Undergraduate algebra: A first course
C. W. Norman
Designed for second-year mathematics students, this book offers a modern, highly systematic approach to thoroughly familiarize students with the theory of rings, fields, vector spaces, and particularly with the techniques of matrix manipulation. In keeping the needs of the learner paramount, the author provides motivation at each difficult point and integrates a wide range of exercises into each chapter. The method is both strong in its presentation of linear algebra and relevant to computer science.
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