Markov's Theorem and 100 Years of the Uniqueness Conjecture : A Mathematical Journey from Irrational Numbers to Perfect Matchings

種類:

電子ブック

責任表示:

by Martin Aigner

出版情報:

Heidelberg : Springer International Publishing : Imprint: Springer, 2013

著者名:

• Aigner, Martin
• SpringerLink (Online service)

ISBN:

9783319008882 [3319008889]    

注記:

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 no

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