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.

This book evolved from our lectures in the advanced algebra courses at Nanjing University. It is intended for use by instructors and undergraduate students in a one-year advanced algebra course.The topics covered in this book consist of integers and polynomials, determinants and matrices, linear systems, linear spaces, linear maps, λ-matrices, quadratic forms, inner product spaces, and bilinear forms.There are sufficient well-selected exercises of a wide range to provide ample practice, expand coverage of topics treated in the text, and challenge the strongest students.Our objective is to prepare students with a solid foundation for pursuing advanced mathematics. We hope that the material presented here will interest the students and help them ask their own questions, look for their own examples, and discover their own proofs.

Intended for the undergraduate students of mathematics, this student-friendly text provides a complete coverage of all topics of Linear, Abstract and Boolean Algebra. The text discusses the matrix and determinants, Cramer’s rule, Vandermonde determinants, vector spaces, inner product space, Jacobi’s theorem, linear transformation, eigenvalues and eigenvectors. Besides, set theory, relations and functions, inclusion and exclusion principle, group, subgroup, semigroup, ring, integral domain, field theories, Boolean algebra and its applications have also been covered thoroughly. Each concept is supported by a large number of illustrations and 600 worked-out examples that help students understand the concepts in a clear way. Besides, MCQs and practice exercises are also provided at the end of each chapter with their answers to reinforce the students’ skill.

This book covers advanced algebra consisting of: types of algebra category theory groups and group theory algebraic structures Galois theory