Modeling Project

The purpose of this assignment is to develop a collection of mathematical models centered upon a singular topic of interest by following the mathematical modeling process outlined in class and your textbooks. There are many details, steps, and hurdles required to accomplish these tasks. This document aims to give insight into the expectations at each step of the modeling process, as well as clarify the format, layout, and required components of your final submission.

Preliminaries

- The word count for this assignment will be at the discretion of your instructor; however, a general guideline is around 6-8 pages for the actual written portion of your overall mathematical modeling content and findings (Times New Roman, 12 font, 1.5 spaced). You should anticipate using Microsoft Word to complete the written report.

- This project has a presentation component, so PowerPoint slides (with detailed notes) will also need to be turned in. You may directly copy/paste written content from your report into your PowerPoint presentation.

- Your final submission should contain a software component that supports and reinforces the written content and results from your report. A Microsoft Excel spreadsheet and/or a MATLAB script are expected in your final submission (as well as any other approved files that will enhance your submission).

- Please read the rubric for this assignment!

Introduction

- In detail and in appropriate academic prose, introduce your topic of interest, why this topic is important to you, and its connection (if any) to your field of study.

- Outline the purpose of your models and state your original hypotheses and ideas for what the mathematical models you create are going to indicate about your topic of interest. Remember: your overall results of your model DO NOT need to reinforce your hypotheses. This is the impartial beauty of the scientific method and why model verification and model modification are both so important!

- Describe which discrete and continuous models will be used in your project with respect to your topic of interest. Justify why these mathematical models are most appropriate and why other mathematical models would not be most appropriate.

Data Collection and Model Fitting

- Provide any real-world, simulated, randomized, or retrospectively collected data in appropriate formats (tables, charts, pictures, Excel, MATLAB, etc.) with corresponding explanations and ties to your overall mathematical models.

- Describe any simplifications you needed to make in order to fit the data to a model without the addition of a significant number of extra variables, e.g. air friction, altitude, heat loss, negligible weight, etc.

- Show the results of fitting your data to different mathematical models (both discrete and continuous). Describe why these are the most appropriate models to represent your data.

Model Analyses

- Discuss any and all analyses conducted with respect to your mathematical models. Discuss any patterns, trends, unexpected deviations, outliers, limitations, equilibria, etc.

- All solutions to the different mathematical models should be included in this section (analytic, qualitative, numerical, graphical). Microsoft Equation Editor may be used here or snapshots of clear, neat handwritten work can be inserted as well (or an appropriate combination of the two).

- If some of your solutions are found on software files, copy/paste relevant components of those results onto your report for reference and reflection.

Model Conclusions

- Discuss all conclusions drawn from your mathematical models, including real-world interpretations, predictions, and any relevant interpolations/extrapolations (if relevant).

- Discuss the connections for the results of your discrete and continuous mathematical models. Do they reinforce each other? Do they complement each other? Are they in conflict? Are the results of one of the models more valuable than the others?

- Discuss how you would talk about these results to a class of younger mathematics students or peers (if relevant to your major). What barriers and challenges would you encounter and how might the instruction benefit your audience in spite of these barriers and challenges?

Software Files (10%)

- Include either a Microsoft Excel spreadsheet or a MATLAB script (or both) to complement and support your reported results for your mathematical models.

- Additional files may be included here as well if you choose to utilize extra software components (Python, C++, Java, Mathematica, CAD, etc.).

Presentation

- Your presentation component requires a set of PowerPoint slides (with detailed notes) about your overall topic, setup, and results for your mathematical modeling objectives.

- Whether or not you will be presenting these results in class depends upon the medium of instruction (ground, online, etc.) and time-permitting circumstances. Ultimately, in-class presentations are intended to take place during the final week(s) of the semester, yet will still be at the discretion of the instructor.

- Include at least one slide outlining how you would teach this content to a particular group of mathematics students or peers (if relevant to your major). What challenges might you encounter in instruction? What challenges might your students or peers encounter in instruction? What mathematical barriers cannot be bypassed to give a rigorous account of your results? How might your presented results be useful?

Academic Writing/Sources

- Strong academic writing is expected throughout the written report and the notes on the PowerPoint slides. Please proofread several times before submitting your files.

- Cite your sources according to directions given by your instructor at the end of your written report. Whether formal or informal citations are to be used will be at the discretion of the instructor.

Additional Notes

- Any extra or replacement instructions for this Modeling Project will be at the consent and discretion of the instructor. Please keep track of and follow all project-related correspondence from your instructor, as they have the final say on how to proceed with the details of this assignment.

Attachment:- Modeling project.rar