Serge Lang

Mit seinem ersten Soloprogramm „Am Beckenrand“ wagt der Schauspieler Serge Falck (bekannt aus:„Kaisermühlenblues“, „CopStories“, „Tatort“ und „Medicopter 117“)" den Sprung ins Kabarett. Der gebürtige Belgier und „lebende Österreicher“ (wie er sich selbst gerne bezeichnet) führt sein Publikum durch einen abwechslungsreichen Abend voll von humorvollen Geschichten und eigenen Songs.

This book is intended as a basic text for a one-year course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text.

For many years Serge Lang has given talks to undergraduates on selected items in mathematics which could be extracted at a level understandable by students who have had calculus. Written in a conversational tone, Lang now presents a collection of those talks as a book. The talks could be given by faculty, but even better, they may be given by students in seminars run by the students themselves. Undergraduates, and even some high school students, will enjoy the talks which cover prime numbers, the abc conjecture, approximation theorems of analysis, Bruhat-Tits spaces, harmonic and symmetric polynomials, and more in a lively and informal style.

This book contains all the exercises and solutions of Serge Lang's Complex Analy­ sis. Chapters I through VITI of Lang's book contain the material of an introductory course at the undergraduate level and the reader will find exercises in all of the fol­ lowing topics: power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings and har­ monic functions. Chapters IX through XVI, which are suitable for a more advanced course at the graduate level, offer exercises in the following subjects: Schwarz re­ flection, analytic continuation, Jensen's formula, the Phragmen-LindelOf theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and the Zeta function. This solutions manual offers a large number of worked out exercises of varying difficulty. I thank Serge Lang for teaching me complex analysis with so much enthusiasm and passion, and for giving me the opportunity to work on this answer book. Without his patience and help, this project would be far from complete. I thank my brother Karim for always being an infinite source of inspiration and wisdom. Finally, I want to thank Mark McKee for his help on some problems and Jennifer Baltzell for the many years of support, friendship and complicity. Rami Shakarchi Princeton, New Jersey 1999 Contents Preface vii I Complex Numbers and Functions 1 1. 1 Definition . . . . . . . . . . 1 1. 2 Polar Form . . . . . . . . . 3 1. 3 Complex Valued Functions . 8 1. 4 Limits and Compact Sets . . 9 1. 6 The Cauchy-Riemann Equations .

Un grand appartement oublié de l’île Saint-Louis dont les portes et les pièces disparaissent les unes après les autres. Un bureau secret du ministère de l’Intérieur chargé d’explorer la banlieue parisienne pour y trouver les preuves de l’existence de Dieu. Une entreprise géante qui fait surveiller ses employés par des espions semi-visibles. Une ville utopique construite d’après Fritz Lang et hantée par un mystérieux  » Charbonnier « . Six histoires étranges, drôles, tragiques, métaphysiques. Six plongées dans l’abîme pour découvrir ce qui se cache de l’autre côté de la réalité. À mi-chemin entre Jules Verne et Jorge Luis Borges : bienvenue dans le monde de Serge Lehman..

A geometry course based on this book was taught success­ fully by Gene Murrow for several years. We are much indebted to Springer-Verlag for publishing Geometry, so that others can try our approach. The publishers and we thought it would be appropriate to issue the book first in a preliml. nary edition, on which we would welcome comments, especially from students and teachers of the high school geometry course. Such comments can bear on any aspect of Geometry, ranging from the choice of topics, the ordering of the topics, and other global considerations, to possible computational errors and misprints.