: The book demonstrates that GA naturally incorporates complex numbers, quaternions, and exterior algebra, providing a common language for physics, computer science, and engineering. Structural Innovation
Alan Macdonald, Professor Emeritus at Luther College, wrote this text to serve as a comprehensive undergraduate introduction. Unlike standard courses that treat quaternions, complex numbers, and cross products as separate "tricks," this book presents them as natural parts of a single algebraic system. The book is structured into three main parts: alan macdonald linear and geometric algebra pdf
: Introduces the geometric product, bivectors, and operations like rotations and reflections. Part III: Linear Transformations : The book demonstrates that GA naturally incorporates
The foundational premise of the text is captured by David Hestenes’ quote: "Geometry without algebra is dumb! - Algebra without geometry is blind!". Macdonald shifts the focus from coordinate-heavy computations to a coordinate-free approach where geometric objects—such as lines, planes, and volumes—are represented directly as members of an algebra called multivectors. This perspective allows students to: The book is structured into three main parts:
A free PDF of the Introduction is available, covering the philosophy behind the book and the basic definition of geometric algebra.