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This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov's theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov's theorem.What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words.

On the way, there are also introductory forays into some fascinating topics that do not belong to the standard...

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,...

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,...

Es kommt nicht oft vor, dass ein einzelnes Problem ein ganzes mathematisches Gebiet hervorruft. Das allseits bekannte 4-Farben Problem war solch ein singulares Ereignis: Aus den Losungsversuchen entwickelte sich die Graphentheorie, die heute zu den unverzichtbaren Grundlagen der Diskreten Mathematik und Informatik und weiterer angewandter Wissenschaften gehort. Das Buch versucht zweierlei: Es will erstens alle wichtigen Begriffe, Ideen und Satze fur eine Einfuhrung in die Graphentheorie im Bachelorstudium bereitstellen, und zweitens ein tieferes Verstandnis fur dieses wunderbare Gebiet...

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 e posto perenne per la matematica brutta. Erdos disse anche che non e 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...

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

Ci siamo ist unser neues und innovatives Lehrwerk für Italienisch als spätbeginnende Fremdsprache. Das zweibändige Lehrwerk bereitet sprachlich, thematisch und methodisch systematisch auf das Erreichen der Stufe B1/B1+ des Gemeinsamen Europäischen Referenzrahmens vor. Dabei wird der Lernerfolg durch durchgängige Kontextualisierung, Kompetenzorientierung und Binnendifferenzierung gesichert.

Durch die sympathischen Lehrbuchfiguren lernen die Schülerinnen und Schüler den italienischen Alltag mit all seinen Facetten kennen und...