Primary brain tumors : a review of histologic classification
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Bibliographic Information
Primary brain tumors : a review of histologic classification
Springer-Verlag, c1989
- : U.S. : Hbk
- : U.S. : paper
- : Germany
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Note
Based on a meeting held in March 1988 at the University of Texas M.D. Anderson and Cancer Center in Houston
Bibliography: p
Includes index
Description and Table of Contents
- Volume
-
: U.S. : paper ISBN 9780387970370
Description
The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nine teenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of bi nary quadratic forms, so elementary and computationally explicit, was indeed just a special case of a much more elega,nt and abstract theory which, unfortunately, is not computationally explicit. In recent years the original theory has been laid aside. Gauss's proofs, which involved brute force computations that can be done in what is essentially a two dimensional vector space, have been dropped in favor of n-dimensional arguments which prove the general theorems of algebraic number the ory. In consequence, this elegant, yet pleasantly simple, theory has been neglected even as some of its results have become extremely useful in certain computations. I find this neglect unfortunate, because binary quadratic forms have two distinct attractions. First, the subject involves explicit computa tion and many of the computer programs can be quite simple. The use of computers in experimenting with examples is both meaningful and enjoyable; one can actually discover interesting results by com puting examples, noticing patterns in the "data," and then proving that the patterns result from the conclusion of some provable theorem.
Table of Contents
1 Elementary Concepts.- 2 Reduction of Positive Definite Forms.- 3 Indefinite Forms.- 3.1 Reduction, Cycles.- 3.2 Automorphs, Pell's Equation.- 3.3 Continued Fractions and Indefinite Forms.- 4 The Class Group.- 4.1 Representation and Genera.- 4.2 Composition Algorithms.- 4.3 Generic Characters Revisited.- 4.4 Representation of Integers.- 5 Miscellaneous Facts.- 5.1 Class Number Computations.- 5.2 Extreme Cases and Asymptotic Results.- 6 Quadratic Number Fields.- 6.1 Basic Algebraic Definitions.- 6.2 Algebraic Numbers and Quadratic Fields.- 6.3 Ideals in Quadratic Fields.- 6.4 Binary Quadratic Forms and Classes of Ideals.- 6.5 History.- 7 Composition of Forms.- 7.1 Nonfundamental Discriminants.- 7.2 The General Problem of Composition.- 7.3 Composition in Different Orders.- 8 Miscellaneous Facts II.- 8.1 The Cohen-Lenstra Heuristics.- 8.2 Decomposing Class Groups.- 8.3 Specifying Subgroups of Class Groups.- 8.3.1 Congruence Conditions.- 8.3.2 Exact and Exotic Groups.- 9 The 2-Sylow Subgroup.- 9.1 Classical Results on the Pell Equation.- 9.2 Modern Results.- 9.3 Reciprocity Laws.- 9.4 Special References for Chapter 9.- 10 Factoring with Binary Quadratic Forms.- 10.1 Classical Methods.- 10.2 SQUFOF.- 10.3 CLASNO.- 10.4 SPAR.- 10.4.1 Pollard p - 1.- 10.4.2 SPAR.- 10.5 CFRAC.- 10.6 A General Analysis.- Appendix 1:Tables, Negative Discriminants.- Appendix 2:Tables, Positive Discriminants.
- Volume
-
: U.S. : Hbk ISBN 9780387970554
Description
This volume represents the formal presentations and discussions which took place during a three-day meeting in March 1988 at The University of Texas M. D. Anderson Cancer Center in Houston. It is" dedicated to my friend of more than thirty years, Prof. Dr. Klaus Joachim Ziilch, who died in Berlin on December 2. 1988 while this volume was still in preparation. Klaus Zulch had devoted a significant portion of his professional life to a better understanding of central nervous tumors. Over the past two decades he served as the Director of the Collaborating Center for CNS Tumors, under the auspices of the World Health Organization (WHO), and it was largely through his efforts that the work of the CelJ. ter in developing criteria for a histologic classification of these neoplasms was kept alive. Without his stimulus this Houston meeting would probably not have taken place. In early 1987 he approached me with the idea of convening, at an early date, a meeting in Houston in collaboration with the Department of Neuro-Oncology of the Cancer Center, of which I was then Chairman. The purpose of this proposed meeting was to discuss recent research developments that might have a profound influence on the classification of brain tumors and ultimately necessitate revision of the "Blue Book" of the WHO on Histological Typing 0/ Tumours 0/ the Central Nervous System.
by "Nielsen BookData"