Antoine Chambert-Loir's Books

A Field Guide to Algebra

By: Antoine Chambert-Loir

Write a review Read reviews Take a Quiz Solve Book Puzzle

This book has a nonstandard choice of topics, including material on differential galois groups and proofs of the transcendence of e and pi. The author uses a conversational tone and has included a selection of stamps to accompany the text.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

199

Publisher

Springer Science & Business Media

Published Date

ISBN 10

038726955X

ISBN 13

9780387269559

Motivic Integration

By: Antoine Chambert-Loir,Johannes Nicaise,Julien Sebag

Write a review Read reviews Take a Quiz Solve Book Puzzle

Motivic Integration

By: Antoine Chambert-Loir,Johannes Nicaise,Julien Sebag

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

541

Publisher

Springer

Published Date

ISBN 10

149397887X

ISBN 13

9781493978878

(Mostly) Commutative Algebra

By: Antoine Chambert-Loir

Write a review Read reviews Take a Quiz Solve Book Puzzle

(Mostly) Commutative Algebra

By: Antoine Chambert-Loir

This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry. More than 300 exercises will allow the reader to deepen his understanding of the subject. The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

466

Publisher

Springer Nature

Published Date

ISBN 10

3030615952

ISBN 13

9783030615956

Information Theory

Three Theorems by Claude Shannon

By: Antoine Chambert-Loir

Write a review Read reviews Take a Quiz Solve Book Puzzle

Information Theory

Three Theorems by Claude Shannon

By: Antoine Chambert-Loir

This book provides an introduction to information theory, focussing on Shannon’s three foundational theorems of 1948–1949. Shannon’s first two theorems, based on the notion of entropy in probability theory, specify the extent to which a message can be compressed for fast transmission and how to erase errors associated with poor transmission. The third theorem, using Fourier theory, ensures that a signal can be reconstructed from a sufficiently fine sampling of it. These three theorems constitute the roadmap of the book. The first chapter studies the entropy of a discrete random variable and related notions. The second chapter, on compression and error correcting, introduces the concept of coding, proves the existence of optimal codes and good codes (Shannon's first theorem), and shows how information can be transmitted in the presence of noise (Shannon's second theorem). The third chapter proves the sampling theorem (Shannon's third theorem) and looks at its connections with other results, such as the Poisson summation formula. Finally, there is a discussion of the uncertainty principle in information theory. Featuring a good supply of exercises (with solutions), and an introductory chapter covering the prerequisites, this text stems out lectures given to mathematics/computer science students at the beginning graduate level.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

221

Publisher

Springer Nature

Published Date

ISBN 10

3031215613

ISBN 13

9783031215612

(Mostly) Commutative Algebra

By: Antoine Chambert-Loir

Write a review Read reviews Take a Quiz Solve Book Puzzle

(Mostly) Commutative Algebra

By: Antoine Chambert-Loir

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

466

Publisher

Springer Nature

Published Date

ISBN 10

3030615952

ISBN 13

9783030615956

A Field Guide to Algebra

By: Antoine Chambert-Loir

Write a review Read reviews Take a Quiz Solve Book Puzzle

A Field Guide to Algebra

By: Antoine Chambert-Loir

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

199

Publisher

Springer Science & Business Media

Published Date

ISBN 10

038726955X

ISBN 13

9780387269559

Book's by Antoine Chambert-Loir

A Field Guide to Algebra

A Field Guide to Algebra

Motivic Integration

Motivic Integration

(Mostly) Commutative Algebra

(Mostly) Commutative Algebra

Information Theory

Information Theory

(Mostly) Commutative Algebra

(Mostly) Commutative Algebra

A Field Guide to Algebra

A Field Guide to Algebra

Username

Password

Username

Password

Password again

Birthday

Email