Contemporary Issues in Mathematics Education: Proceedings of by Estela A. Gavosto, Steven G. Krantz, William McCallum

Show description

Also find a 3 × 3 matrix S and a diagonal matrix D so that S −1 AS = D. 3. (5%) If Q is an n × n orthogonal matrix, what is det Q? What are the eigenvalues of Q? Give reasons. 4. (15%) Let Fk denote the Fourier matrix of dimension k. Define      y0 y1 y0  y1   y3   y2           Y2n =  y2  , Yodd =  y5  , Yeven =  y4  .   .   .  ..   ..   .. y2n−1  i 2π 2n Also let w = e 1  w  2  and W =  w  ..  . y2n−1  for each n:        y2n−2    . Then the fast Fourier transform   wn−1 can be described as follows: F2n Y2n = Fn Yeven + W Fn Yodd Fn Yeven − W Fn Yodd Now let ρ(2n) denote the minimum number of operations needed to compute F2n Y2n .

First, the students do not retain material as well as we would like. Second, the students do not recognize concepts in a new context (which in this case was any context outside the calculus class). Once we agreed on these two problems as the focus of our efforts to improve calculus instruction for physical science students, all of these faculty were able to collaborate together to create a joint syllabus in mathematics, physics, and chemistry. The mathematicians argued for covering less material in order to achieve greater student retention.

Rather, the ability areas most often mentioned to us by alumni in the field are problem-solving, breaking complex problems into solvable pieces, adapting a solution from one problem setting to another, writing and otherwise communicating with clients and co-workers, decision making, working well with others in a team, and a willingness to work hard. Many of these are standard components of an undergraduate mathematics curriculum. Much of mathematics deals with solving problems, and usually requires breaking them down into smaller pieces.