model theory encyclopedia of mathematics and its applications

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Model Theory

Author : Wilfrid Hodges
ISBN : 0521304423
Genre : Mathematics
File Size : 46. 21 MB
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Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.

The Theory Of Partitions

Author : George E. Andrews
ISBN : 052163766X
Genre : Mathematics
File Size : 24. 56 MB
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Discusses mathematics related to partitions of numbers into sums of positive integers.

Theory Of Matroids

Author : Neil White
ISBN : 9780521309370
Genre : Mathematics
File Size : 27. 43 MB
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The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory and field theory. Furthermore, matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems. Indeed, matroids are amazingly versatile and the approaches to the subject are varied and numerous. This book is a primer in the basic axioms and constructions of matroids. The contributions by various leaders in the field include chapters on axiom systems, lattices, basis exchange properties, orthogonality, graphs and networks, constructions, maps, semi-modular functions and an appendix on cryptomorphisms. The authors have concentrated on giving a lucid exposition of the individual topics; explanations of theorems are preferred to complete proofs and original work is thoroughly referenced. In addition, exercises are included for each topic.

The Foundations Of Mathematics In The Theory Of Sets

Author : John P. Mayberry
ISBN : 0521770343
Genre : Mathematics
File Size : 29. 99 MB
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This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.

Sperner Theory

Author : Konrad Engel
ISBN : 0521452066
Genre : Mathematics
File Size : 43. 71 MB
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Emphasises the powerful methods arising from the fusion of combinatorial techniques with programming, linear algebra, and probability theory.

Algorithmic Algebraic Number Theory

Author : M. Pohst
ISBN : 0521596696
Genre : Mathematics
File Size : 71. 40 MB
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Classic book, addressed to all lovers of number theory.

Boolean Functions

Author : Yves Crama
ISBN : 9781139498630
Genre : Mathematics
File Size : 70. 78 MB
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Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.

Field Extensions And Galois Theory

Author : Julio R. Bastida
ISBN : 0201135213
Genre : Extensions de corps (Mathématiques)
File Size : 74. 7 MB
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Mathematical Theory Of Entropy

Author : Nathaniel F. G. Martin
ISBN : 0521177383
Genre : Mathematics
File Size : 21. 33 MB
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This excellent 1981 treatment of the mathematical theory of entropy gives an accessible exposition its application to other fields.

Semimodular Lattices

Author : Manfred Stern
ISBN : 0521461057
Genre : Mathematics
File Size : 22. 13 MB
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A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.

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