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Visual Group Theory

Nathan Carter


Over 300 illustrations in full color.

Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music, and many other contexts. Its beauty is often lost on students because it is typically 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.

Although the book stands on its own, the free software Group Explorer makes an excellent companion. It enables the reader to interact visually with groups, including asking questions, creating subgroups, defining homomorphisms, and saving visualizations for use in other media. It is open source software available for Windows, Macintosh, and Unix systems from

Nathan Carter's website for this book features further info, including an image gallery, sample chapters, and links to podcasts.

This book is also available in hardcover from the MAA Store.

* As a textbook, Visual Group Theory does have DRM. Our DRM protected PDFs can be downloaded to three computers. iOS and Android tablets can open secure PDFs using the AWReader app (available in the App Store and the Play Store). The iOS app uses the native iPad PDF reader so it is a very basic reader, no frills. Linux is not supported at this time for our secure PDFs.

Electronic ISBN:  9781614441021

Visual Group Theory $29.00


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