Problems and Theorems in Analysis, Volume II

Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry

George Polya, Gabor Szego

392 pages, parution le 01/01/1998

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Résumé

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.

Contents

Part Four : Functions of One Complex Variable.

Maximum Term and Central Index, Maximum Modulus and Number of Zeros.
Schlicht Mappings.
Miscellaneous Problems.

Part Five : The Location of Zeros.

Rolle's Theorem and Descartes' Rule of Signs.
The Geometry of the Complex Plane and the Zeros of Polynomials.
Miscellaneous Problems.

Part Six: Polynomials and Trigonometric Polynomials.

Part Seven : Determinants and Quadratic Forms.

Part Eight : Number Theory.

Arithmetical Functions.
Polynomials with Integral Coefficients and Integral-Valued Functions.
Arithmetical Aspects of Power Series.
Some Problems on Algebraic Integers.
Miscellaneous Problems.

Part Nine : Geometric Problems.

Appendix: Additional Problems.

Author Index.
Subject Index.
Topics.
Errata.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	George Polya, Gabor Szego
Parution	01/01/1998
Nb. de pages	392
Format	15,5 x 23,5
Couverture	Broché
Poids	618g
Intérieur	Noir et Blanc
EAN13	9783540636861