Bøger af Martin Aigner

Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result.

Diese sorgfaltig uberarbeitete und deutlich erweiterte vierte deutsche Auflage von "e;Das BUCH der Beweise"e; enthalt auch vier neue Kapitel: Diese prasentieren originelle und elegante Beweise fur Klassiker, wie den Spektralsatz der Linearen Algebra, aber auch neuere Brillanten, wie zum Beispiel die Nichtexistenz der Borromaischen Ringe - und weitere Uberraschungen. Aus den Rezensionen: "e;Was hier vorliegt ist eine Sammlung von Beweisen, die in das von Paul Erdos immer wieder zitierte BUCH gehoren, das vom lieben (?) Gott verwahrt wird und das die perfekten Beweise aller mathematischen Satze enthalt. Manchmal lasst der Herrgott auch einige von uns Sterblichen in das BUCH blicken, und die so resultierenden Geistesblitze erhellen den Mathematikeralltag mit eleganten Argumenten, uberraschenden Zusammenhangen und unerwarteten Volten."e;www.mathematik.de, Mai 2002"e;Eine einzigartige Sammlung eleganter mathematischer Beweise nach der Idee von Paul Erdos, verstandlich geschrieben von exzellenten Mathematikern. Dieses Buch gibt anregende Losungen mit Aha-Effekt, auch fur Nicht-Mathematiker."e;www.vismath.de"e;Ein prachtiges, auerst sorgfaltig und liebevoll gestaltetes Buch! Erdos hatte die Idee DES BUCHES, in dem Gott die perfekten Beweise mathematischer Satze eingeschrieben hat. Das hier gedruckte Buch will eine "e;very modest approximation"e; an dieses BUCH sein.... Das Buch von Aigner und Ziegler ist gelungen ..."e; Mathematische Semesterberichte, November 1999"e;Wer (wie ich) bislang vergeblich versucht hat, einen Blick ins BUCH zu werfen, wird begierig in Aigners und Zieglers BUCH der Beweise schmokern."e;www.mathematik.de, Mai 2002

First, there exist several older books on the subject, such as Ryser [1] (which I still think is the most seductive introduction to combinatorics), Hall [2], and more recent ones such as Cameron-Van Lint [1] on groups and designs, and Blake-Mullin [1] on coding theory, whereas no compre hensive book exists on (a) and (b).

This book takes the reader on a mathematical journey from the number-theoretic setting of the Theorem of Markov and its Uniqueness Conjecture, gradually unfolding many beautiful connections, until in the proof of the Theorem everything falls into place.

Paul Erdos amava parlare del Libro in cui Dio conserva le dimostrazioni perfette per i teoremi matematici, seguendo il detto di G. H. Hardy secondo il quale non vi è posto perenne per la matematica brutta. Erdos disse anche che non è necessario credere in Dio, tuttavia in quanto matematici si deve credere nel Libro. Alcuni anni fa gli autori gli suggerirono di scrivere una prima (e assai modesta) approssimazione del Libro. Egli fu entusiasta e, come gli era peculiare, si mise immediatamente al lavoro, riempiendo pagine su pagine con i suoi suggerimenti. Essendo sfortunatamente morto nell'estate del 1996, Paul non compare come co-autore. Tuttavia questo libro è dedicato alla sua memoria.

Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics.

Proceedings of the NATO Advanced Study Institute, Berlin, Germany, September 1-10, 1976

This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ". . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen