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Chapter 1: Vectors 1.0: Introduction: The Racetrack Game
1.1: The Geometry and Algebra of Vectors (35)
1.2: Length and Angle: The Dot Product (58)
1.3: Lines and Planes (35)
1.4: Applications (9)
1: Chapter Review

Chapter 2: Systems of Linear Equations 2.0: Introduction: Triviality
2.1: Introduction to Systems of Linear Equations (26)
2.2: Direct Methods for Solving Linear Systems (40)
2.3: Spanning Sets and Linear Independence (40)
2.4: Applications (31)
2.5: Iterative Methods for Solving Linear Systems (15)
2: Chapter Review

Chapter 3: Matrices 3.0: Introduction: Matrices in Action
3.1: Matrix Operations (31)
3.2: Matrix Algebra (35)
3.3: The Inverse of a Matrix (44)
3.4: The LU Factorization (25)
3.5: Subspaces, Basis, Dimension, and Rank (47)
3.6: Introduction to Linear Transformations (36)
3.7: Applications (44)
3: Chapter Review

Chapter 4: Eigenvalues and Eigenvectors 4.0: Introduction: A Dynamical System on Graphs
4.1: Introduction to Eigenvalues and Eigenvectors (22)
4.2: Determinants (49)
4.3: Eigenvalues and Eigenvectors of n x n Matrices (29)
4.4: Similarity and Diagonalization (39)
4.5: Iterative Methods for Computing Eigenvalues (32)
4.6: Applications and the Perron-Frobenius Theorem (51)
4: Chapter Review

Chapter 5: Orthogonality 5.0: Introduction: Shadows on a Wall
5.1: Orthogonality in ℜn (30)
5.2: Orthogonal Complements and Orthogonal Projections (21)
5.3: The Gram-Schmidt Process and the QR Factorization (15)
5.4: Orthogonal Diagonalization of Symmetric Matrices (24)
5.5: Applications (41)
5: Chapter Review

Chapter 6: Vector Spaces 6.0: Introduction: Fibonacci in (Vector) Space
6.1: Vector Spaces and Subspaces (47)
6.2: Linear Independence, Basis, and Dimension (42)
6.3: Change of Basis (17)
6.4: Linear Transformations (24)
6.5: The Kernel and Range of a Linear Transformation (25)
6.6: The Matrix of a Linear Transformation (28)
6.7: Applications (14)
6: Chapter Review

Chapter 7: Distance and Approximation 7.0: Introduction: Taxicab Geometry
7.1: Inner Product Spaces (29)
7.2: Norms and Distance Functions (33)
7.3: Least Squares Approximation (36)
7.4: The Singular Value Decomposition (42)
7.5: Applications (16)
7: Chapter Review

Chapter 8: Codes (Online only) 8.1: Code Vectors (12)
8.2: Error-Correcting (8)
8.3: Dual Codes (11)
8.4: Linear Codes (9)
8.5: The Minimum Distance of a Code (8)

Chapter A: Appendices A.A: Mathematical Notation and Methods of Proof
A.B: Mathematical Induction
A.C: Complex Numbers
A.D: Polynomials
A.E: Technology Bytes (Online only)

David Poole is Professor of Mathematics at Trent University, where he has been a faculty member since 1984.

Dr. 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.

From 2002-2007, Dr. Poole was Trent University's Associate Dean (Teaching & Learning). His research interests include discrete mathematics, ring theory, and mathematics education. He received his B.Sc. from Acadia University in 1976 before earning his M.Sc. (1977) and Ph.D. (1984) from McMaster University. When he is not doing mathematics, David Poole enjoys hiking and cooking, and he is an avid film buff.

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