Probabilistic machine learning increasingly informs critical decisions in medicine, economics, politics, and beyond. To aid the development of trust in these decisions, we develop a taxonomy delineating where trust in an analysis can break down: (1) in the translation of real-world goals to goals on a particular set of training data, (2) in the…

A previously developed program for the HP-41C programmable calculator is extended to handle models of differential and difference equations with multiple eigenvalues. How to obtain difference equation solutions via the Z transform is described. (MNS)

Presents a theorem and its converse to generate all of the primitive Pythagorean quadruples. Provides a BASIC program generating them. (YP)

Discusses a numerical technique called the method of adjoints, turning a linear two-point boundary value problem into an initial value problem. Described are steps for using the method in linear or nonlinear systems. Applies the technique to solve a simple pendulum problem. Lists 15 references. (YP)

Suggests and illustrates ways in which systematic consideration of selected unary operations can be facilitated by using electronic calculators. Emphasis is placed upon unary operations suitable for exploration and investigation at the pre-algebra level, using calculation algorithms as a basis for generating examples and non-examples to develop…

Presents two methods for replacing a series by one converging more rapidly: regrouping the terms of a series and manipulations of power series. Describes a general algorithm for approximating the natural logarithm of any number. (YP)

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

Describes a pattern which emerged from an examination of the digits of the squares of numbers. Provides eight examples having the pattern at the units or tens digit of the number. (YP)

Provides four examples for testing the validity of logical arguments by using the method of truth trees. (YP)

Describes examples of rational representation as a guide for translating terminology and information encountered in manuals for computers. Discusses four limitations of the representation. (YP)

Presents an example from the combinatorial theory of partially ordered sets. Discusses algorithms of on-line antichain partitioning problems, a topic in discrete optimization. (YP)

Describes the algorithm used to select a simple random sample of certain size without having to list all possible samples and a justification based on Pascal's triangle. Provides testing results by various computers. (YP)

Defines one approach to problem solving in terms of student use of algorithms to find their solutions and gives examples. Discusses how problems and algorithms relate to each other. Describes strategies for teaching problem solving using algorithms. (CW)

Discusses ways to integrate computers into mathematically oriented classes effectively so that advantages are obtained without increasing detrimental effects. Three sections detail use of computers as experimental tools, to implement and understand algorithms, and to solve realistic size problems. These ideas are illustrated with examples from a…

This article develops an algorithm to find all solutions to the problem, making all sums of a hexagram's nine lines the same. It shows how to exploit the geometric structure of the hexagram and its group of automorphisms. (YP)