Abstract Algebra with Applications (Cambridge Mathematical Textbooks)

Abstract Algebra with Applications offers a concise and approachable introduction to algebra, focusing on its practical applications in the modern world. The initial section of the book covers groups, preceded by an overview of sets, functions, relations, and induction. It highlights various applications, including public-key cryptography, Sudoku, the finite Fourier transform, and symmetry in chemistry and physics. The latter section explores rings and fields, featuring applications such as random number generators, error correcting codes, the Google page rank algorithm, communication networks, and elliptic curve cryptography. Throughout the text, vibrant figures and images effectively illustrate the concepts and applications. Real-world examples and exercises provide students with a contextual understanding of the material. Designed for a year-long undergraduate algebra course aimed at mathematics, engineering, and computer science majors, the only prerequisites are calculus and a willingness to tackle short proofs.

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