Linear Algebra A Modern Introduction

ISBN-10: 0534998453

ISBN-13: 9780534998455

Edition: 2nd 2006

Authors: David Poole

List price: $362.95
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Description:

David Poole's innovative book emphasizes vectors and geometric intuition from the start and better prepares students to make the transition from the computational aspects of the course to the theoretical. Poole covers vectors and vector geometry first to enable students to visualize the mathematics while they are doing matrix operations. With a concrete understanding of vector geometry, students are able to visualize and understand the meaning of the calculations that they will encounter. By seeing the mathematics and understanding the underlying geometry, students develop mathematical maturity and can think abstractly when they reach vector spaces. Throughout the text, Poole's direct conversational writing style connects with students, and an abundant selection of applications from a broad range of disciplines clearly demonstrates the relevance of linear algebra.
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Book details

List price: $362.95
Edition: 2nd
Copyright year: 2006
Publisher: Brooks/Cole
Publication date: 1/24/2005
Binding: Hardcover
Pages: 684
Size: 8.00" wide x 9.75" long x 1.00" tall
Weight: 3.498
Language: English

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.

Vectors
Introduction: The Racetrack Game
The Geometry and Algebra of Vectors
Length and Angle: The Dot Product
Exploration: Vectors and Geometry
Lines and Planes
Exploration: The Cross Product
Code Vectors and Modular Arithmetic
Vignette: The Codabar System
Chapter Review
Systems of Linear Equations
Introduction: Triviality
Introduction to Systems of Linear Equations
Exploration: Lies My Computer Told Me
Direct Methods for Solving Linear Systems
Exploration: Partial Pivoting
Exploration: Counting Operations
An Introduction to the Analysis of Algorithms
Spanning Sets and Linear Independence
Applications: Allocation of Resources
Balancing Chemical Equations
Network Analysis
Electrical Networks
Finite Linear Games
Vignette: The Global Positioning System
Iterative Methods for Solving Linear Systems
Chapter Review
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: Markov Chains
Population Growth
Graph Theory
Error-Correcting Codes
Vignette: Robotics
Chapter Review
Eigenvalues and Eigenvectors
Introduction: A Dynamical System on Graphs
Eigenvalues and Eigenvectors
Determinants
Exploration: Geometric Applications of Determinants
Eigenvalues and Eigenvectors of n x n Matrices
Similarity and Diagonalization
Iterative Methods for Computing Eigenvalues
Applications: Markov Chains
Population Growth; the Perron-Frobenius Theorem
Linear Recurrence Relations
Systems of Linear Differential Equations
Linear Dynamical Systems
Vignette: Ranking Sports Teams and Searching the Internet
Chapter Review
Orthogonality
Introduction: Shadows on a Wall
Orthogonality in Rn
Orthogonal Complements and Orthogonal Projections
The Gram-Schmidt Process and the QR Factorization
Exploration: The Modified QR Factorization
Exploration: Approximating Eigenvalues with the QR Algorithm
Orthogonal Diagonalization of Symmetric Matrices
Applications: Dual Codes
Quadratic Forms
Graphing Quadratic Forms
Chapter Review
Vector Spaces
Introduction: Fibonacci in (Vector) Space
Vector Spaces and Subspaces
Linear Independence, Basis, and Dimension
Exploration: Magic Squares
Change of Basis
Linear Transformations
The Kernel and Range of a Linear Transformation
The Matrix of a Linear Transformation
Exploration: Tilings, Lattices and the Crystallographic Restriction
Applications: Homogeneous Linear Differential Equations
Linear Codes
Chapter Review
Distance and Approximation
Introduction: Taxicab Geometry
Inner Product Spaces
Exploration: Vectors and Matrices with Complex Entries
Exploration: Geometric Inequalities and Optimization Problems
Norms and Distance Functions
Least Squares Approximation
The Singular Value Decomposition
Vignette: Digital Image Compression
Applications: Approximation of Functions
Error-Correcting Codes
Chapter Review
Mathematical Notation and Methods of Proof
Mathematical Induction
Complex Numbers
Polynomials
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