Mark A. Armstrong

Groups and Symmetry (eBook, PDF)

• Format: PDF

Produktbeschreibung

This is 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. Includes more than 300 exercises and approximately 60 illustrations.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 187
• Erscheinungstermin: 14. März 2013
• Englisch
• ISBN-13: 9781475740349
• Artikelnr.: 44179884

Inhaltsangabe

From the contents: Symmetries of the Tetrahedron.- Axioms.- Numbers.- Dihedral Groups.- Subgroups and Generators.- Permutations.- Isomorphisms.- Plato's Solids and Cayley's Theorem.- Matrix Groups.- Products.- Lagrange's Theorem.- Partitions.- Cauchy's Theorem.- Conjugacy.- Quotient Groups.- Homomorphisms.- Actions, Orbits, and Stabilizers.- Counting Orbits.- Finite Rotation Groups.- The Sylow Theorems.- Finitely Generated Abelian Groups.- Row and Column Operations.- Automorphisms.- The Euclidean Group.- Lattices and Point Groups.- Wallpaper Patterns.- Free Groups and Presentations.- Trees and the Nielsen-Schreier Theorem.- Bibliography.- Index.

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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.- 10 Products.- 11 Lagrange's Theorem.- 12 Partitions.- 13 Cauchy's Theorem.- 14 Conjugacy.- 15 Quotient Groups.- 16 Homomorphisms.- 17 Actions, Orbits, and Stabilizers.- 18 Counting Orbits.- 19 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.

Rezensionen

"This book is a gentle introductory text on group theory and its application to the measurement of symmetry. It covers most of the material that one might expect to see in an undergraduate course . . . The theory is amplified, exemplified and properly related to what this part of algebra is really for by discussion of a wide variety of geometrical phenomena in which groups measure symmetry. Overall, the author's plan, to base his treatment on the premise that groups and symmetry go together, is a very good one, and the book deserves to succeed." MATHEMATICAL REVIEWS

M.A. Armstrong Groups and Symmetry "This book is a gentle introductory text on group theory and its application to the measurement of symmetry. It covers most of the material that one might expect to see in an undergraduate course . . . The theory is amplified, exemplified and properly related to what this part of algebra is really for by discussion of a wide variety of geometrical phenomena in which groups measure symmetry. Overall, the author's plan, to base his treatment on the premise that groups and symmetry go together, is a very good one, and the book deserves to succeed."-MATHEMATICAL REVIEWS