**Student Mathematical Library**

Volume: 36;
2007;
314 pp;
Softcover

MSC: Primary 13;
Secondary 20

**Print ISBN: 978-0-8218-4132-7
Product Code: STML/36**

List Price: $53.00

Individual Price: $42.40

**Electronic ISBN: 978-1-4704-2147-2
Product Code: STML/36.E**

List Price: $50.00

Individual Price: $40.00

#### Supplemental Materials

# Invariant Theory

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*Mara D. Neusel*

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 first-year graduate level course.

#### Readership

Undergraduate and graduate students interested in invariant theory and its applications.

#### Reviews & Endorsements

...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 student-friendly 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 first-year 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 self-contained. I strongly recommend this book for an advanced undergraduate or first-year 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 first-year graduate level courses.

-- Anne Moreau for Mathematical Reviews

#### Table of Contents

# Table of Contents

## Invariant Theory

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents v6 free
- Introduction 110 free
- Part 1. Recollections 716 free
- Part 2. Introduction and Göbel's Bound 4352
- Part 3. The First Fundamental Theorem of Invariant Theory and Noether's Bound 97106
- Part 4. Noether's Theorems 159168
- Part 5. Advanced Counting Methods and the Shephard-Todd-Chevalley Theorem 223232
- Appendix A. Rational Invariants 287296
- Suggestions for Further Reading 303312
- Notation Index 305314
- Subject Index 307316
- Back Cover Back Cover1326