David Lay - Recent advances in teaching linear algebra

In recent years, the exponential increase in computing power has driven a corresponding increase in the use of linear algebraic techniques to model and solve engineering and scientific problems that were computationally inaccessible a few decades ago. The language of linear algebra has become an essential part of the basic training of engineers and computer scientists, and this has influenced both the content and modes of instruction of linear algebra courses. The lecture will focus on three areas in which significant advances have been made--mathematical content, pedagogy, and the use of technology.

(1)  The mathematical focus of a first course in linear algebra has shifted somewhat, from an abstract inward-looking subject to a more concrete matrix-oriented approach. Yet the insistence on precision of language and careful proof remains.

(2)  Advances in the mathematical presentation of linear algebra have simplified the teaching of the material and made it more accessible to students. Improved pedagogy has also resulted from the influence of reform in the calculus courses and from a new understanding of how mathematical concepts are internalized by average students.

(3)  Technology is, of course, widely used in linear algebra courses. But its use is driven more by the needs of the students to understand the its role in linear algebra than by the popularity of technology for collegiate instruction. The lecture will conclude with a discussion of how technology is being used today in linear algebra instruction.