MATH 1711 Finite Mathematics:
Maple Explorations

Here you will find a collection of Maple worksheets designed to help you in your studies. The following online resourses were written with this course in mind.

• An Introduction to Maple, by Dr. George Cain
• Drawing Graphs, by Dr. James V. Herod
• A Maple worksheet on computing permutations and combinations. This worksheet shows how Maple can compute permutations and combinations of sets, as well as compute the number of permutations or combinations desired.
• A Maple worksheet on binomials and multinomials, and the binomial theorem. In this Maple exercise, we look at the meanings of binomials and multinomials in terms of the binomial theorem and as applications to counting problems. This worksheet contains some examples of counting problems that you can try with or without Maple.
• A Maple worksheet on statistics, including frequency distributions, cumulative frequency distributions, and histograms.  This worksheet also explores Maple commands for measures of centrality and dispersion.
• A Maple worksheet on the binomial distribution and histograms.  In this worksheet, we explore how Maple can generate the probability distributions and histograms of binomial trials.
• A Maple worksheet on graphing the feasible set of a system of inequalities.  We learn how to use Maple to help graph the feasible set of a system of inequalities and find the corner points of the feasible set.
• A Maple worksheet on the least-squares problem. We explore the solution to the least-squares problem using Maple's matrix operations. Given n data points, we wish to find the line, y=mx+b, that "best fits" the data. Transforming our data points into matrices yields a matrix equation Y=AX. Our goal is to solve for the matrix X. Since our matrix A is not a square matrix, we multiply both sides by the transpose of A and then use previously learned methods to solve the system. As an example, we try to find a linear relationship between high school and college GPA's.
• Maple commands for matrix arithmetic and multiplication. In this Maple worksheet, we introduce the basic commands for adding, multiplying, inverting, and finding the transpose of a matrix. Try this worksheet before trying the least-squares application.
• A Maple worksheet on solving systems of equations with a unique solution. This worksheet explores various methods of solving a system of linear equations on Maple. We use four methods, three of which use a form of matrix elimination: the "solve" command, Gaussian elimination, Gauss-Jordan elimination, and the "linsolve" command for solving matrix equations.
• A Maple worksheet on solving systems of equations without a unique solution. We use the method of Gauss-Jordan elimination to solve some systems of linear equations that have either no solution or infinitely many solutions.
• A Maple worksheet on finding the inverse of an n x n matrix.
• A Maple worksheet on linear programming.  In this worksheet, we see how Maple can be used to help sketch and solve linear programming problems in two variables.
• A Maple worksheet on the Simplex method.  This worksheet explains how to use Maple to pivot the Simplex tableau in order to obtain a final tableau for maximization problems.
• A Maple worksheet on minimization.  Here, we use the Simplex method to minimize a given objective function with a system of constraints.
• A Maple worksheet on duals and matrix formulations.  This worksheet introduces the reader to commands that produce a matrix formulation or the dual of a given linear programming problem.

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Last Modified: . School of Mathematics, Georgia Institute of Technology.