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Mathematical Induction: The Basis Step Of Verification And Validation In A Modeling And Simulation Course

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2004 Annual Conference


Salt Lake City, Utah

Publication Date

June 20, 2004

Start Date

June 20, 2004

End Date

June 23, 2004



Conference Session

Integrating Math into Engineering

Page Count


Page Numbers

9.895.1 - 9.895.11



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Paper Authors

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Legand Burge

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John Kaplan

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Kathleen Kaplan

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Moses Garuba

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Session Number: 1465

Mathematical Induction: The Basis Step of Verification and Validation in a Modeling and Simulation Course

Kathleen M. Kaplan, D.Sc., Legand Burge, Ph.D., Moses Garuba, Ph.D., Lt Col John J. Kaplan (Ph.D., J.D.) USAF

Howard University/USAF


Most Engineering Schools offer a course in Modeling and Simulation. This is an important area of exploration as indicated by many driving forces of current research including the U.S. Department of Defense Modeling and Simulation Office, the Air Force Agency for Modeling and Simulation, and the U.S. Navy Air Defense Threat Simulation & Validation Office. Thus, the study of Modeling and Simulation (M&S) should be included in any engineering program. Unfortunately, the basic foundations of the area are not being taught; university courses in M&S have shifted from the introduction and use of formal techniques to application of software packages, such as Arena. While the use of application software is a favorable teaching tool, the programs do not allow students to fully understand and appreciate the underlying concepts of M&S. For example, a large part of M&S is in Verification and Validation (V&V). There are four V&V categories of techniques for simulation models: Informal, Static, Dynamic, and Formal, yet students who are exposed solely to application software programs may not be knowledgeable about V&V, let alone know the names of these four categories. A popular textbook regarding a widely-used M&S program does not discuss V&V until its seventh chapter, wherein it has a four page discussion of verification; later, in its thirteenth chapter, three pages are dedicated to both V&V. Out of a six hundred sixty eight page M&S book, only seven pages are dedicated to V&V. This does not coincide with the demand for the knowledge of V&V as evident by specific Department of Defense offices dedicated to V&V. M&S educators must bring back to the classroom the use of V&V techniques for simulation models, starting at ground zero: the formal technique using mathematical induction.

This paper will discuss the M&S, V&V, and the current educational trend in M&S, specifically in the areas of V&V, and provide ways to incorporate the use of mathematical induction, an area of the four technique categories of V&V, into the teaching of M&S. In combining both a computer application program and V&V techniques, the student will be able to fully appreciate the connection of mathematics and engineering, required in all ABET accredited programs.

“Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright ©2004, American Society for Engineering Education”

Burge, L., & Kaplan, J., & Kaplan, K., & Garuba, M. (2004, June), Mathematical Induction: The Basis Step Of Verification And Validation In A Modeling And Simulation Course Paper presented at 2004 Annual Conference, Salt Lake City, Utah. 10.18260/1-2--14066

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