CCICADA Education Modules

CCICADA’s educational modules are designed for undergraduate students and high school students in grades 10-12. They are intended for five to eight days of instruction in mathematics, science, and computer science classes. They are updated as new information becomes available.

The modules cover a variety homeland security topics from a quantitative perspective, including: the risk of competition for a water supply, the use of CT scans to assess structural integrity before an attack, the forensics needed after a cyberattack to determine the causes, and tools to improve computer efficiency. These topics are related to research conducted by CCICADA and other US Department of Homeland Security University Centers of Excellence.

These modules have been distributed to tens of thousands of students and practitioners nationwide. They are classroom-tested and comprehensively reviewed. Extensive notes for teachers and faculty are provided.

Modules:

• Community Detection with Hierarchical
  Clustering Algorithms
• Competition or Collusion? Game Theory in Security, Sports, and Business
• Connecting Forensics and Linear Algebra
• Cryptography in Forensics
• Food Safety, Structural Integrity, and Medical Imaging–What Do They Have in Common? Tomography
• Foolproof Codes and Ciphers
• Gently Down the Stream: The Mathematics of Streaming Information
• Network Capacity
• Passwords, Heroin, and Timelines: Forensics and Graph Theory
• Privacy: Do You Know What They Know about You?
• Recursion–Problem Solving and Efficiency – How to Define an Infinite Set Finitely
• Selection of Early Warning Test Sites for Foot and Mouth Disease in Dairy Cattle—A Biosurveillance Model
• Tomography: A Geometric and Computational Approach
• Water: The Risky Business

 

Community Detection with Hierarchical Clustering Algorithms by Donna Beers, Simmons College and Robert Campbell, College of St. Benedict and St. John’s University. The goal of this module is to introduce undergraduates from the sciences and social sciences to the interdisciplinary field of network science. Students will learn how mathematical and
computational tools can be used to analyze complex systems to advance science and prosperity
as well as to promote public health and safety. Students will understand the role of community
detection within network analysis and learn hierarchical clustering methods for carrying it out.

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Competition or Collusion? Game Theory in Security, Sports, and Business  by James Kupetz, Luzerne County Community College; Choong-Soo Lee, St. Lawrence University; and Steve Leonhardi, Winona State University. Competition or Collusion introduces students to game theory concepts and methods, starting with zero-sum games and then moving on to non-zero-sum games. Students learn techniques for classifying games, for computing optimal solutions where known, and for analyzing various strategies for games in which no optimal solution exists. Finally, students have the opportunity to transfer what they’ve learned to new game-theoretic situations.
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Connecting Forensics and Linear Algebra by Donna Beers, Simmons College, and Catherine Crawford, Elmhurst College. This module aims to enrich a first course in undergraduate linear algebra by introducing students to the concepts of linear combination, spanning set, linearly independent set, and basis by engaging real-world examples drawn from the field of forensics. The module also explores the variety of career options in forensic science. Download full module

Cryptography in Forensics Check Sums, Hash Functions, and the MD5 Algorithm by Melanie Brown, Champlain College; Catherine Buell, Fitchburg State University; and Alison Marr, Southwestern University. The MD5 Message-Digest Algorithm (MD5) is one of the current standards for data integrity verification for law enforcement and digital forensics. The algorithm uses a cryptographic function called a hash to produce a 32-character “word” or string from any type of data. This “word” or string is a nearly unique hexadecimal representation of the data. Law enforcement uses these unique signatures to prove the existence of particular data and as proof that data has not been compromised. This module begins with modular arithmetic, binary and hexadecimal expressions, and bit operations in order to motivate the mathematics and the logic behind hash functions and the MD5 algorithm. The algorithm is considered with both a cryptographic and a forensic lens. The module concludes with a discussion of current trends in digital verification and cybersecurity. Download full module

Food Safety, Structural Integrity, and Medical Imaging–What Do They Have in Common? Tomography by Midge Cozzens, Rutgers University; and Katrina Palmer, Appalachian State University. This is the first of two tomography modules. Tomography is the science of examining internal structures with external measurements. Most think of tomography in the context of medical testing, such as CT scans, but tomography is also used in analyzing food safety, ocean acoustics, oil pipelines, optics, and any time it is impossible to directly look inside something. Students will learn the mathematics underlying imaging techniques and apply these techniques to analyze various foods, such as cantaloupes; perform virtual autopsies; determine the structural soundness of a building or pipeline; and find airplanes that have crashed in the deepest parts of our oceans. Download full module

Foolproof Codes and Ciphers  by James Kupetz, Luzerne County Community College; and Steven J. Miller, Williams College. This module introduces some of the issues in information theory, ranging from protecting credit card information during online purchasing to securing communications in wartime. The unit mixes the mathematics of theory and historical examples with current issues in homeland security, and then builds to a complete description and discussion of the implementation issues of RSA, for years the gold standard in encryption. Students are encouraged to think about how one produces a foolproof code for transmission of information and to imagine and compare possible encoding devices and/or schemes. The module discusses challenges faced in developing a foolproof encryption that can still be decrypted. The role of codes in data compression is also discussed, as well as the importance of disinformation. This module will be made available soon.

Gently Down the Stream: The Mathematics of Streaming Information by James Kupetz, Luzerne County Community College; and Steven J. Miller, Williams College. Gently Down the Stream introduces students to the issues, methods, and challenges in successfully transmitting information. Topics include error detection, error correction, data authentication, data compression, and efficient transmission. Data authentication is vital for numerous homeland security areas. This module will be made available soon.

Network Capacity by Aaron Jaggard, Rutgers University, and James Kupetz, Luzerne County Community College. This module develops the skills and perspectives used in modeling real-world situations as networks. Using the demand on networks familiar to students as a motivating point (text messaging, cell phone, Internet), the module attempts to model some simple networks (school hallways) and build upon that to more complicated networks. It concentrates more on allowing students to experiment with and think about networks and network capacity than on describing the algorithms used to determine optimal network settings/behavior. As the simulations increase in complexity, the idea that computers are essential for solving the more complex problems is introduced. Download full module

Passwords, Heroin, Timelines: Forensics and Graph Theory by Lila Ghemri, Texas Southern University; Carol Gibbons, Salve Regina University; and Carol Overdeep, Saint Martin’s University. Thanks to the popularity and longevity of such television shows as “CSI” and “NCIS”, forensics and/or forensic science are common household words. The television shows tend to focus on solving crimes involving dead and/or missing victims, and as a result, forensics tends to be equated with chemical and biological lab work in popular culture. However, forensics runs a much larger gamut of disciplines (accounting and digital security to name but two areas), and one of the purposes of this module is to alert students to the depth and breadth of the discipline. From a simplified perspective, forensics consists of two steps: 1) gathering facts and 2) drawing conclusions. It’s imperative that these two things be viewed as disjointed activities. For the latter, graph theory can be used to help find patterns in the facts which lead to conclusions. The remaining two goals of this module are to provide students with the basics of graph theory and the ability to apply it to a variety of situations. The primary target audience includes undergraduates in a “Math for Liberal Arts” course. By increasing the complexity of subsequent examples, students in an undergraduate discrete mathematics course could also be targeted. Other appropriate audiences include introductory Computer Science students and introductory Criminal Justice students.
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Privacy: Do You Know What They Know About You? by Paul Kehle, Hobart and William Smith Colleges; and Rebecca Wright, Rutgers University. This module explores how people can use and enjoy technology such as social networks (like Facebook and Twitter), while still having some kind of privacy. It introduces students to privacy issues that are created, worsened or solved by computer technology. The module is driven by a series of case studies drawn primarily from various well-known websites. The overall focus of the module is on how our ideas about privacy and our behaviors might need to change—and how we need to become more informed—in response to changing computing technologies. This module will be made available soon.

Recursion – Problem Solving and Efficiency – How to Define an Infinite Set Finitely by Carl Alphonce, SUNY Buffalo & CST, and Margaret (Midge) Cozzens, Rutgers University.  Recursion can be used in many areas, from modeling population growth and the spread of disease to determining how much money you will have in an account at retirement. The purpose of the module is to provide a general background on the process of recursion, a method for solving problems where the solution to a problem depends on solutions to smaller instances of the same problem. A recursive process is one in which objects (a whole system) are defined in terms of other objects (stages of the system) of the same type. The whole system can be built knowing only a few initial values or stage of the system and applying a small set of rules. Computers routinely use recursion in performing many standard operations or processes. Download full module

Selection of Early Warning Test Sites for Foot and Mouth Disease in Dairy Cattle—A Biosurveillance Model by Kim A. S. Factor, Marquette University. This module explains how the transmission of infectious diseases in our nation’s food sources is a method of terrorism that concerns us all. One of these diseases is foot-and-mouth disease (FMD), which can be contracted by cloven-footed animals and is highly contagious. If FMD is found in a herd, all herds within 10 km must be destroyed, financially devastating farmers in the area. This module produces an easily understandable graph theoretical model for use in locating a select group of farms to serve as testing sites for early warning signs of an FMD infection. Download full module

Tomography: A Geometric and Computational Approach by Midge Cozzens, Rutgers University; and Katrina Palmer, Appalachian State University. This is the second of two tomography modules by Cozzens and Palmer. Tomography is the science of examining internal structures with external measurements. Most think of tomography in the context of medical testing, such as CT scans, but tomography is also used in analyzing food safety, ocean acoustics, oil pipelines, optics, and any time it is impossible to directly look inside something. In this module, students tackle activities where they attempt to determine what is inside an object, how one would measure its components, and how these measurements can be made more precise. Students study how CT scan images are created using 3-D reconstruction of objects and 2 dimensional pieces (slices) of the object, and by constructing 3-D images of objects using shadows, pin prints, graphs, and more. The main questions posted by the module are: How can 3-D images be created from 2-D images? How much computational power and skill are required to create these reconstructions and on what do they depend? Download full module

Water: The Risky Business by Joyati Debnath, Winona State University; and M. A. Karim, Kennesaw State University. Water sources can be divided into two categories: surface water and ground water. The focus in this module is to make the students more aware of water pollution, either industrial or domestic. More than 840,000 people worldwide die each year from water-related diseases. Developing mathematical models that help to understand how to control water quality is of great importance. Pertaining to water, the questions and issues addressed in the first part of the module are: 1) What is risk? 2) Why risk perception is important. 3) Why risk assessment is critical, 4) What kind of data is necessary? 5) What methodology is needed? 6) How risk assessment results are used. In the second part of the module, data analysis technique and mathematical models will be developed for assessing the quality of water based on the many factors that affect that quality, namely: the levels of dissolved oxygen; the presence of nitrates, chlorides, phosphates; the level of suspended solids; environmental hormones; chemical oxygen demand, such as heavy metals; and the presence of bacteria. Pollutants from agricultural operations also contribute to the water quality.
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