Mark A. Armstrong: Groups and Symmetry

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Cover: 9781441930859 | Groups and Symmetry | Mark A. Armstrong | Taschenbuch | Paperback | xi

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Sprache: Englisch

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Beschreibung

Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or a new idea. Throughout the book, the emphasis is placed on concrete examples, many of them geometrical in nature, so that finite rotation groups and the seventeen wallpaper groups are treated in detail alongside theoretical results such as Lagrange's theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof of the Nielsen-Schreier theorem, using group actions on trees. There are more than three hundred exercises and approximately sixty illustrations to help develop the student's intuition.

Zusammenfassung

This text, designed for undergraduate mathematics students, provides a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. There are more than 300 exercises and approximately 60 illustrations to help develop the student's intuition.

Inhaltsverzeichnis

Preface. 1: Symmetries of the Tetrahedron. 2: Axioms. 3: Numbers. 4: Dihedral Groups. 5: Subgroups and Generators. 6: Permutations. 7: Isomorphisms. 8: Plato's Solids and Cayley's Theorem. 9: Matrix Groups. 10: Products. 11: Lagrange's Theorem. 12: Partitions. 13: Cauchy's Theorem. 14: Conjugacy. 15: Quotient Groups. 16: Homomorphisms. 17: Actions, Orbits, and Stabalizers. 18: Counting Orbits. 19: Finite Rotation Groups. 20: The Sylow Theorems. 21: Finitely Generated Abelian Groups. 22: Row and Column Operations. 23: Automorphisms. 24: The Euclidean Group. 25: Lattices and Point Groups. 26: Wallpaper Patterns. 27: Free Groups and Presentations. 28: Trees and the Nielsen-Schreier Theorem. Bibliography. Index.

Erscheinungsjahr:	2010
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	204
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xi 187 S.
ISBN-13:	9781441930859
ISBN-10:	144193085X
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Armstrong, Mark A.
Auflage:	Softcover reprint of hardcover 1st ed. 1988
Hersteller:	Springer US Springer New York Undergraduate Texts in Mathematics
Maße:	234 x 156 x 12 mm
Von/Mit:	Mark A. Armstrong
Erscheinungsdatum:	01.12.2010
Gewicht:	0,319 kg

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