Softcover ISBN:  9781470456344 
Product Code:  SURV/249 
List Price:  $140.00 
MAA Member Price:  $126.00 
AMS Member Price:  $112.00 
eBook ISBN:  9781470460297 
Product Code:  SURV/249.E 
List Price:  $140.00 
MAA Member Price:  $126.00 
AMS Member Price:  $112.00 
Softcover ISBN:  9781470456344 
eBook: ISBN:  9781470460297 
Product Code:  SURV/249.B 
List Price:  $280.00 $210.00 
MAA Member Price:  $252.00 $189.00 
AMS Member Price:  $224.00 $168.00 
Softcover ISBN:  9781470456344 
Product Code:  SURV/249 
List Price:  $140.00 
MAA Member Price:  $126.00 
AMS Member Price:  $112.00 
eBook ISBN:  9781470460297 
Product Code:  SURV/249.E 
List Price:  $140.00 
MAA Member Price:  $126.00 
AMS Member Price:  $112.00 
Softcover ISBN:  9781470456344 
eBook ISBN:  9781470460297 
Product Code:  SURV/249.B 
List Price:  $280.00 $210.00 
MAA Member Price:  $252.00 $189.00 
AMS Member Price:  $224.00 $168.00 

Book DetailsMathematical Surveys and MonographsVolume: 249; 2020; 187 ppMSC: Primary 11; Secondary 05; 12; 20
The French expression “dessins d'enfants” means children's drawings. This term was coined by the great French mathematician Alexandre Grothendieck in order to denominate a method of pictorial representation of some highly interesting classes of polynomials and rational functions. The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some longstanding conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.
The major part of the book is quite elementary and is easily accessible to an undergraduate student. The less elementary parts, such as Galois theory or group representations and their characters, would need a more profound knowledge of mathematics. The reader may either take the basic facts of these theories for granted or use our book as a motivation and a first approach to these subjects.
ReadershipGraduate students and researchers interested in learning about combinatorics of polynomials as part of the new theory of dessins d'enfants.

Table of Contents

Chapters

Introduction

Dessins d’enfants: From polynomials through Belyĭ functions to weighted trees

Existence theorem

Recapitulation and perspective

Classification of unitrees

Computation of DavenportZannier pairs for unitrees

Primitive monodromy groups of weighted trees

Trees with primitive monodromy groups

A zoo of examples and constructions

Diophantine invariants

Enumeration

What remains to be done


Additional Material

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The French expression “dessins d'enfants” means children's drawings. This term was coined by the great French mathematician Alexandre Grothendieck in order to denominate a method of pictorial representation of some highly interesting classes of polynomials and rational functions. The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some longstanding conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.
The major part of the book is quite elementary and is easily accessible to an undergraduate student. The less elementary parts, such as Galois theory or group representations and their characters, would need a more profound knowledge of mathematics. The reader may either take the basic facts of these theories for granted or use our book as a motivation and a first approach to these subjects.
Graduate students and researchers interested in learning about combinatorics of polynomials as part of the new theory of dessins d'enfants.

Chapters

Introduction

Dessins d’enfants: From polynomials through Belyĭ functions to weighted trees

Existence theorem

Recapitulation and perspective

Classification of unitrees

Computation of DavenportZannier pairs for unitrees

Primitive monodromy groups of weighted trees

Trees with primitive monodromy groups

A zoo of examples and constructions

Diophantine invariants

Enumeration

What remains to be done