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 [...]

This revised and enlarged fourth edition features five new chapters, which treat classical results such as the "Fundamental Theorem of Algebra", problems about tilings, but also quite recent proofs, for example of the Kneser conjecture in graph theory. The new edition also presents further improveme[...]

This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews ..". Insi[...]

Das Standardwerk uber Diskrete Mathematik in deutscher Sprache. Grosser Wert wird auf die Ubungen gelegt, die etwa ein Viertel des Textes ausmachen. Die Ubungen sind nach Schwierigkeitsgrad gegliedert, im Anhang findet man Losungen fur etwa die Halfte der Ubungen. Das Buch eignet sich fur Lehrverans[...]