THERE'S NO BRICK WALL BECAUSE PENNEY DIDN'T BUILD ONE!
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 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.
More Information About This New Approach