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Record Nr. |
UNINA9910139338903321 |
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Autore |
Foldes Stephan <1951-> |
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Titolo |
Fundamental structures of algebra and discrete mathematics / / Stephan Foldes |
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Pubbl/distr/stampa |
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ISBN |
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1-282-24250-4 |
9786613813626 |
1-118-03318-3 |
1-118-03143-1 |
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Descrizione fisica |
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1 online resource (362 p.) |
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Disciplina |
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Soggetti |
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Algebra |
Mathematics |
Àlgebra |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"A Wiley-Interscience publication." |
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Nota di bibliografia |
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Includes bibliographical references and indexes. |
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Nota di contenuto |
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Fundamental Structures of Algebra and Discrete Mathematics; Contents; ILLUSTRATIONS; PREFACE; I. SETS; 1. Elementary Constructions and Axioms; 2. Cardinal and Ordinal Numbers; 3. Intersections; Bibliography; II. ORDERED SETS; 1. Relations, Orders, and Zorn's Lemma; 2. Lattices and Closures; 3. Covering Relations; 4. Intersecting Convex Sets; Bibliography; III. GROUPS; 1. Binary Operations, Homomorphisms, and Congruences; 2. Permutation Groups; 3. Integers and Cyclic Groups; 4. Alternating Groups; Bibliography; IV. RINGS; 1. Ideals; 2. Polynomials; 3. Factorization and the Euclidean Algorithm |
BibliographyV. FIELDS; 1. Rational and Real Numbers; 2. Galois Groups and Imaginary Roots; Bibliography; VI. VECTOR SPACES; 1. Bases; 2. Linear Maps and Equations; 3. Affine and Projective Geometry; 4. Hyperplanes in Linear Programming; 5. Time and Speed in Special Relativity; Bibliography; VII. GRAPHS; 1. Trees and Median Graphs; 2. Games; 3. Chromatic Polynomials; Bibliography; VIII. LATTICES; 1. |
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Complements and Distributivity; 2. Boolean Algebra; 3. Modular and Geometric Lattices; Bibliography; IX. MATROIDS; 1. Linear and Abstract Independence; 2. Minors and Tutte Polynomials |
3. Greedy Optimization ProceduresBibliography; X. TOPOLOGICAL SPACES; 1. Filters; 2. Closure, Convergence, and Continuity; 3. Distances and Entourages; Bibliography; XI. UNIVERSAL ALGEBRAS; 1. Homomorphisms and Congruences; 2. Algebra of Syntax; 3. Truth and Formal Proof; Bibliography; XII. CATEGORIES; Bibliography; INDEX OF DEFINITIONS; INDEX OF NOTATION; INDEX OF THEOREMS |
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Sommario/riassunto |
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Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples. |
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