This paper describes creating a new course for engineering technology students at Southeast Missouri State University that focuses on application-based mathematics instruction through laboratory experiments. The course structure comprises beginning the semester with pre-calculus and trigonometry and progressing to calculus and differential equations. The topics are covered from the engineering and engineering technology applications standpoint, with examples from electrical and mechanical systems. A hands-on, problem-based learning approach is selected for teaching the application of mathematics to engineering technology students. This entails students being presented with real-world problems, solving them using mathematical concepts, and then verifying results by using software tools. Specifically, twelve laboratory exercises using Scilab have been incorporated into the course. For engineering students, using engineering examples improves both their ability to understand the material’s relevance and their understanding of mathematical techniques that may be applied to real-world problems that they will likely encounter in their future jobs.

Background: Environmental exposures are biologically plausible contributors to thyroid cancer outcomes, but population-based evidence is heterogeneous and often focuses on incidence rather than stage at diagnosis. Objective: This study aimed to evaluate whether ecological state-year environmental indicators add predictive information for advanced-stage thyroid cancer at diagnosis in a large SEER-based cohort (U.S. National Cancer Institute’s Surveillance, Epidemiology, and End Results Program). Methods: We conducted a retrospective registry-linked analysis of 368,726 SEER thyroid cancer cases with valid combined summary stage. Advanced stage was defined as regional or distant disease and occurred in 118,509 cases (32.14%). Environmental variables were linked as state-year indicators using five-year moving averages from the years preceding diagnosis. Regularized logistic regression, gradient boosting, and Extra Trees models evaluated incremental predictive performance. Results: Adding environmental variables to demographic, socioeconomic, histology, and laterality predictors produced small random-split improvements across model families. However, after SEER registry was added before environmental variables, the remaining environmental increment was minimal. Registry-group holdout validation did not support improved geographic generalizability from the environmental feature set. Conclusions: State-year environmental indicators carried limited predictive information for advanced thyroid cancer stage, and much of this information overlapped with registry and geographic structure. These findings clarify both the potential and limitations of ecological environmental linkage in SEER-based prediction studies.