Described are some major developments in the history of ideas in which mathematics has played a central role. The discussion is organized around four key features of mathematics: certainty, applicability, more than one geometry, and opposition. (MNS)

In the seventh century, around 650 A.D., the Indian mathematician Brahmagupta came up with a remarkable formula expressing the area E of a cyclic quadrilateral in terms of the lengths a, b, c, d of its sides. In his formula E = [square root](s-a)(s-b)(s-c)(s-d), s stands for the semiperimeter 1/2(a+b+c+d). The fact that Brahmagupta's formula is…

The results of a survey of the mathematics provision within UK university computer science departments are presented. In particular it is found that many academics are dissatisfied with the level of "mathematical preparedness" of their students. A number of recommendations and resources are suggested to address this. (Contains 6 figures.)

This is the first volume of the proceedings of the Committee on the Undergraduate Program in Mathematics (CUPM) Geometry Conference, held at Santa Barbara in June, 1967. The purpose of the conference was to consider the status of geometry in colleges at the undergraduate level. The conference, attended by undergraduate mathematics teachers,…

Presented is a linear program for matrix algebra required in a first course in multivariate educational statistics. The purpose of the program is to enable graduate students, through self instruction, to acquire sufficient knowledge of matrix algebra to meet the prerequisite of a course in multivariate statistics of a type taught in a department…

The second of three volumes of a mathematics training course for Navy personnel, this document contains material primarily found at the college level. Beginning with logarithms and trigonometry, the text moves into vectors and static equilibrium (physics). Coordinate geometry, conic sections, and the tangents, normals, and slopes of curves follow.…

An exhibit at the San Francisco Exploratorium is used to discuss problem solving and illustrate optimization. The solution is discussed in detail. (MNS)

How current calculus textbooks consider the relationship between the tangent line and the derivative are discussed, with three theorems presented. (MNS)

An extension of the integration by parts formula, useful in the classroom for products of three functions, is illustrated with several examples. (MNS)

An interesting graphical interpretation of complex roots is presented, since it is probably unfamiliar to many mathematics teachers. (MNS)

Two methods for solving matrix equations are discussed. Both operate entirely on a matrix level. (MNS)