These exciting topics are unified through the steady, consistent development of algebraic structures and techniques. Students who read this book will walk away with a broad exposure to both the theory and the concrete application of groups, finite fields, and vector spaces.This undergraduate introduction to error correction and cryptography is unique in devoting several chapters to quantum cryptography and quantum computing, thus providing a context in which ideas from mathematics and physics meet. By covering such topics as Shor's quantum factoring algorithm, this text informs the reader about current thinking in quantum information theory and encourages an appreciation of the connections between mathematics and science.