The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The modules also introduce students to real world math concepts and problems that property and casualty actuaries come across in their work. They are designed to be used by teachers and…

This document consists of three modules concerned with aspects of statistics. The first provides knowledge of the effect of imperfect correlation and random error on differences between means, and the reasons for the necessity of random allocation of objects to experimental and control conditions in scientific experimentation. The second unit…

The described learning module is designed for teachers at the middle school level who wish to improve specific basic mathematics teaching skills. The contents of the module are outlined, and activities and resources involved in its use are described. Ordering information for materials is included, and a critique of the module is provided. (JD)

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…

A group is viewed to be one of the simplest and most interesting algebraic structures. The theory of groups has been applied to many branches of mathematics as well as to crystallography, coding theory, quantum mechanics, and the physics of elementary particles. This material is designed to help the user: 1) understand what groups are and why they…

This module considers ordinary linear differential equations with constant coefficients. The "complex method" used to find solutions is discussed, with numerous examples. The unit includes both problem sets and an exam, with answers provided for both. (MP)

Vector analysis is viewed to play a key role in many branches of engineering and the physical sciences. This unit is geared towards deriving identities and establishing "machinery" to make derivations a routine task. It is noted that the module is not an applications unit, but has as its primary objective the goal of providing science,…

The inservice learning module described focuses on teaching mathematical concepts at the elementary grade level. Specifically covered in the module are discovery learning, drill activities, understanding number concepts, and introduction to geometry. Information is provided in this descriptive report on the scope and sequencing of topics and the…

This document is designed to provide a concise introduction to the theory of generalized inverses of matrices that is accessible to undergraduate mathematics majors. The approach used is to: (1) develop the material in terms of full-rank factorizations and to relegate all discussions using eigenvalues and eigenvectors to exercises, and (2) include…

Applied mathematics is seen often to involve the solution of single equations or systems of equations. A particular technique for solving equations in the context of functions on the real line is examined. This technique includes an iterative process, which is viewed as an algorithm that can be implemented readily on inexpensive and widely…

This unit introduces analytic solutions of ordinary differential equations. The objective is to enable the student to decide whether a given function solves a given differential equation. Examples of problems from biology and chemistry are covered. Problem sets, quizzes, and a model exam are included, and answers to all items are provided. The…

It is noted that there are some integrals which cannot be evaluated by determining an antiderivative, and these integrals must be subjected to other techniques. Numerical integration is one such method; it provides a sum that is an approximate value for some integral types. This module's purpose is to introduce methods of numerical integration and…

This preapprenticeship preparation curriculum consists of 13 learning modules. Covered in the modules are the following: the nature and scope of apprenticeships, a pretest to assess students' mathematical skills, the General Aptitude Test Battery, interviews for an apprenticeship program, whole numbers, common fractions, decimal fractions,…

This document is designed to help the user recognize problems which can be solved by use of the exponential function, to show a wide variety of such problems, and to teach how to actually solve them. The material is divided into five individual units, numbered and labeled as follows: 84-Recognition of Problems Solved by Exponential Functions;…