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Squares

Author: A R Rajwade
Publisher: Cambridge : Cambridge Univ. Press, 1993.
Series: London Mathematical Society lecture note series, 171.
Edition/Format:   Print bookView all editions and formats
Summary:

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.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: A R Rajwade
ISBN: 0521426685 9780521426688
OCLC Number: 246645069
Description: XII, 286 Seiten : Diagramme.
Contents: 1. 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.
Series Title: London Mathematical Society lecture note series, 171.
Responsibility: A.R. Rajwade.
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"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 Read more...

 
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