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.
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Produktdetaljer
ISBN
9783319008882
Publisert
2018
Utgiver
Vendor
Springer
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter