Summary and Info
The third edition of Linear Algebra: A Modern Introduction preserves the approach and features that users found to be strengths of the previous editions. However, some new material have added to make the book useful to a wider audience, and I have also freshened up the exercises.This book is designed for use in an introductory one- or two-semester course sequence in linear algebra. First and foremost, it is intended for students, and have been tried be to writen so that students not only will find it readable but also will want to read it. As in the first and second editions taken into account the reality that students taking introductory linear algebra are likely to come from a varietyof disciplines. In addition to mathematics majors, there are apt to be majors from engineering, physics, chemistry, computer science, biology, environmental science, geography, economics, psychology, business, and education, as well as other students taking the course as an elective or to fulfill degree requirements. Accordingly, the book balances theory and applications, is written in a conversational style yet is fully rigorous, and combines a traditional presentation with concern for student-centered learning.There is no such thing as a single-best learning style. In any class, there will be some students who work well independently and others who work best in groups; some who prefer lecture-based learning and others who thrive in a workshop setting,doing explorations; some who enjoy algebraic manipulations, some who are adept at numerical calculations (with and without a computer), and some who exhibit stronggeometric intuition. In this book, I continue to present material in a variety of ways—algebraically, geometrically, numerically, and verbally—so that all types of learners can find a path to follow. I have also attempted to present the theoretical, computational, and applied topics in a flexible yet integrated way. In doing so, it is my hope that all students will be exposed to the many sides of linear algebra.This book is compatible with the recommendations of the Linear Algebra Curriculum Study Group. From a pedagogical point of view, there is no doubt that for most students concrete examples should precede abstraction. I have taken this approach here. I also believe strongly that linear algebra is essentially about vectors and that students need to see vectors first (in a concrete setting) in order to gain some geometric insight.Moreover, introducing vectors early allows students to see how systems of linearequations arise naturally from geometric problems.Matrices then arise equally naturally as coefficient matrices of linear systems and as agents of change (linear transformations).This sets the stage for eigenvectors and orthogonal projections, both of which are best understood geometrically. The darts that appear on the cover of this book symbolize vectors and reflect my conviction that geometric understanding should precede computational techniques.