Concrete Abstract Algebra

Concrete Abstract Algebra: From Numbers to Gröbner Bases by Niels Lauritzen presents a clear and thorough introduction to abstract algebra, moving steadily from the familiar world of numbers to the advanced theory of Gröbner bases. The book covers standard topics of an introductory course while also exploring areas such as cryptography, integer factorization algorithms, quadratic residues, finite fields, and polynomial factorization methods. One of the key strengths of this work is its integrated approach to Gröbner bases, woven seamlessly into the overall discussion rather than treated as a standalone topic. Lauritzen relies on a wealth of examples, applications, and exercises to illuminate abstract concepts, demonstrating how real-world problems can provide both motivation and clarity in understanding complex ideas. Drawing on years of teaching experience, this text offers a balanced blend of theory and practice that enriches the learning experience.