Algebra in action : a course in groups, rings, and fields / Shahriar Shahriari

Von:

Shahriari, Shahriar, 1956- [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch, Deutsch Reihen: Pure and applied undergraduate texts ; 27Verlag: Providence, Rhode Island : American Mathematical Society, 2017Beschreibung: 1 Online-RessourceISBN:

9781470428495

Schlagwörter:

Andere physische Formen: 1470428490 | 9781470428495 | 1470436612. | 9781470436612. | Erscheint auch als: Kein Titel Druck-Ausgabe | Print version: Kein Titel DDC-Klassifikation:

512
512.02 DDC23eng

MSC: MSC: *00A05 | 20-01 | 13-01 | 12-01 | 00A07LOC-Klassifikation:

QA162

Online-Ressourcen:

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Zusammenfassung: 11.6. Automorphisms and Inner-automorphisms^{⋆}11.7. More Problems and Projects; Chapter 12. Using Sylow Theorems to Analyze Finite Groups*; 12.1. -groups; 12.2. Acting on Cosets and Existence of Normal Subgroups; 12.3. Applying the Sylow Theorems; 12.4. ₅ Is the Only Simple Group of Order 60; Chapter 13. Direct and Semidirect Products^{⋆}; 13.1. Direct Products of Groups; 13.2. Fundamental Theorem of Finite Abelian Groups; 13.3. Semidirect Products; 13.4. Groups of Very Small Order; Chapter 14. Solvable and Nilpotent Groups^{⋆}; 14.1. Solvable Groups; 14.2. Nilpotent GroupsZusammenfassung: 6.1. The Fundamental Counting Principle6.2. The Conjugation Action; 6.3. The Class Equation and Groups of Order ²; 6.4. More Problems and Projects; Chapter 7. Acting on Subsets, Cosets, and Subgroups: The Sylow Theorems; 7.1. Binomial Coefficients \bmod ; 7.2. The Sylow E(xistence) Theorem; 7.3. The Number and Conjugacy of Sylow Subgroups^{⋆}; Chapter 8. Counting the Number of Orbits^{⋆}; 8.1. The Cauchy-Frobenius Counting Lemma; 8.2. Combinatorial Applications of the Counting Lemma; 8.3. More Problems and Projects; Chapter 9. The Lattice of Subgroups^{⋆}Zusammenfassung: Cover; Title page; Contents; Preface; Part 1 . (Mostly Finite) Group Theory; Chapter 1. Four Basic Examples; 1.1. Symmetries of a Square; 1.2. 1-1 and Onto Functions; 1.3. Integers \bmod and Elementary Properties of Integers; 1.4. Invertible Matrices; 1.5. More Problems and Projects; Chapter 2. Groups: The Basics; 2.1. Definitions and Examples; 2.2. Cancellation Properties; 2.3. Cyclic Groups and the Order of an Element; 2.4. Isomorphisms; 2.5. Direct Products (New Groups from Old Groups); 2.6. Subgroups; 2.7. More Problems and Projects; Chapter 3. The Alternating GroupsZusammenfassung: This text-based on the author's popular courses at Pomona College-provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of thPPN: PPN: 1003152953Package identifier: Produktsigel: ZDB-4-NLEBK

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