SENTRY/CCICADA Education Modules

SENTRY Courses and Materials

SENTRY through a subaward to CCICADA develops homeland security materials and courses that are distributed to tens of thousands of students and practitioners nationwide. These modules are based on research conducted by SENTRY and CCICADA and other DHS Centers of Excellence. They are classroom-tested, widely used, and cover five to eight days of instruction. As noted in some modules, there will be professional development modules on CANVAS for the modules that can be used in the first two years of undergraduate courses. This Canvas site will be available by the end of 2023.

Sentry  Modules:

• • String Art: Creating, Constructing, and Computing
  • Rank, Predict, Program, Play, Repeat: An Introduction to Linear Programming
  • Legos Optimization
  • Data Analytics Using Linear Programming and the AMPL Algebraic Modelling Language

• Simplex Algorithm
  • Simplex Introduction to Optimization from Theory to Data – Option 1
  • The Simplex Algorithm – Option 2

String Art: Creating, Constructing, and Computing by Melanie Brown, Catherine Buell, and Alison Marr.
Note: A professional development module will be available on Canvas by the end of 2023.
This module includes an introduction to String Art and the work of Mary Everest Boole and then an application of optimization using string art in differential calculus. It is designed to be flexible in its deployment in the classroom. The first part requires no prerequisite knowledge and is an ideal opportunity to highlight marginalized mathematicians while engaging a general education audience in finding patterns related to modular arithmetic. It is formatted as a guided worksheet for student use. The second part is a research question using Desmos and is formatted to guide the instructor supervising the research project. The module in its entirety is appropriate for a Calculus I audience to demonstrate another use for tangent lines that also provides an example of optimization beyond the traditional single-variable calculus optimization problems.
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Rank, Predict, Program, Play, Repeat: An Introduction to Linear Programming by Melanie Brown, Catherine Buell, and Alison Marr. This module is aimed to provide students beginning Linear Algebra an opportunity to play with advanced ideas of optimization and linear programming, typically reserved for a course in Optimization or Operations Research. The module builds upon introductory Linear Algebra ideas and implements code in MATLAB (using the Symbolic and Optimization Toolboxes) to allow students the ability to explore complex systems through framed examples and research questions. No previous knowledge of MATLAB or programming is required. It can be used as a classroom exercise or an out-of-class project.
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Legos Optimization by James Kupetz, Rusty Lee, Karl Levy, Daphne Skipper.
Note: A professional development module will be available in Canvas by the end of 2023.
Many STEM majors would be well-suited to study optimization or, more broadly, industrial engineering, in graduate school, but most are not aware of this exciting, in-demand field. We envision Linear Algebra students as the primary target for this module because students who are studying Linear Algebra are also a likely audience for optimization, and because Linear Algebra is so fundamental to the study of optimization. We seek to introduce the field of optimization to these students through an engaging activity that both reinforces concepts from Linear Algebra and develops a conceptual framework that will be useful for students who go on to study optimization in a later course.

After a fun, hands-on activity, we introduce optimization modeling and a simple (albeit computationally expensive) algorithm for solving linear optimization models, commonly called Linear Programs or LPs, with bounded feasible regions. The algorithm relies on the basic geometry of systems of linear inequalities. The ideas in this simple algorithm are fundamental to the Simplex Method, the linear optimization algorithm that is implemented in commercial optimization solvers and that is typically taught in a first course in optimization.
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Data Analytics Using Linear Programming and the AMPL Algebraic Modelling Language by Monika Keindl, Yu-Ju Kuo, and Nándor Sieben. Data analytics explores information contained in data sets. We start from building simple linear integer programming models, then use nonlinear and linear programming to find the optimal parameter values by minimizing the error between the observed data and the predicted results. We utilize the algebraic modeling language AMPL to build our models and then call a solver like CPLEX to find optimizers to our models. The module will introduce students to AMPL and optimization through several examples of increasing complexity.
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Simplex Algorithm

Simplex Introduction to Optimization from Theory to Data – Option 1 by Joyati Debnath, Filippo Posta, and Violeta Vasilevska. The mathematical concept of optimization is the one that is used in everyday life constantly. Almost every situation (financial, economic, business, etc.) can be modeled as an optimization problem. The mathematical field of optimization offers various principles and methods for solving quantitative problems that require maximizing or minimizing a quantity. This module aims to introduce some of these methods and algorithms (such as the linear optimization and the simplex algorithm) to an undergraduate audience. Specific class activities are suggested to be performed that will help students become familiar with the optimization in real-life problems.
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The Simplex Algorithm – Option 2 by James Kupetz, Earl Lee, Karl Levy, and Daphne Skipper.
Note: This module will have a professional development module available on Canvas by the end of 2023.
The simplex algorithm is a common method of solving linear programs. This module will define common terms used for linear programs; provide a step by step explanation of the method; provide a two dimensional graphical interpretation of the method; and demonstrate a free software tool that replicates the simplex method.
In linear algebra, the goal is to find the point that satisfies a set of equations. In linear programs, we have a set of equations that form a feasible space. Any point within that space satisfies those constraints. Another function is introduced where the goal is to maximize or minimize its value. This function is called the objective. So, the goal is to find the best solution from that set of solutions in the feasible space.
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