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

• Main Author: Aigner, Martin. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Heidelberg : Springer International Publishing : Imprint: Springer, 2013.
• Subjects: Mathematics.; Group theory.; Combinatorics.; Number theory.; Number Theory.; Group Theory and Generalizations.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-319-00888-2

This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markovs theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markovs theorem.�What makes the Markov theme...

Table of Contents:

• Approximation of Irrational�Numbers
• Markov's Theorem and the Uniqueness Conjecture
• The Markov Tree
• The Cohn Tree
• The Modular Group SL(2,Z)
• The Free Group F2
• Christoffel Words
• Sturmian Words
• Proof of Markov's Theorem
• The Uniqueness Conjecture. �.