MARKOV'S THEOREM AND 100 YEARS OF THE UNIQUENESS CONJECTURE

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.

Idioma: INGLÉS