Pooles "Linear Algebra: A Modern Introduction, Cengage International Edition", 5th, emphasizes a vectors approach and prepares students to transition from computational to theoretical mathematics. Balancing theory and applications, the conversational writing style combines traditional presentation with student-centered learning. Theoretical, computational, and applied topics are presented in a flexible, integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Applications drawn from a variety of disciplines reinforce linear algebra as a valuable tool for modeling real-life problems. Exercises allow students to practice linear algebra concepts and techniques. Learning objectives in each section serve as a guide for students and instructors.
Chapter 1: Vectors
Introduction: The Racetrack Game. The Geometry and Algebra of Vectors.
Length and Angle: The Dot Product. Lines and Planes. Applications.
Chapter
Review.
Chapter 2: Systems of Linear Equations
Introduction: Triviality. Introduction to Systems of Linear Equations.
Direct Methods for Solving Linear Systems. Spanning Sets and Linear
Independence. Applications. Iterative Methods for Solving Linear Systems.
Chapter Review.
Chapter 3: Matrices
Introduction: Matrices in Action. Matrix Operations. Matrix Algebra. The
Inverse of a Matrix. The LU Factorization. Subspaces, Basis, Dimension, and
Rank. Introduction to Linear Transformations. Applications.
Chapter
Review.
Chapter 4: Eigenvalues and Eigenvectors
Introduction: A Dynamical System on Graphs. Introduction to Eigenvalues and
Eigenvectors. Determinants. Eigenvalues and Eigenvectors of n × n Matrices.
Similarity and Diagonalization. Iterative Methods for Computing
Eigenvalues. Applications and the Perron-Frobenius Theorem.
Chapter Review
Chapter 5: Orthogonality
Introduction: Shadows on a Wall. Orthogonality in Rn. Orthogonal
Complements and Orthogonal Projections. The Gram-Schmidt Process and the QR
Factorization. Orthogonal Diagonalization of Symmetric Matrices.
Applications.
Chapter Review.
Chapter 6: Vector Spaces
Introduction: Fibonacci in (Vector) Space. Vector Spaces and Subspaces.
Linear Independence, Basis, and Dimension. Change of Basis. Linear
Transformations. The Kernel and Range of a Linear Transformation. The
Matrix of a Linear Transformation. Applications.
Chapter Review.
Chapter 7: Distance and Approximation
Introduction: Taxicab Geometry. Inner Product Spaces. Norms and Distance
Functions. Least Squares Approximation. The Singular Value Decomposition.
Applications.
Chapter Review.
Chapter 8: Codes
Introduction: ASCII. Code Vectors. Error-Correcting Codes. Dual Codes.
Linear Codes. The Minimum Distance of a Code.
Chapter Review.
Chapter A: Appendices
Mathematical Notation and Methods of Proof. Mathematical Induction. Complex
Numbers. Polynomials. Technology Bytes.
David Poole is Professor Emeritus of Mathematics at Trent University, where he was a faculty member from 19842016. Prof. Poole has won numerous teaching awards: Trent University's Symons Award for Excellence in Teaching (the university's top teaching award), three merit awards for teaching excellence, a 2002 Ontario Confederation of University Faculty Associations Teaching Award (the top university teaching award in the province), a 2003 3M Teaching Fellowship (the top university teaching award in Canada, sponsored by 3M Canada Ltd.), a 2007 Leadership in Faculty Teaching Award from the province of Ontario, and the Canadian Mathematical Society's 2009 Excellence in Teaching Award. For his services to mathematics education, Prof. Poole was named a Fellow of the Canadian Mathematical Society in 2018. Prof. Poole served as chair of Trents Mathematics Department on three occasions, and from 20022007 he was Associate Dean of Arts and Science (Teaching & Learning). His dedication to high quality teaching extends to policy development: he has been involved with teaching committees, task forces on mathematics education, and he has produced reports on teaching and learning approaches. His research interests include discrete mathematics, ring theory, and mathematics education. He received his B.Sc. from Acadia University (1976) before earning his M.Sc. (1977) and Ph.D. (1984) from McMaster University. When he is not doing mathematics, David Pooles hobbies include cooking and constructing crossword puzzles, and he is an avid film buff.
