Squares

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Paperback | 13 December 1993

At a Glance

Paperback
300 Pages

Dimensions(cm)
22.86 x 15.24 x 1.7

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Many classical and modern results and quadratic forms are brought together in this book. The treatment is self-contained and of a totally elementary nature requiring only a basic knowledge of rings, fields, polynomials, and matrices, such that the works of Pfister, Hilbert, Hurwitz and others are easily accessible to non-experts and undergraduates alike. The author deals with many different approaches to the study of squares; from the classical works of the late 19th century, to areas of current research. Anyone with an interest in algebra or number theory will find this a most fascinating volume.

Industry Reviews

"A well-written, unpretentious introduction to squares and sums of squares in fields." American Mathematical Monthly "...Rajwade's exposition...is richly detailed: the reader is not forced to reproduce complicated algebraic calculations just to follow the arguments. Even more delightful is how Rajwade approaches the frontiers of current research in certain aspects of the algebraic theory of quadratic forms without significantly increasing demands on the reader! Highly recommended." D.V. Feldman, Choice "Anyone wanting to learn something about the algebraic theory of quadratic forms will find this book useful. It is written at an elementary level, accessible to undergraduate students. At the same time, it contains several important topics, including the classical theorems of Hilbert, Hurwitz and Radon, not covered in the standard references." Murray Marshall, Mathematical Reviews "...this book includes beautiful and important mathematics which can be explained at a fairly elementary level. Many of these theorems have appeared only in research journals and certainly deserve to be advertised in expository books and appreciated by a wide audience." Daniel B. Shapiro, The American Mathematical Monthly

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The theorem of Hurwitz
The 2n theorems and the Stufe of fields
Examples of the Stufe of fields and related topics
Hilbert's 17th problem
Positive definite functions and sums of squares
An introduction to Hilbert's theorem
The two proofs of Hilbert's theorem
Theorems of Reznick and Choi, Lam and Reznick
Theorems of Choi, Calderon and Robinson
The theorem of Hurwitz-Radon
An introduction to quadratic form theory
The theory of multiplicative forms and Pfister forms
The Hopf condition
Examples of bilinear identities and a theorem of Gabel
Artin-Schreier theory of formally real fields
Squares and sums of squares in fields and their extension fields
Pourchet's theorem and related results
Examples of the Stufe and Pythagoras number of fields using the Hasse-Minkowski theorem
Appendix: Reduction of matrices to canonical form
Table of Contents provided by Publisher. All Rights Reserved.

Squares

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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