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Markov's Theorem and 100 Years of the Uniqueness Conjecture (2013) {=IMPAVIDUS=}

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Description

 							
  
  Book Description:
  
  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.
  
  Product Details:
  
  PDF: 257
pages
  Publisher: Springer; 2013 edition (July 29, 2013)
  Language: English
  ISBN-10: 3319008870

 ISBN-13: 978-3319008875
  Amazon Link:
http://www.amazon.com/Markovs-Theorem-Years-Uniqueness-Conjecture/dp/3319008870/
  
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