Shiny Applications - Math Games, Demos, Computational Aids, and Other Nonsense

All applications linked to on this page are the intellectual property of Richard C. Gayle and the ideas contained therein may not be used for any commercial purpose without his explicit written consent.

Elementary Statistical Applications:These applications are designed to support an introductory statistics course. Some provide facile interfaces for performing standard computations associated with the sort of information, for example summary statistics, customarily provided by routine textbook problems. Others are aimed at giving students an opportunity to rehearse concepts via graphical interfaces. The applications are front-ended by a decision tree to aid students in finding the appropriate application for the task they face.

Calculus Games: This app is a little calculus game in which you (a student, a bored person with time on his/her hands, etc.) are shown the graph of f, f', or f'' and asked a question about it, or more generally, one of the other two. Versions available in English, German, and Dutch. A version someday, I hope, in Spanish. Ein Bißchen Geduld, Mensch! A second application explores the second fundamental theorem of the calculus through three graphical games.

Elementary Algebra Games: This little app allows students to hone their skills at factoring quadratic trinomials. Here students (or any joe blow) can practice solving simple absolute value inequalities using a graphical interface. This app asks users to identify the algebraic modifications in a function which lead to identifiable changes in its graph. Next are two apps which deal with that perennial favorite topic of elementary algebra students the world over, graphs of lines in the Cartesian Plane. The first involves finding line's graphs from their equations in 'standard form', the second requires finding the slope and y-intercept of a line from its graph. In January, 2020 I wrote an app which graphs user-entered functions. It's obviously not a 'needed' thing from a practical point of view but it has a couple of interesting features and was fun to construct. Lastly, here's an app from August 2020 which asks users to use the horizontal line test to determine whether functions are one-one or not.

Crypto-Math: This app came about as an attempt to help a friend who was struggling with a 'Mathematical Cryptography' course he was taking as part of an MS program in 'information security'. Thereby hangs a tale (which I will share elsewhere, perhaps). My friend ultimately failed the course and left the program (Oops! It really was never in the cards, though) but at least I learned a little new math and wrote this app (which doesn't really qualify as a game but....)

Vector Operations: This app performs standard vector operations, visually in the Cartesian plane and merely arithmetically in higher dimensions. Again, this isn't really a game, more of a `demo' for possible classroom use but it belongs with the math stuff.

Permutations: With this app users can use a graphical interface to specify one or permutations on the set {1,2,....n} and then either compose those permutations or, if only one is selected, form the cyclic subgroup which it generates in S(n).

Lagrange Interpolation: Use this app to compute Lagrange interpolating polynomials. It allows the use of a variety of data input methods and the downloading of the coefficients of the Lagrange polynomial as well as its values and those of the target function at user selected inputs.

Means and Mean Deviations, Illustrated:The ordinary arithmetic mean is the real number which has the least root-mean square distance to a given data set consisting of real numbers. The median, on the other hand, minimizes the mean absolute deviation from the data and the midrange minimizes, trivially, the maximum absolute deviation for the data. For the 'Lp' analogies of these distances, the minimizer lacks a concise formulation. Nonetheless, for specfic data and p, it can be calculated numerically which is what this app does, providing some nice pictures along the way.

Buffon's Needle: This app app simulates the experiment known as "Buffon's Needle" which provides an estimate of π.

Estimating e: This app uses a sum of random draws from the distribution U[0,1] to estimate e. A linked pdf explains how and why the method works.