This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida.

Numerical linear algebra, no longer a subtopic of numerical analysis, has grown into an independent topic for research and teaching. It is not certainly an overstatement that numerical linear algebra is the "mother" of scientific computing, a major component of modern applied and engineering research.

It is, therefore, essential that numerical linear algebra forms a visible component in the training of applied mathematics and scientific computations for our future scientists and engineers. In my opinion, such a training should begin right at undergraduate level.

Though some major universities have now numerical linear algebra courses at undergraduate levels, the subject, as such, has not become an integral component of our undergraduate curricular yet. It is very often embedded in a numerical analysis course, and not taught with a proper care so that the subject can make an impact on the students training.

In this talk, I shall present my own thoughts on the development of numerical linear algebra and scientific computing courses at undergraduate and beginning graduate levels, and, outline some "tips" of teaching numerical linear algebra properly, based on my own long experience.

In particular, I shall discuss the teaching methodologies that help the students develop a firm grasp of the rather "strange" concepts of round-off errors, stability, conditioning, and accuracy, and appreciate the core algorithms, their usefulness, and proper implementations.

Biswa Nath Datta, Northern Illinois University