Linear Algebra: A Modern Introduction

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Overview

David Poole's innovative LINEAR ALGEBRA: A MODERN INTRODUCTION, 4e emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning. Theoretical, computational, and applied topics are presented in a flexible yet 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. Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems.

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Editorial Reviews

From The Critics
Designed for either a one- or two-semester course, this college-level introductory algebra textbook covers vectors, linear equations, matrices, eigenvalues and eigenvectors, orthogonality, vector spaces, and distance and approximation. Appendices discuss mathematical notation and methods of proof, mathematical induction, complex numbers, polynomials, and technology. Concrete examples are emphasized over abstract principles or theoretical concerns. Poole teaches at Trent University. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780538735445
  • Publisher: Cengage Learning
  • Publication date: 9/28/2010

Meet the Author

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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Table of Contents

1. 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. Writing Project: Origins of the Dot Product and the Cross Product. Applications. 2. SYSTEMS OF LINEAR EQUATIONS. Introduction: Triviality. Introduction to Systems of Linear Equations. Direct Methods for Solving Linear Systems. Writing Project: A History of Gaussian Elimination. Explorations: Lies My Computer Told Me; Partial Pivoting; Counting Operations: An Introduction to the Analysis of Algorithms. Spanning Sets and Linear Independence. Applications. Vignette: The Global Positioning System. Iterative Methods for Solving Linear Systems. 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. Vignette: Robotics. Applications. 4. EIGENVALUES AND EIGENVECTORS. Introduction: A Dynamical System on Graphs. Introduction to Eigenvalues and Eigenvectors. Determinants. Writing Project: Which Came First-the Matrix or the Determinant? Vignette: Lewis Carroll's Condensation Method. Exploration: Geometric Applications of Determinants. Eigenvalues and Eigenvectors of n x n Matrices. Writing Project: The History of Eigenvalues. Similarity and Diagonalization. Iterative Methods for Computing Eigenvalues. Applications and the Perron-Frobenius Theorem. Vignette: Ranking Sports Teams and Searching the Internet. 5. ORTHOGONALITY. Introduction: Shadows on a Wall. Orthogonality in Rn. Orthogonal Complements and Orthogonal Projections. The Gram-Schmidt Process and the QR Factorization. Explorations: The Modified QR Factorization; Approximating Eigenvalues with the QR Algorithm. Orthogonal Diagonalization of Symmetric Matrices. Applications. 6. VECTOR SPACES. Introduction: Fibonacci in (Vector) Space. Vector Spaces and Subspaces. Linear Independence, Basis, and Dimension. Writing Project: The Rise of Vector Spaces. 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. 7. DISTANCE AND APPROXIMATION. Introduction: Taxicab Geometry. Inner Product Spaces. Explorations: Vectors and Matrices with Complex Entries; Geometric Inequalities and Optimization Problems. Norms and Distance Functions. Least Squares Approximation. The Singular Value Decomposition. Vignette: Digital Image Compression. Applications. 8. CODES. (Online) Code Vectors. Vignette: The Codabar System. Error-Correcting Codes. Dual Codes. Linear Codes. The Minimum Distance of a Code. Appendix A: Mathematical Notation and Methods of Proof. Appendix B: Mathematical Induction. Appendix C: Complex Numbers. Appendix D: Polynomials.

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Sort by: Showing all of 2 Customer Reviews
  • Anonymous

    Posted August 5, 2004

    Linear algebra written as if students matter!

    I'm a sophomore math/computer major who just took linear algebra (for my degree requirements). I like math but am no genius. I've always found calculus more to my liking than algebra though. So I had no great hopes for my linalg course, I just wanted to get through it. The prof had just switched textbooks and the new book was Linear Algebra by David Poole. Like another reviewer said: WOW! This book was so well written that I really didn't need my class notes except for a couple of topics that weren't in the text. Prof. Poole has written a clear, interesting, and USEFUL book that seems to have been written with people like me in mind. I enjoyed the course, thanks mainly to the book, and have revised my opinion of algebra! Buy this book!! A++++

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  • Anonymous

    Posted November 18, 2002

    The best linear algebra book!!!

    I am a student taking a college linear algebra course. I'm not a math major but I like math and have generally done pretty well at it. The course I'm taking is OK and the prof is pretty good but the textbook SUCKS. Maybe if you're a math genius it's OK but for the average student (like me) it's hopeless. (I won't mention the name to protect the guilty!) I saw Poole's book in my campus bookstore and, after browsing through it, decided to buy it. Wow! Am I ever glad I did! This is how to write a textbook, folks. The author writes very clearly and there are plenty of examples to help you understand the basic concepts. Some of the applications (and there are LOTS) are REALLY interesting. I particularly like the way he helps you to see how everything fits together by emphasizing the geometric side of the subject. So now I only use my textbook for assigned homework exercises -- I refer to Poole for everything else. I envy this guy's students -- his linear algebra class must be outstanding! If you're looking to buy one linear algebra book, this is the one to buy. JP

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