Linear Algebra: Ideas and Applications

By Richard C. Penney and Richard C Penney

Book Overview

Praise for the Third Edition

"This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications."

- Electric Review

A comprehensive introduction, Linear Algebra: Ideas and Applications, Fourth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique.

The book introduces each new concept in the context of an explicit numerical example, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs.

Linear Algebra: Ideas and Applications, Fourth Edition also features:

Two new and independent sections on the rapidly developing subject of waveletsA thoroughly updated section on electrical circuit theoryIlluminating applications of linear algebra with self-study questions for additional studyEnd-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented materialNumerous computer exercises throughout using MATLAB(R) code

Linear Algebra: Ideas and Applications, Fourth Edition is an excellent undergraduate-level textbook for one or two semester courses for students majoring in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.

• Format: Hardcover
• Language: English
• ISBN: 1118909585
• ISBN13: 9781118909584
• Release Date: November 2015
• Publisher: Wiley
• Length: 512 Pages
• Weight: 0.65 lbs.
• Dimensions: 1.3" x 6.4" x 9.3"

Customer Reviews

Great for transitioning to abstract math

All right, I'll admit it: when it came to math, for most of my life I was a ninety-eight-pound weakling. I excelled at analogies, reading comprehension, vocabulary, people called me "Verbal" -- but when it came to equations and theorems, I was useless. At the same time, I was fascinated by math, resulting in my picking up quite a number of algebra and analysis books I was woefully unprepared to comprehend. This book changed that. I took a linear algebra class where it was the assigned textbook, and for the first time I would read the textbook to understand what was going on in class, not the other way around. The particular strength of this book is in encouraging what is called "mathematical maturity" (usually cited as a "prerequisite" in the introductions to books on higher mathematics). Mathematical maturity is not simply a "formal" grasp of mathematical operations: learning how to formalize the Peano axioms in a logic class won't cut it. It's about learning how to balance mathematical exigency with theoretical elegance, and this book is specifically designed to get you to grasp such issues. It does this by emphasizing the importance of proofs, without forcing you to deduce all necessary principles from axioms. In this, it differs quite markedly from other introductory linear algebra textbooks, such as Howard Anton's. Anton et al., like calculus and high school algebra texts, are designed in a "cookbook" format: they offer you numerical recipes for getting desirable outcomes from given data. That is not to say they are uniformly less advanced: Anton's text covers topics, like the Vronskian, which this textbook does not. And on the other side of the scale, there probably isn't much difference if you only want to learn Gaussian elimination. However, if you're in the market for a linear algebra textbook, you are probably needing to grasp not only matrix operations but also how mathematics proceeds beyond solving equations: and I can tell you from experience, learning from this book is one of the easiest ways to do so. For someone with a year of calculus under their belt, a course using this book would be an excellent choice: the book would also be cost-effective for self-study by a person with a little money but not much time. Errors are commonplace in any textbook in the exact sciences: a program for making essential skills comprehensible to many is rare indeed.