Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found…

A way of presenting the Poisson process and deriving the Poisson distribution for upper-division courses in probability or mathematical statistics is presented. The main feature of the approach lies in the formulation of Poisson postulates with immediate intuitive appeal. (MNS)

Historical problems are presented which can readily be solved by students once some elementary probability concepts are developed. The Duke of Tuscany's Problem; the problem of points; and the question of proportions, divination, and Bertrand's Paradox are included. (MNS)

The author suggests several problems which can be investigated by beginning statistics students. All the problems discussed arise from the game Bingo. (SD)

A sequence of numbers from combinatorial theory called the Bell numbers is discussed, along with several problems and examples that demonstrate their usefulness. (MN)

After studying a unit on probability students "put it all together" by analyzing outcomes of real and computer-simulated games of craps. FORTRAN and APL programs for generation of the games are provided in this article. (SD)

One way in which a computer simulation can convince students of the validity of formulas for the density and distributive functions of the sum of two variables is described. Four computer program listings are included. (MNS)

An exercise simulating the tossing of N dice is described. Calculation of expected gain and extension to a two-person game are each discussed. (MNS)

The Monte Carlo method and its logic are reviewed, then three experiments that tested the value of the method in a variety of class settings are described. (DT)

Describes the "Buffon's Needle" problem, which is calculating the probability that a needle will cross one of two separated lines. Calculates the probability when the length of the needle is greater than the space of the two lines. Provides an analytic solution and the results of a computer simulation. (YP)

A hypothetical classroom discussion is used to present concepts and problems students can master. Three computer programs are listed for binomial probabilities. (MNS)

The game of craps is analyzed in terms of mathematical expectation. Betting examples are presented and discussed, and a computer simulation program in BASIC is included. (MNS)

Presents an application of the binomial distribution in which the distribution is used to detect differences between the sensory properties of food products. Included is a BASIC computer program listing used to generate triangle and duo-trio test results. (JN)

The use of indicator functions is promoted as a vehicle for providing students with greater appreciation and understanding of the function concept, which might be good preparation for the functional concepts of probability and random variable. The use is seen to provide a reasonably accessible method of verifying set-theoretic statements. (MP)

Presents the game of Keno as an interesting, realistic model for applying mathematics that can be an excellent aid in teaching some basic probability concepts. It is felt that having students examine the probabilities may convince them that winning at Keno is unlikely, and it is an unfair game. (MP)