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  • © 1998

Problems and Theorems in Analysis I

Series. Integral Calculus. Theory of Functions

  • Very few mathematical books are worth translating 50 years after their original publication. Polyá-Szegö is one!

  • It was published in German by Springer in 1924, its English edition was widely acclaimed when it appeared from 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

Part of the book series: Classics in Mathematics (CLASSICS)

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Table of contents (18 chapters)

  1. Front Matter

    Pages I-XIX
  2. Infinite Series and Infinite Sequences

    1. Operations with Power Series

      • George Pólya, Gabor Szegö
      Pages 1-15
    2. Linear Transformations of Series. A Theorem of Cesàro

      • George Pólya, Gabor Szegö
      Pages 15-23
    3. The Structure of Real Sequences and Series

      • George Pólya, Gabor Szegö
      Pages 23-32
    4. Miscellaneous Problems

      • George Pólya, Gabor Szegö
      Pages 32-45
  3. Integration

    1. The Integral as the Limit of a Sum of Rectangles

      • George Pólya, Gabor Szegö
      Pages 46-62
    2. Inequalities

      • George Pólya, Gabor Szegö
      Pages 62-75
    3. Some Properties of Real Functions

      • George Pólya, Gabor Szegö
      Pages 75-84
    4. Various Types of Equidistribution

      • George Pólya, Gabor Szegö
      Pages 85-95
    5. Functions of Large Numbers

      • George Pólya, Gabor Szegö
      Pages 95-102
  4. Functions of One Complex Variable General Part

    1. Complex Numbers and Number Sequences

      • George Pólya, Gabor Szegö
      Pages 103-113
    2. Mappings and Vector Fields

      • George Pólya, Gabor Szegö
      Pages 113-124
    3. Some Geometrical Aspects of Complex Variables

      • George Pólya, Gabor Szegö
      Pages 125-132
    4. Cauchy’s Theorem. The Argument Principle

      • George Pólya, Gabor Szegö
      Pages 133-145
    5. Sequences of Analytic Functions

      • George Pólya, Gabor Szegö
      Pages 145-157
    6. The Maximum Principle

      • George Pólya, Gabor Szegö
      Pages 157-172
  5. Solutions

    1. Infinite Series and Infinite Sequences

      • George Pólya, Gabor Szegö
      Pages 173-229
    2. Integration

      • George Pólya, Gabor Szegö
      Pages 230-296
    3. Functions of One Complex Variable

      • George Pólya, Gabor Szegö
      Pages 297-384
  6. Back Matter

    Pages 385-393

About this book

From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems. These volumes contain many extraordinary problems and sequences of problems, mostly from some time past, well worth attention today and tomorrow. Written in the early twenties by two young mathematicians of outstanding talent, taste, breadth, perception, perseverence, and pedagogical skill, this work broke new ground in the teaching of mathematics and how to do mathematical research. (Bulletin of the American Mathematical Society)

Reviews

From the reviews: "The present English edition is not a mere translation of the German original. Many new problems have been added. (Jahresb. DMV) "There are some excellent books which are indispensable to the instruction of indeed good mathematicians and this volume is, without any doubt, one of them. The broad horizon of the book, its clear style and logical construction are some of the qualities which assure

From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems. These volumes contain many extraordinary problems and sequences of problems, mostly from some time past, well worth attention today and tomorrow. Written in the early twenties by two young mathematicians of outstanding talent, taste, breadth, perception, perseverence, and pedagogical skill, this work broke new ground in the teaching of mathematics and how to do mathematical research."  -Bulletin of the American Mathematical Society

Authors and Affiliations

  • Department of Mathematics, Stanford University, Stanford, USA

    George Pólya, Gabor Szegö

About the authors

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.

Bibliographic Information

  • Book Title: Problems and Theorems in Analysis I

  • Book Subtitle: Series. Integral Calculus. Theory of Functions

  • Authors: George Pólya, Gabor Szegö

  • Series Title: Classics in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-61983-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Softcover ISBN: 978-3-540-63640-3Published: 11 December 1997

  • eBook ISBN: 978-3-642-61983-0Published: 06 December 2012

  • Series ISSN: 1431-0821

  • Series E-ISSN: 2512-5257

  • Edition Number: 1

  • Number of Pages: XIX, 393

  • Additional Information: Originally published as Volume 193 in the series: Grundlehren der mathematischen Wissenschaften

  • Topics: Analysis

Buy it now

Buying options

eBook USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access