Advanced Algebra and Analytic Geometry (Volume 2)

Author: Chen Zhijie
Publisher:
Publish Date: 2001-02-01
Features: This book contains the main content of the original two foundational courses, Linear Algebra and Analytic Geometry. The textbook strives to be both profound and accessible, organically integrating algebra and geometry to enable students not only to solve geometric problems using algebraic methods but also to see the geometric background of algebraic concepts, thereby enhancing their geometric intuition. Additionally, the book introduces the use of symbolic computation software (Maple V) in synchronization with the course material, accompanied by hands-on laboratory exercises. The textbook offers considerable flexibility, catering to the needs of students at different levels. The book is published in two volumes. The first volume includes: Vector Algebra, Determinants, Systems of Linear Equations and Linear Subspaces (including affine properties of planes and lines), Rank of Matrices and Matrix Operations, Linear Spaces and Euclidean Spaces (including metric properties of planes and lines). The second volume includes: Common Surfaces in Geometric Spaces, Linear Transformations, Functions on Linear Spaces, Coordinate Transformations and Point Transformations (including classification of quadratic curves and surfaces), Univariate Polynomials and Factorization of Integers, Multivariate Polynomials (including Wu's Elimination Method and machine proof of geometric theorems), Polynomial Matrices and Jordan Canonical Form, Applications of Jordan Canonical Form, etc. This book can be used as a textbook for advanced algebra and analytic geometry courses in normal universities, comprehensive universities' mathematics departments, and applied mathematics departments, as well as a reference book for teaching.