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Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts. But its beauty is lost on students when it is taught in a technical style that is difficult to understand.

Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.

Tabla de contenidos provista por Syndetics

• Preface
• Overview
• 1 What is a group?
• 2 What do groups look like?
• 3 Why study groups?
• 4 Algebra at last
• 5 Five families
• 6 Subgroups
• 7 Products and quotients
• 8 The power of homomorphisms
• 9 Sylow Theory
• 10 Galois theory

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CHOICE Review

An introductory course in abstract algebra is often a student's first exposure not only to abstract mathematical thinking but also to writing rigorous proofs. Here, Carter (Bentley Univ.) presents the group theory portion of abstract algebra in a way that allows students to actually see, using a multitude of examples and applications, the basic concepts of group theory. Although the work contains few exercises requiring students to write rigorous mathematical proofs, students are asked to delve deeply into the structure of specific finite groups. The numerous images (more than 300) are the heart of the text. As this work enables readers to see, experiment with, and understand the significance of groups, they will accumulate examples of groups and their properties that will serve them well in future endeavors in mathematics. This book can stand alone as a first course in group theory or as a supplement to a more traditional course in abstract algebra. Although not required, the free software, Group Explorer, can enhance the student's hands-on learning experience presented in this volume. Summing Up: Recommended. Lower- and upper-division undergraduates and faculty interested in group theory. J. T. Zerger Catawba College