Algebraic Structure and Matrices Book 2

This book was originally published in 1965. Dr Maxwell relates the ideas being introduced into the teaching of elementary university and advanced school algebra to the topics and methods with which teachers and students are already familiar and which are treated in the author's Advanced Algebra, Part I. Dr Maxwell shows the student meeting modern algebra for the first time what it is all about and leads those who will be taking the subject further to a firm grasp of the details that will come later in their course. From a discussion of algebraic systems with a single operation, he introduces the idea of a group and goes on to survey other algebraic structures: vector spaces, fields and rings. The second section is on linear algebra, mainly in terms of matrices and the solution of linear equations. A final section introduces the reader to more advanced concepts, including eigenvectors and eigenvalues and their use for quadratic forms. There is a large number of examples, with answers.

Preface; Introduction; Bibliography; Part I. Algebraic Structure: 1. One-process algebra; 2. Neutral elements and inverse operations; 3. The group structure; 4. Euclidean spaces; 5. Two-process algebra: vector spaces; 6. Two-process algebra: single set, rings and fields; 7. Subsets; 8. Theory of numbers: congruences; 9. Modules of integers; 10. Polynomial forms; Part II. Matrices: 11. Matrices and mappings; 12. The elementary manipulation of matrices; 13. Matrices of orders 2 and 3; 14. Partitioned matrices; 15. Mappings and vector spaces; 16. Linear equations: rank; Part III. Introduction to more Advanced Work: 17. Quadratic forms: eigenvectors; 18. Eigenvalues and eigenvectors: special matrices; 19. Some abstract conceptions; 20. Some matrix groups; Index.