This dissertation has two primary concerns: (i) evaluating the uncertainty and prediction capabilities of a nanodiamond drug delivery model using Bayesian calibration and bias correction, and (ii) determining conceptual difficulties of multi-scale analysis from an engineering education perspective. A Bayesian uncertainty quantification scheme is used to analyze computational and experimental data for the localized cancer drug delivery system. Since this system is largely unknown, assessing the uncertainty at various developmental stages as well as on different physical scales is important to determine functioning of this system. Adsorption of DOX (a cancer fighting drug) to nanodiamonds is measured in two ways: (1) experimentally via UV Visible Spectroscopy and (2) numerically using stochastic molecular dynamics simulations. These two sets of data are used in a Bayesian calibration and bias correction analysis such that the pH is the input parameter, the percentage of carboxyl, the functional group on the surface of the nanodiamond, is the calibration parameter, and both modeling and experimental errors are accounted for in the uncertainty analysis. The acid dissociating constant pK[subscript a] value of the nanodiamond is also used for system calibration. A Bayesian bias correction analysis is also performed to measure the impact of nanodiamond aggregation. From these analyses, an estimate of the uncertainty in the system is determined, the optimal pK[subscript a] value and percentage of carboxyl is found, the impact of the experimental and modeling physical scale differences is examined, the impact of clustering is measured, and a research path to further reducing the system uncertainty is given. The second research issue covered in this dissertation addresses how to effectively teach this type of high-level, cross-disciplinary thinking, and multi-scale research to future engineers. The conceptual hurtles present in understanding multi-scale analysis were identified through one-on-one interviews with scientists and engineers spanning the experience spectrum (undergraduate students, graduate students, postdoctoral fellows, and professors). From these interviews, important issues involving understanding and teaching multi-scale analysis were documented. From there, a Northwestern course was modified and taught to specifically address many of these issues. Then a follow-up survey was conducted to rank these many issues in terms of importance. This is the first research to specifically address the role that multi-scale thinking has on conceptual understanding. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]