Markov's Theorem and 100 Years of the Uniqueness Conjecture: A Mathematical Journey from Irrational Numbers to Perfect Matchings - Image 1

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

Name: Markov's Theorem and 100 Years of the Uniqueness Conjecture: A Mathematical Journey from Irrational Numbers to Perfect Matchings
Brand: Springer
Price: 100.1 GBP
Availability: InStock

Algebra

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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 isfully 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 Specifications

Brand: Springer
Format: paperback
ASIN: 3319033093
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 08 August 2015
Listed Since: 08 August 2015

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

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