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.
Contents:
- Integers and Polynomials
- Determinants and Matrices
- Linear Systems
- Linear Spaces
- Linear Maps
- Λ-Matrices
- Quadratic Forms
- Inner Product Spaces
- Bilinear Forms
Readership: A textbook for the undergraduate advanced algebra course; a reference for teaching advanced or linear algebra courses.
Key Features:
- Motivate and stimulate interest of students by starting topics with research background and development context
- Cultivate thinking and exploration spirit by presenting the formation and development process of mathematical knowledge
- Connect high school curriculum, future studies, and scientific research
- Promote and cultivate student's own ability to ask questions, find examples, and provide proofs
- Special attention to the promotion of traditional Chinese mathematical culture and highlights the contributions from Chinese mathematicians
