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Principles of Linear Algebra with Mathematica, by Kenneth M. Shiskowski, Karl Frinkle
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A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica�
Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica� are essential not only for learning to apply the concepts to computationally challenging problems, but also for visualizing many of the geometric aspects within this field of study. Principles of Linear Algebra with Mathematica uniquely bridges the gap between beginning linear algebra and computational linear algebra that is often encountered in applied settings, and the commands required to solve complex and computationally challenging problems using Mathematica are provided.
The book begins with an introduction to the commands and programming guidelines for working with Mathematica. Next, the authors explore linear systems of equations and matrices, applications of linear systems and matrices, determinants, inverses, and Cramer's rule. Basic linear algebra topics, such as vectors, dot product, cross product, and vector projection are explored, as well as a unique variety of more advanced topics including rotations in space, 'rolling' a circle along a curve, and the TNB Frame. Subsequent chapters feature coverage of linear transformations from Rn to Rm, the geometry of linear and affine transformations, with an exploration of their effect on arclength, area, and volume, least squares fits, and pseudoinverses.
Mathematica is used to enhance concepts and is seamlessly integrated throughout the book through symbolic manipulations, numerical computations, graphics in two and three dimensions, animations, and programming. Each section concludes with standard problems in addition to problems that were specifically designed to be solved with Mathematica, allowing readers to test their comprehension of the presented material. All related Mathematica code is available on a corresponding website, along with solutions to problems and additional topical resources.
Extensively class-tested to ensure an accessible presentation, Principles of Linear Algebra with Mathematica is an excellent book for courses on linear algebra at the undergraduate level. The book is also an ideal reference for students and professionals who would like to gain a further understanding of the use of Mathematica to solve linear algebra problems.
- Sales Rank: #1826690 in Books
- Published on: 2011-08-02
- Original language: English
- Number of items: 1
- Dimensions: 9.51" h x 1.32" w x 6.40" l, 2.33 pounds
- Binding: Hardcover
- 616 pages
Review
"An accessible introduction to the theoretical and computational aspects of linear algebra using Maple(TM)." (TMCnet.com, 16 April 2011)
About the Author
Kenneth Shiskowski, PhD, is Professor of Mathematics at Eastern Michigan University. His areas of research interest include numerical analysis, history of mathematics, the integration of technology into mathematics, differential geometry, and dynamical systems. Dr. Shiskowski is the coauthor of Principles of Linear Algebra with Maple, published by Wiley.
Karl Frinkle, PhD, is Associate Professor of Mathematics at Southeastern Oklahoma State University. His areas of research include Bose-Einstein condensates, nonlinear optics, dynamical systems, and integrating technology into mathematics. Dr. Frinkle is the coauthor of Principles of Linear Algebra with Maple, published by Wiley.
Most helpful customer reviews
11 of 11 people found the following review helpful.
Undergrad indie student likes this book so far
By Amilein Zenomans
I'm finishing Chapter 5, and here is some of what I like about this book (in no particular order of presentation).
1. Written about as clearly as popular texts such as Howard Anton's Elementary...
2. Good balance of theory/proof and calculation.
3. Introductory chapter on Mathematica is good.
4. For students new to Mathematica, downloadable code is available at the book's website. Code is written such that it appears to run on MMA 6, 7, and 8.
5. Authors respect the past, but are not stuck in it. They clearly understand that computer algebra systems need not rot a student's brain.
6. The proof of many important linear algebra relationships presented in the text are left as exercises for the student (in the homework sections of the text). This helps the motivated student develop independence so important to maths.
7. Solutions manual (comes with book) is no lazy thing. As necessary, steps are clearly shown and good explanations given.
I have the impression that Shiskowski and Frinkle are unpretentious fellows, at least as interested in teaching as in pleasing those maths instructors who still won't embrace CAS's (at least when others are looking). Quite clearly, S and F value and enjoy theorems and proof; just as clearly, they value and enjoy the integration of modern CAS's into the teaching process. This is a huge plus in my opinion because is saves a great deal of study/practice time, expands what can be covered in a course, and allows students to be exposed to more realistic problems - not just problems so simplified that they are manageable with paper, pencil, and hand calculator. Also, CAS's like Mathematica and Maple make possible study of some of the informative (and I think beautiful) geometric bases, interpretations, and applications of linear algebra.
This book is in its first, but I hope not last, edition. As such, it doesn't give one all the colorful formatting and non-substantive content commonly found in more established works. But who cares about this besides greedy publishers and poor students? The absence of fluff in this book keeps the price relatively low. Compare others at $120 for text plus $35 for solutions manual and about $40 more for a CAS manual (that is likely not really integrated into the text, but more like slapped onto the end of it).
9 of 9 people found the following review helpful.
Highly recommended for the ambitious EE student
By AMNorse
I am an electrical engineering student in the northern US, but my university has very separate math and engineering departments. The linear algebra class at my school does not focus on applications or technology at all, so I decided to teach myself and took a gamble on this book.
I've read many math texts and found that the common theme among those that teach well is a conversational style of language combined with many examples, problem sets, and solutions. This book is written in an enjoyable and accessible manner that does not attempt to cut words so that it can have the appearance of added rigor. It has plenty of rigor all on it's own, and the material is that much more accessible because the author is willing to talk the reader through things. The integration of Mathematica is equally enjoyable and will no doubt provide me with a tool that is very handy for solving problems that would be tedious or nearly impossible to do by hand.
The problems at the end of the sections are on point for the preceding lesson. They are separated into problems meant to be done by hand and those meant for Mathematica. Many of the Mathematica problems are tailored to serve as a teaching tool to show someone why they would want (or need) a computer algebra system. This could have been something that got in the way of learning the math, but it isn't overbearing and adds to the text.
My only critique is that this is not the right book for people who do not want to learn a computer algebra system. Obviously, as that's ~30% of what the book is teaching. It's right in the title. But then why wouldn't someone be interested? Mathematicians and engineers need a computer algebra system to speed up their workflow, and this book helps you kill two birds with one stone.
Also of note is the companion website which contains Mathematica code for problems and examples, as well as a comprehensive solutions manual. Problems are thoroughly worked out and explained which is utterly critical and something I wish more texts put emphasis on.
I have not finished the book and will update when I do, but I honestly couldn't wait to review this text. This is a real treat after a year of some very inaccessible math texts.
TLDR: Overall, very impressive! If you want to learn Mathematica and linear algebra, especially if you are teaching yourself, this is the way to do it!
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