Advanced Algebra and Analytic Geometry (Volumes 1 and 2) - Second Edition

Author: Meng Daoji
Publisher:
Publish Date: 2004-05-01
Features: Mathematical analysis, advanced algebra, and analytic geometry are the three major foundational courses in university mathematics departments. The Department of Mathematics at Nankai University unifies analytic geometry and advanced algebra into a single course, an initiative widely recognized by peers. This book attempts to reflect this approach. The book is divided into two volumes. Chapter 1 discusses polynomial theory; Chapter 2 introduces determinants, including Cramer's rule for solving systems of linear equations using determinants; Chapter 3 covers matrices, focusing on matrix computations, elementary transformations, and the relationship between matrices and systems of linear equations; Chapter 4 introduces linear spaces; Chapter 5 introduces linear transformations; Chapter 6, polynomial matrices, is designed for discussing complex linear transformations; Chapter 7 introduces Euclidean spaces; Chapter 8 covers bilinear functions and quadratic forms; Chapter 9 discusses quadratic surfaces; Chapter 10 introduces affine geometry and projective geometry. The book includes a rich selection of exercises. It can be used as a textbook for students in mathematics departments of higher education institutions, as well as a reference for mathematics teachers and researchers.