Knapp Basic Algebra

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.

In the years since publication of the first editions of Basic Algebra and Advanced Algebra, many readers have reacted to the books by sending comments, suggestions, and corrections. They appreciated the overall comprehensive nature of the books, associating this feature with the large number of problems that develop so many sidelights and applications of the theory.

In the years since publication of the first edition of Basic Algebra, many readers have reacted to the book by sending comments, suggestions, and corrections. People especially approved of the inclusion of some linear algebra before any group theory, and they liked the ideas of proceeding from the particular to the general and of giving examples of computational techniques right from the start. They appreciated the overall comprehensive nature of the book, associating this feature with the large number of problems that develop so many sidelights and applications of the theory.

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.

In the years since publication of the first editions of Basic Algebra and Advanced Algebra, many readers have reacted to the books by sending comments, suggestions, and corrections. They appreciated the overall comprehensive nature of the books, associating this feature with the large number of problems that develop so many sidelights and applications of the theory.
Along with the general comments and specific suggestions were corrections, and there were enough corrections to the first volume to warrant a second edition. A second edition of Advanced Algebra was then needed for compatibility.

An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group.