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- catalog abstract ""Many classical and modern results about 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 in order to be able to tackle the work of Pfister, Hilbert, Radon, Hurwitz, Pourchet and others as it relates to the study of numbers that can be expressed as squares, or sums of squares." "The author deals with different approaches to their study, from classical results to the area of current research." "This will be a fascinating volume for mathematicians in number theory or algebra."--BOOK JACKET.".
- catalog contributor b5421045.
- catalog created "c1993.".
- catalog date "1993".
- catalog date "c1993.".
- catalog dateCopyrighted "c1993.".
- catalog description ""Many classical and modern results about 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 in order to be able to tackle the work of Pfister, Hilbert, Radon, Hurwitz, Pourchet and others as it relates to the study of numbers that can be expressed as squares, or sums of squares." "The author deals with different approaches to their study, from classical results to the area of current research." "This will be a fascinating volume for mathematicians in number theory or algebra."--BOOK JACKET.".
- catalog description "Includes bibliographical references (p. [279]-284) and index.".
- catalog description "The theorem of Hurwitz (1898) on the 2, 4, 8-identities -- The 2n-identities and the Stufe of fields : theorems of Pfister and Cassels -- Examples of the Stufe of fields and related topics -- Hilbert's 17th problem and the function fields R(X), Q(X), and R(X, Y) -- Positive semi-definite functions and sums of squares in R(X1,X2, ..., Xn) -- Introduction to Hilbert's theorem (1888) in the ring R[X1,X2, ..., Xn] -- The two proofs of Hilbert's main theorem; Hilbert's own and the other of Choi and Lam -- Theorems of Reznick and of Choi, Lam and Reznick -- Theorems of Choi, Calderon and of Robinson -- The Radon function and the theorem of Hurwitz-Radon (1922-23) -- Introduction to the teory of quadratic forms -- Theory of multiplicative forms and of Pfister forms -- The rational admissibility of the triple (r, s, n) and the Hopf condition -- Some interesting 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 that P(Q(X)) = 5 and related results -- Examples of the Stufe and pythagroas number of fields using the Hasse-Minkowski theorem -- Reduction of matrices to canonical forms (for Chapter 10) -- Convex sets (for chaptes 6,7,8,9).".
- catalog extent "xii, 286 p. :".
- catalog identifier "0521426685".
- catalog isPartOf "London Mathematical Society lecture note series ; 171".
- catalog issued "1993".
- catalog issued "c1993.".
- catalog language "eng".
- catalog publisher "Cambridge ; New York : Cambridge University Press,".
- catalog subject "512 20".
- catalog subject "Algebra".
- catalog subject "Forms, Quadratic.".
- catalog subject "QA243 .R35 1993".
- catalog subject "Sequences (Mathematics)".
- catalog tableOfContents "The theorem of Hurwitz (1898) on the 2, 4, 8-identities -- The 2n-identities and the Stufe of fields : theorems of Pfister and Cassels -- Examples of the Stufe of fields and related topics -- Hilbert's 17th problem and the function fields R(X), Q(X), and R(X, Y) -- Positive semi-definite functions and sums of squares in R(X1,X2, ..., Xn) -- Introduction to Hilbert's theorem (1888) in the ring R[X1,X2, ..., Xn] -- The two proofs of Hilbert's main theorem; Hilbert's own and the other of Choi and Lam -- Theorems of Reznick and of Choi, Lam and Reznick -- Theorems of Choi, Calderon and of Robinson -- The Radon function and the theorem of Hurwitz-Radon (1922-23) -- Introduction to the teory of quadratic forms -- Theory of multiplicative forms and of Pfister forms -- The rational admissibility of the triple (r, s, n) and the Hopf condition -- Some interesting 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 that P(Q(X)) = 5 and related results -- Examples of the Stufe and pythagroas number of fields using the Hasse-Minkowski theorem -- Reduction of matrices to canonical forms (for Chapter 10) -- Convex sets (for chaptes 6,7,8,9).".
- catalog title "Squares / A.R. Rajwade.".
- catalog type "text".