Electronic Resource

Markov's theorem and 100 years of the uniqueness conjecture

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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.

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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

E714

Penerbit

Swiss : Springer Cham., 2013

Deskripsi Fisik

x, 257 hlm.

Bahasa

English

ISBN/ISSN

9783319008882

Klasifikasi

NONE

Tipe Isi

text

Tipe Media

computer

Tipe Pembawa

online resource

Edisi

Ed.1

Subjek

Teori bilangan

Info Detail Spesifik

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Pernyataan Tanggungjawab

Martin Aigner

Versi lain/terkait

Lampiran Berkas

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