This paper deals with a brief history of the most remarkable Euler numbers "e,"?"i"?and?"?" in mathematical sciences. Included are many properties of the constants "e,"?"i"?and?"?" and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special…

In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

Computing the mean and covariance matrix of some multivariate distributions, in particular, multivariate normal distribution and Wishart distribution are considered in this article. It involves a matrix transformation of the normal random vector into a random vector whose components are independent normal random variables, and then integrating…

Excel assignments were used as extra credit in an intermediate algebra course. Ninety percent of the students had a home computer and seventy per cent were familiar with Excel. There was not a significant linear correlation between the amount of Excel that the students performed and their achievement in algebra. One-third of the students did less…

Computer operations involving complex numbers, essential in such applications as Fourier transforms or image processing, are normally performed in a "divide-and-conquer" approach dealing separately with real and imaginary parts. A number of proposals have treated complex numbers as a single unit but all have foundered on the problem of the…

The author argues that programs to prepare the casual computer user are needed. Too much emphasis has been placed on thorough understanding of the working of the machine, and not enough on general principles of man-machine interaction. (SD)

Problems of designing a college honors program in computer science as an academic discipline are disucssed. (MM)

In this paper, prepared for a European conference on mathematics education, the author examines three types of computer use in undergraduate and high school classrooms: Using the computer as an instructional tool for student development of algorithms, teaching about the computer itself, and use of computer-assisted instruction. (SD)