Problems and Theorems in Analysis I

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 Königsberg. 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.

One Infinite Series and Infinite Sequences.- 1 Operations with Power Series.- 2 Linear Transformations of Series. A Theorem of Cesàro.- 3 The Structure of Real Sequences and Series.- 4 Miscellaneous Problems.- Two Integration.- 1 The Integral as the Limit of a Sum of Rectangles.- 2 Inequalities.- 3 Some Properties of Real Functions.- 4 Various Types of Equidistribution.- 5 Functions of Large Numbers.- Three Functions of One Complex Variable. General Part.- 1 Complex Numbers and Number Sequences.- 2 Mappings and Vector Fields.- 3 Some Geometrical Aspects of Complex Variables.- 4 Cauchy's Theorem - The Argument Principle.- 5 Sequences of Analytic Functions.- 6 The Maximum Principle.- Author Index.

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