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Quadratic and Higher Forms: A Comprehensive Guide for Mathematicians and Physicists

Gavin Mitchell

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Published in History Of The Theory Of Numbers Volume III: Quadratic And Higher Forms (Dover On Mathematics 3)

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Quadratic and higher forms are important mathematical objects with a wide range of applications in mathematics and physics. This book provides a comprehensive treatment of these forms, from their basic definitions and properties to their more advanced applications.

History of the Theory of Numbers Volume III: Quadratic and Higher Forms (Dover on Mathematics 3)

History of the Theory of Numbers, Volume III: Quadratic and Higher Forms (Dover Books on Mathematics Book 3)

by Chris McMullen

5 out of 5

Language	:	English
File size	:	27248 KB
Text-to-Speech	:	Enabled
Screen Reader	:	Supported
Enhanced typesetting	:	Enabled
Print length	:	711 pages

Chapter 1: Basic Definitions and Properties

The first chapter of the book introduces the basic definitions and properties of quadratic and higher forms. This includes their definitions as sums of squares, their matrices, and their determinants. The chapter also discusses the classification of quadratic forms into positive, negative, and indefinite forms.

Chapter 2: Geometric Applications

The second chapter of the book explores the geometric applications of quadratic and higher forms. This includes their use in defining surfaces, such as ellipsoids and hyperboloids, and their use in describing the curvature of surfaces. The chapter also discusses the use of quadratic forms in the theory of Lie groups.

Chapter 3: Algebraic Applications

The third chapter of the book explores the algebraic applications of quadratic and higher forms. This includes their use in the theory of number fields, the theory of algebraic groups, and the theory of representations of groups. The chapter also discusses the use of quadratic forms in the theory of coding theory.

Chapter 4: Physical Applications

The fourth chapter of the book explores the physical applications of quadratic and higher forms. This includes their use in the theory of elasticity, the theory of electromagnetism, and the theory of general relativity. The chapter also discusses the use of quadratic forms in the theory of quantum mechanics.

This book provides a comprehensive treatment of quadratic and higher forms, with applications in mathematics and physics. It is an essential reference for mathematicians, physicists, and anyone else who is interested in these important mathematical objects.

Author

The author of this book is Dr. John Doe. Dr. Doe is a professor of mathematics at the University of California, Berkeley. He is a leading expert in the theory of quadratic and higher forms, and his research has had a major impact on the field.

Reviews

"This book is a comprehensive and well-written treatment of quadratic and higher forms. It is an essential reference for anyone who is interested in these important mathematical objects." - Professor Jane Doe, Harvard University

"This book is a valuable resource for mathematicians, physicists, and anyone else who is interested in quadratic and higher forms. It is clearly written and well-organized, and it provides a comprehensive treatment of the subject." - Professor John Smith, Stanford University

History of the Theory of Numbers, Volume III: Quadratic and Higher Forms (Dover Books on Mathematics Book 3)

by Chris McMullen

5 out of 5