Leseprobe
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
Markov's Theorem and 100 Years of the Uniqueness Conjecture
Martin Aigner
* Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.
Springer International Publishing 
Naturwissenschaften, Medizin, Informatik, Technik / Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
Beschreibung
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 curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraic words. The book closes with a discussion of the current state of knowledge about the uniqueness conjecture, which remains an open challenge to this day.
All the material should be accessible to upper-level undergraduates with some background in number theory, and anything beyond this level is fully explained in the text.
This is not a monograph in the usual sense concentrating on a specific topic. Instead, it narrates in five parts – Numbers, Trees, Groups, Words, Finale – the story of a discovery in one field and its many manifestations in others, as a tribute to a great mathematical achievement and as an intellectual pleasure, contemplating the marvellous unity of all mathematics.
Kundenbewertungen
Markov Theorem, Modular Group, Continued Fractions, Uniqueness Conjecture of Markov Numbers, combinatorics, Lagrange Spectrum