About this product

Product Identifiers

PublisherCambridge University Press

ISBN-100521426685

ISBN-139780521426688

eBay Product ID (ePID)303615

Product Key Features

Number of Pages300 Pages

LanguageEnglish

Publication NameSquares

SubjectNumber Theory

Publication Year1993

TypeTextbook

AuthorA. R. Rajwade

Subject AreaMathematics

SeriesLondon Mathematical Society Lecture Note Ser.

FormatTrade Paperback

Dimensions

Item Height0.8 in

Item Weight13.9 Oz

Item Length9 in

Item Width5.9 in

Additional Product Features

Intended AudienceCollege Audience

LCCN93-167566

Dewey Edition20

Reviews"...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, "A well-written, unpretentious introduction to squares and sums of squares in fields." American Mathematical Monthly, "A well-written, unpretentious introduction to squares and sums of squares in fields."American Mathematical Monthly, "...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

Series Volume NumberSeries Number 171

IllustratedYes

Dewey Decimal512.74

Table Of Content1. The theorem of Hurwitz; 2. The 2n theorems and the Stufe of fields; 3. Examples of the Stufe of fields and related topics; 4. Hilbert's 17th problem; 5. Positive definite functions and sums of squares; 6. An introduction to Hilbert's theorem; 7. The two proofs of Hilbert's theorem; 8. Theorems of Reznick and Choi, Lam and Reznick; 9. Theorems of Choi, Calderon and Robinson; 10. The theorem of Hurwitz-Radon; 11. An introduction to quadratic form theory; 12. The theory of multiplicative forms and Pfister forms; 13. The Hopf condition; 14. Examples of bilinear identities and a theorem of Gabel; 15. Artin-Schreier theory of formally real fields; 16. Squares and sums of squares in fields and their extension fields; 17. Pourchet's theorem and related results; 18. Examples of the Stufe and Pythagoras number of fields using the Hasse-Minkowski theorem; Appendix: Reduction of matrices to canonical form.

SynopsisMany 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., Many classical and modern results and quadratic forms are brought together in this book. 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., This work is a self-contained treatise on the research conducted on squares by Pfister, Hilbert, Hurwitz, and others. Many classical and modern results and quadratic forms are brought together in this book, and the treatment requires only a basic knowledge of rings, fields, polynomials, and matrices. The author deals with many different approaches to the study of squares, from the classical works of the late nineteenth century, to areas of current research.

LC Classification NumberQA243 .R35 1993