# Welcome To A New Experience In Linear Algebra!

LINEAR ALGEBRA: Ideas and Applications
Richard C. Penney, Purdue University
18179-X, 525 Pages, Cloth, 1998

Richard C. Penney was selected by his students at Purdue University as the Most Outstanding Teacher in the School of Science for 1995-1996, and as one of the top ten teachers in the School for Science for 1994-1995. His vision of mathematical truth and falsehood as something students can personally decide rather than as a body of facts to be blindly accepted has made linear algebra come alive for his students.

In LINEAR ALGEBRA: Ideas and Applications Penney shares his vision in an eloquent, new approach to teaching linear algebra. Penney's deep devotion both to educating students and to imparting the beauty and utility of the subject can be found on every page of this remarkable text!

## NO BRICK WALL!

• Parallel Development of Concepts
Penney introduces abstract concepts from the very beginning, and only as they are needed to understand the computations. Because the text justifies the importance of each new concept and relates it to something in the students sphere of experience, students have the time and the tools to fully absorb each concept and to make the connection between theory and application.

• Gradual Development of Vector Spaces
Many texts introduce vector spaces relatively late in the course, leaving students insufficient time to absorb the concept before it is used. Penney introduces vector spaces early, but more difficult concepts such as linear independence, spanning and inner product spaces are presented gradually.

• Fully Integrated Applications
Penney shows students how the theory grows out of necessity to solve concrete applied problems. Students connect the power and applicability of the ideas as they learn them.

• Conceptual Exercises
Too often students learn how to use techniques without understanding them. Penney's conceptual (not theoretical) exercises require students to think abstractly about concrete questions, and show them that there is a need to understand theory in order to answer concrete questions about computations.

• Technology
Technology can be a powerful tool for making abstract concepts more concrete and visual. Penney provides ample free standing computer exercises that support and extend the concepts discussed in the section. Matlab specific exercises are provided in the text and Mathematica and Maple translations in supplements and on the world wide web.

• The Writing Style
Penney's casual, informal style uses language that all students can understand. The mathematics is complete, but explanations are given in contexts that students can relate to.