Using Mathematica in a Biomedical Statistics Classroom: Blood Glucose Level Analysis

This contribution demonstrates an example of the possible use of Mathematica in statistics courses for biomedical students. The text, combined seamlessly with statistical computations using built-in features of Mathematica, provides the students a step-by-step guide through statistical analysis pitfalls using a particular case study: blood glucose measurement of a patient suffering from type 1 (juvenile) diabetes mellitus. Both exploratory and inference analysis are included. Attention is particularly paid to the ability of students to select the correct hypothesis test.

Interval Computations and Differential Equations

Interval computations are becoming a well-accepted method of rigorous mathematical proofs. We discuss some possibilities of deploying Mathematica into interval-computation proofs of theorems concerning boundary-value problems for strongly nonlinear differential equations. Alternatively, we also describe development of a highly optimized library supporting special functions from the theory of nonlinear differential equations. For performance and correctness reasons, our library is written in GNU Assembler for Intel Pentium. We use new LibraryLink Mathematica 8 technology for calling user-defined C functions. A C interface is used for accessibility of our library functions from Mathematica. In order to improve performance of our library, we derived various approximate formulas for our special functions using symbolic calculations. The library will be used in proving theorems in the theory of nonlinear differential equations.

Graph Visualization

Numerical Solutions of Differential Equations II

Create Your Own Distribution

Using the Mathematica framework to create your own statistics distribution and have it behave just as one of the built-in ones.

Graph Data Analysis

Social Network Analysis

Survival Analysis in Mathematica

Solving Railway Mazes: From Image to Solution

Roger and Lionel Penrose have created some interesting railway mazes. A railway maze asks the solver to get from start to finish by pretending to be a train that cannot go backward. Thus at every junction the train must follow the curve of the track; it cannot make sharp turns at intersections. We will present a method that starts with an image of such a maze, such as a JPEG file, and finds all solutions. One of the Penrose mazes can be found in the attached notebook. The challenge is to get from A to B by following the curves at each junction.

Linear Algebraic Queueing Theory Approach to Reliability

We utilize techniques from a linear algebraic approach to queueing theory to develop a comprehensive set of symbolic reliability formulas, starting from the matrix exponential. Along the way, we also demonstrate some interesting connections to symmetric polynomials and integer partitions and compositions. These methods are quick and easy to illustrate, explain, and use within Mathematica.