13: 978-3540636861 | Publication Date: November 10, 2004

Few mathematical books are worth translating 50 years after original publication. Polyá-Szegö is one! It was published in German in 1924, and its English edition was widely acclaimed when it appeared in 1972. In the past, more of the leading mathematicians proposed and solved problems than today. Their collection of the best in analysis is a heritage of lasting value.

Editorial Reviews

Review

From the reviews: "... In the past, more of the leading mathematicians proposed and solved problems than today, and there were problem departments in many journals. Pólya and Szego must have combed all of the large problem literature from about 1850 to 1925 for their material, and their collection of the best in analysis is a heritage of lasting value. The work is unashamedly dated. With few exceptions, all of its material comes from before 1925. We can judge its vintage by a brief look at the author indices (combined). Let's start on the C's: Cantor, Carathéodory, Carleman, Carlson, Catalan, Cauchy, Cayley, Cesàro,... Or the L's: Lacour, Lagrange, Laguerre, Laisant, Lambert, Landau, Laplace, Lasker, Laurent, Lebesgue, Legendre,... Omission is also information: Carlitz, Erdös, Moser, etc." -Bull.Americ.Math.Soc.

About the Author

Biography of George Pólya Born in Budapest, December 13, 1887, George Pólya initially studied law, then languages and literature in Budapest. He came to mathematics in order to understand philosophy, but the subject of his doctorate in 1912 was in probability theory and he promptly abandoned philosophy. After a year in Göttingen and a short stay in Paris, he received an appointment at the ETH in Zürich. His research was multi-faceted, ranging from series, probability, number theory and combinatorics to astronomy and voting systems. Some of his deepest work was on entire functions. He also worked in conformal mappings, potential theory, boundary value problems, and isoperimetric problems in mathematical physics, as well as heuristics late in his career. When Pólya left Europe in 1940, he first went to Brown University, then two years later to Stanford, where he remained until his death on September 7, 1985. Biography of Gabor Szegö Born in Kunhegyes, Hungary, January 20, 1895, Szegö studied in Budapest and Vienna, where he received his Ph. D. in 1918, after serving in the Austro-Hungarian army in the First World War. He became a privatdozent at the University of Berlin and in 1926 succeeded Knopp at the University of Kšnigsberg. It was during his time in Berlin that he and Pólya collaborated on their great joint work, the Problems and Theorems in Analysis. Szegö's own research concentrated on orthogonal polynomials and Toeplitz matrices. With the deteriorating situation in Germany at that time, he moved in 1934 to Washington University, St. Louis, where he remained until 1938, when he moved to Stanford. As department head at Stanford, he arranged for Pólya to join the Stanford faculty in 1942. Szegö remained at Stanford until his death on August 7, 1985.

Product Details

• Paperback: 404 pages
• Publisher: Springer (November 10, 2004)
• Language: English
• ISBN-10: 3540636862
• ISBN-13: 978-3540636861
• Product Dimensions: 9.2 x 6.1 x 0.4 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #889,720 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

19 of 19 people found the following review helpful:

5.0 out of 5 stars THE BOOK OF PROBLEMS, March 24, 2000

By 

Richard Askey (Madison, Wisconsin) - See all my reviews

This review is from: Problems and Theorems in Analysis. Volume II: Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry (Classics in Mathematics) (v. 2) (Paperback)

Polya and Szego's 1923 two volumes of mathematics problems are still the best collections of problems for people who want to learn advanced undergraduate and graduate level mathematics. When I want to know something about zeros of polynomials, about inequalities for polynomials or trigonometric polynomials, or determinants and quadratic forms, the first place I look is volume 2 of Polya and Szego. It is a great source of problems to give to students if you are a teacher, and the best set of problems to work through if you are learning mathematics at the advanced undergraduate level or higher. Volume 2 contains long chapters on complex variables and number theory and some problems in geometry. Both volumes belong on a shelf close to the desk of anyone who teaches college level mathematics. They are also very useful for those who use mathematics. These two volumes are gems, and would be rated above 5 stars if possible. The German original is available here in a nice English translation. Some new material was added when the translation was first published.