Algebra and Geometry

Author: Xiao Shuti
Publisher:
Publish Date: 2002-01-01
Features: This book is a research outcome of the "Reform Plan for Teaching Content and Curriculum System in Higher Education Towards the 21st Century" by the Ministry of Education, and is a textbook for the 21st-century curriculum. It updates the mathematical content of "Algebra and Geometry" for non-mathematics majors, better integrating algebra and geometry, allowing them to permeate and promote each other. The book begins with the fundamental knowledge of modern mathematics—sets, relations, operations, and mappings, as well as the basic concepts of groups, rings, and fields. It then explores linear spaces and linear mappings, proceeding in the order of linear spaces and inner product spaces, linear mappings, matrices, determinants, systems of linear equations, eigenvalues and eigenvectors, standard forms of matrices, and quadratic forms, to develop the content of linear algebra. The concepts of linear spaces and linear mappings run through the entire book, playing a central role in unifying the material.
The geometry section, in addition to spatial analytical geometry, also includes introductions to affine and projective geometry, as well as non-Euclidean geometry, to deepen students' understanding of "shapes" and more comprehensively cultivate their rational thinking, spatial reasoning abilities, and aesthetic awareness. This book can serve as a textbook for science and engineering majors in higher education institutions and is also suitable for reference by professionals in various fields.