Advanced Algebra and Analytic Geometry (I)

Author: Chen Zhijie
Publisher:
Publish Date: 2000-06-01
Features: This book contains the main content of the original two foundational courses, Higher Algebra and Analytic Geometry. The textbook strives to be both profound and accessible, integrating algebra and geometry organically, enabling students not only to use algebraic methods to solve geometric problems 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 content, 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), the 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 and point transformations (including classification of quadratic curves and surfaces), polynomial functions and the factorization of integers, multivariate polynomials (including Wu Wenjun elimination method and machine proof of geometric theorems), polynomial matrices and Jordan canonical forms, and applications of Jordan canonical forms, etc. This book can be used as a textbook for higher algebra and analytic geometry courses in normal universities, comprehensive universities' mathematics departments, and applied mathematics departments, and can also serve as a reference book for teaching.