In this regard, Oliver and Myers report that, "There is value in translating mathematics into words, so that those who do not readily grasp equations can appreciate the ideas they convey" (p. 33). While there are increasingly sophisticated mathematical modeling applications available, a number of businesses use conventional spreadsheet programs such as Excel for a wide range of valuable mathematical modeling purposes (Ellington & Hardin, 2008). It should be pointed out, however, that Excel and more sophisticated mathematical modeling applications facilitate the analyses process, but they do not replace the need for a firm foundation in the fundamentals. In this regard, Ellington and Hardin (2008) add that, "A solid understanding of mathematical modeling requires a blend of mathematical skills and conceptual understanding. The technology available today may reduce, but does not eliminate the need for mathematical skills. Future analysts need a solid understanding of mathematical modeling when they enter the workforce" (p. 110).

This assertion was certainly the case with one of this author's positions in the past as a Department of Veterans Affairs program specialist tasked with reducing the number of patient incidents in a tertiary medical center. Every time there was an incident such as a fall or medication error involving a patient, an incident report would be completed by the individual witnessing the incident and the report filed with my office. Prior to my assuming this position, these incidents were investigated if they were serious enough but there was no effort made to aggregate these reports to identify trends or problem areas except that patients who fell twice were "flagged" in the hospital-wide intranet as potential "fallers." Following my assumption of this position, all of the patient incident reports for the previous year were plugged in to a Harvard Graphics software program and the results trended graphically by ward and shift. It quickly became apparent that most of the medication errors were being made by one shift on one patient ward and steps were taken to counsel and educate the nurses involved. In addition, patients who fell once were assigned a fall flag rather than waiting for them to fall again. As a result of these simple mathematical modeling...

Even in these fairly clear-cut instances, though, human interpretation of the data analysis results was necessary to ensure that other factors did not contribute to these incidents, indicating that mathematical modeling has its limitations in any setting.
Conclusion

The research showed that mathematical modeling consists of using quantifiable metrics to analyze various systems and processes to identify trends and patterns that can be used to identify opportunities for improvement or areas in need of attention. The research also showed that mathematical modeling is currently used for an enormous array of applications, including gambling and sports simulations, weather modeling applications and even how couples behave in a relationship. One of the common themes that characterized all of these mathematical modeling applications, though, was the need for accurate data and careful interpretation of the analytical results to ensure that the models provide the type of information desired and that is adequately models the real-world setting.