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Markov's Theorem and 100 Years of the Uniqueness Conjecture A Mathematical Journey from Irrational Numbers to Perfect Matchings /
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 Mar...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2013.
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| Edición: | 1st ed. 2013. |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-319-00888-2 | ||
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| 005 | 20220117045035.0 | ||
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| 100 | 1 | |a Aigner, Martin. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Markov's Theorem and 100 Years of the Uniqueness Conjecture |h [electronic resource] : |b A Mathematical Journey from Irrational Numbers to Perfect Matchings / |c by Martin Aigner. |
| 250 | |a 1st ed. 2013. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2013. | |
| 300 | |a X, 257 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 505 | 0 | |a 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. . | |
| 520 | |a 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. | ||
| 650 | 0 | |a Number theory. | |
| 650 | 0 | |a Group theory. | |
| 650 | 0 | |a Discrete mathematics. | |
| 650 | 1 | 4 | |a Number Theory. |
| 650 | 2 | 4 | |a Group Theory and Generalizations. |
| 650 | 2 | 4 | |a Discrete Mathematics. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319033099 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319008875 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319008899 |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-00888-2 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||