Foundations of Mathematics: Volume 2: Introductory Linear Algebra & Analytical Geometry
暫譯: 數學基礎：第二卷：線性代數與解析幾何入門

One of the greatest mathematicians of all time is reported to have said, "Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty." Foundations of Mathematics is devoted to awakening such a love for Mathematics, among first year university students. It is a two volume series-Volume 1, Sets and Number Systems, introduces the student to concepts in Abstract Algebra; while this volume, Introductory Linear Algebra & Analytical Geometry, introduces the student to basic concepts in Linear Algebra, with applications to Coordinate Geometry. The material presented here is intended to cover a one semester course in Introductory Linear Algebra and Coordinate Geometry. It begins with a treatment of Complex Numbers; necessary to complete the study of the Number Systems, begun in the first volume. It then transitions to a study of vectors in two and three dimensions, with applications to lines and planes in two and three dimensions. Matrices and determinants are then introduced; and this sets the stage for introducing methods of solving systems of linear equations, which is the culmination of the study. The emphasis is on developing the student's ability to think and express him/herself mathematically, and to appreciate the concepts on which Mathematics is built. This aims to lay a solid foundation on which to pursue second year mathematics courses; while, at the same time, equipping those not continuing in Mathematics, with the basic tools of Linear Algebra. The author offers a wealth of experience in teaching introductory mathematics courses at universities and colleges. Students are sure to appreciate her detailed notes, the many worked-examples and exercises, as well as, the inspiring stories of mathematicians, featured at the end of each chapter. The appendix contains material specially designed for the Introductory Linear Algebra and Analytical Geometry Course offered at the University of the West Indies, St Augustine, Trinidad and Tobago.