Softcover ISBN:  9780821841327 
Product Code:  STML/36 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470421472 
Product Code:  STML/36.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821841327 
eBook: ISBN:  9781470421472 
Product Code:  STML/36.B 
List Price:  $108.00 $83.50 
Softcover ISBN:  9780821841327 
Product Code:  STML/36 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470421472 
Product Code:  STML/36.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821841327 
eBook ISBN:  9781470421472 
Product Code:  STML/36.B 
List Price:  $108.00 $83.50 

Book DetailsStudent Mathematical LibraryVolume: 36; 2007; 314 ppMSC: Primary 13; Secondary 20
This book presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples and applications to physics, engineering, numerical analysis, combinatorics, coding theory, and graph theory. A wide selection of exercises and suggestions for further reading makes the book appropriate for an advanced undergraduate or firstyear graduate level course.
ReadershipUndergraduate and graduate students interested in invariant theory and its applications.

Table of Contents

Chapters

1. Introduction

Part 1. Recollections

Chapter 1. Linear representations of finite groups

Chapter 2. Rings and algebras

Part 2. Introduction and Göbel’s bound

Chapter 3. Rings of polynomial invariants

Chapter 4. Permutation representations

Application: Decay of a spinless particle

Application: Counting weighted graphs

Part 3. The first fundamental theorem of invariant theory and Noether’s bound

Chapter 5. Construction of invariants

Chapter 6. Noether’s bound

Chapter 7. Some families of invariants

Application: Production of fibre composites

Application: Gaussian quadrature

Part 4. Noether’s theorems

Chapter 8. Modules

Chapter 9. Integral dependence and the Krull relations

Chapter 10. Noether’s theorems

Application: Selfdual codes

Part 5. Advanced counting methods and the ShephardToddChevalley theorem

Chapter 11. Poincaré series

Chapter 12. Systems of parameters

Chapter 13. Pseudoreflection representations

Application: Counting partitions

Appendix A. Rational invariants


Additional Material

Reviews

...a large part of the book is written in a friendly style and all notions are carefully explained and immediately demonstrated in concrete examples. Each chapter contains a lot of exercises.
EMS Newsletter 
All together, the expostion of the book under review stands out by its masterly clarity, comprehensiveness, profundity, and didactical disposition. The author has conclusively demonstrated that invariant theory can be taught from scratch, in a studentfriendly manner, and by exhibiting both its fascinating beauty and its broad feasibility to very beginners in the field. In this fashion, the present book is fairly unique in the literature on introductory invariant theory.
Zentralblatt MATH 
If you are an undergraduate, or firstyear graduate student, and you love algebra, certainly you will enjoy this book, and you will learn a lot from it. It is pleasant reading, and it is selfcontained. I strongly recommend this book for an advanced undergraduate or firstyear graduate course, and also for independent study.
MAA Online 
Most of the examples and applications are based on recent work of students. This makes the reading of this book very pleasant. Necessary basic information is recalled throughout the book. In addition, all the examples are extremely well detailed. For these two reasons, although some results are recent and subtle, this book seems to be quite appropriate for advanced undergraduate or firstyear graduate level courses.
Anne Moreau for Mathematical Reviews


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This book presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples and applications to physics, engineering, numerical analysis, combinatorics, coding theory, and graph theory. A wide selection of exercises and suggestions for further reading makes the book appropriate for an advanced undergraduate or firstyear graduate level course.
Undergraduate and graduate students interested in invariant theory and its applications.

Chapters

1. Introduction

Part 1. Recollections

Chapter 1. Linear representations of finite groups

Chapter 2. Rings and algebras

Part 2. Introduction and Göbel’s bound

Chapter 3. Rings of polynomial invariants

Chapter 4. Permutation representations

Application: Decay of a spinless particle

Application: Counting weighted graphs

Part 3. The first fundamental theorem of invariant theory and Noether’s bound

Chapter 5. Construction of invariants

Chapter 6. Noether’s bound

Chapter 7. Some families of invariants

Application: Production of fibre composites

Application: Gaussian quadrature

Part 4. Noether’s theorems

Chapter 8. Modules

Chapter 9. Integral dependence and the Krull relations

Chapter 10. Noether’s theorems

Application: Selfdual codes

Part 5. Advanced counting methods and the ShephardToddChevalley theorem

Chapter 11. Poincaré series

Chapter 12. Systems of parameters

Chapter 13. Pseudoreflection representations

Application: Counting partitions

Appendix A. Rational invariants

...a large part of the book is written in a friendly style and all notions are carefully explained and immediately demonstrated in concrete examples. Each chapter contains a lot of exercises.
EMS Newsletter 
All together, the expostion of the book under review stands out by its masterly clarity, comprehensiveness, profundity, and didactical disposition. The author has conclusively demonstrated that invariant theory can be taught from scratch, in a studentfriendly manner, and by exhibiting both its fascinating beauty and its broad feasibility to very beginners in the field. In this fashion, the present book is fairly unique in the literature on introductory invariant theory.
Zentralblatt MATH 
If you are an undergraduate, or firstyear graduate student, and you love algebra, certainly you will enjoy this book, and you will learn a lot from it. It is pleasant reading, and it is selfcontained. I strongly recommend this book for an advanced undergraduate or firstyear graduate course, and also for independent study.
MAA Online 
Most of the examples and applications are based on recent work of students. This makes the reading of this book very pleasant. Necessary basic information is recalled throughout the book. In addition, all the examples are extremely well detailed. For these two reasons, although some results are recent and subtle, this book seems to be quite appropriate for advanced undergraduate or firstyear graduate level courses.
Anne Moreau for Mathematical Reviews