Syllabus for MAT-351

MATHEMATICAL MODELING

COURSE DESCRIPTION

This course is designed to be a bridge between the study of mathematics and the application of mathematics to various fields. It provides an overview of how the mathematical pieces of an applied problem fit together. This course also presents an investigation of meaningful and realistic problems encompassing many academic disciplines including management, economics, ecology, environmental science, sociology, and psychology.

Mathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon. The main goal of this course is to learn how to make a creative use of some mathematical tools, such as difference equations, ordinary and partial differential equations, and numerical analysis, to build a mathematical description of realistic problems. This includes models dealing with traffic flow, communications, energy, air pollution, currency transfer, ecosystems, inheritance, populations, bargaining, and decision making.

COURSE TOPICS

• Ordinary differential equations
• Optimization
• Sensitivity analysis
• Probability
• Simulation

COURSE OBJECTIVES

After completing this course, you should be able to:

• CO1 Develop and construct appropriate models for various problems and situations.
• CO2 Analyze existing models to identify underlying assumptions and limitations.
• CO3 Apply the modeling process to translate problem situations to mathematical expressions.
• CO4 Use difference equations to model change and dynamical systems.
• CO5 Use graphical and analytic methods to fit a model to a given data set.
• CO6 Construct empirical higher-order models to fit a given data set.
• CO7 Simulate deterministic and probabilistic problems using Monte Carlo simulation.
• CO8 Develop a probabilistic model for a Markov process.
• CO9 Apply linear programming methods for constrained discrete optimization problems.
• CO10 Use graph models to solve real-world problems.
• CO11 Apply dimensional analysis in the model-building process.
• CO12 Develop and solve continuous models using differential equations.
• CO13 Use Lagrange multipliers for the optimization of continuous models.

COURSE MATERIAL

You will need the following materials to do the work of the course. The required textbook is available from the University’s textbook supplier, MBS Direct.

Required Textbook

• Giordano, Frank R., Fox, William P., & Horton, Steven B. (2014). A First Course in Mathematical Modeling 5th ed. Boston, MA: Brooks/Cole, Cengage Learning.

ISBN-13: 978-1285050904

• Chapters 14 and 15 of the textbook A First Course in Mathematical Modeling 5th edition can be found in the Resources area of the course website.

COURSE STRUCTURE

Mathematical Modeling is a three-credit online course, consisting of six modules. Modules include an overview, topics, learning objectives, study materials, and activities. Module titles are listed below.

• Module 1: The Modeling Process, Proportionality and Geometric Similarity
• Module 2: Experimental and Simulation Modeling
• Module 3: Discrete Probabilistic and Optimization of Discrete Models
• Module 4: Modeling using Graph Theory and Dimensional Analysis

• Module 5: Graphs of Functions as Models and Modeling with Differential Equations
• Module 6: Modeling with Systems of Differential Equations and Optimization of Continuous Models

ASSESSMENT METHODS

For your formal work in the course, you are required to participate in online discussion forums, complete written assignments, and prepare reports of a midterm project and a final project. See below for details.

Consult the Course Calendar for assignment due dates.

Discussion Forums

This course requires you to participate in six graded discussion forums. There is also an ungraded but required introductions forum in module 1.

Online discussions provide an opportunity for you to interact with your classmates. During this aspect of the course, you respond to prompts that assist you in developing your ideas, you share those ideas with your classmates, and you comment on their posts. Discussion board interactions promote development of a community of learners, critical thinking, and exploratory learning.

Please participate in online discussions as you would in constructive face-to-face discussions. You are expected to post well-reasoned and thoughtful reflections for each item, making reference, as appropriate, to your readings. You are also expected to reply to your classmates' posts in a respectful, professional, and courteous manner. You may, of course, post questions asking for clarification or further elucidation on a topic.

Written Assignments

You are required to complete six written assignments. The written assignments draw on section problems from the textbook. For each assignment, answer all assigned exercises, and show all work.

Assignments must be prepared electronically with a word processor, preferably using whatever equation editor comes with your word processing software. However, if your word processor is not compatible with your mentor's word processor, you will need to save your document as a rich-text file (.rtf) before submitting it. Check with your mentor first to determine file compatibility. (Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.)

When preparing your answers, please identify each exercise clearly by textbook section and exercise number. Be sure to include your name at the top of the paper, as well as the course name and code and the semester and year in which you are enrolled. To receive full credit for your answers, you must show all work and include complete solutions.

Midterm Project

You are required to complete a midterm project instead of taking a proctored midterm exam. This project will focus on the topics covered in the first three modules of the course.

See the Midterm Paper area of the course website for further details.

Final Project

You are required to complete a final project instead of taking a proctored final exam. This project will address a simulation modeling problem. It requires you follow three requirements to construct and analyze the scenario using modeling.

See the Final Project area of the course website for further details.

• Online discussions (6)18 percent
• Written assignments (6)36 percent
• Midterm project16 percent
• Final project30 percent

 A = 93–100 C+ = 78–79 A– = 90–92 C = 73–77 B+ = 88–89 C– = 70–72 B = 83–87 D = 60–69 B– = 80–82 F = Below 60

To receive credit for the course, you must earn a letter grade of C or better (for an area of study course) or D or better (for a course not in your area of study), based on the weighted average of all assigned course work (e.g., exams, assignments, discussion postings, etc.).

STRATEGIES FOR SUCCESS

First Steps to Success

To succeed in this course, take the following first steps:

• Read carefully the entire Syllabus, making sure that all aspects of the course are clear to you and that you have all the materials required for the course.
• Take time to read the entire Online Student Handbook. The Handbook answers many questions about how to proceed through the course, how to schedule exams, and how to get the most from your educational experience at Thomas Edison State University.

• Familiarize yourself with the learning management systems environment—how to navigate it and what the various course areas contain. If you know what to expect as you navigate the course, you can better pace yourself and complete the work on time.
• If you are not familiar with Web-based learning be sure to review the processes for posting responses online and submitting assignments before class begins.

Study Tips

Consider the following study tips for success:

• To stay on track throughout the course, begin each week by consulting the Course Calendar. The Calendar provides an overview of the course and indicates due dates for submitting assignments, posting discussions, and scheduling and taking examinations.
• Check Announcements regularly for new course information.

Thomas Edison State University is committed to maintaining academic quality, excellence, and honesty. The University expects all members of its community to share the commitment to academic integrity, an essential component of a quality academic experience.

Students at Thomas Edison State University are expected to exhibit the highest level of academic citizenship. In particular, students are expected to read and follow all policies, procedures, and program information guidelines contained in publications; pursue their learning goals with honesty and integrity; demonstrate that they are progressing satisfactorily and in a timely fashion by meeting course deadlines and following outlined procedures; observe a code of mutual respect in dealing with mentors, staff, and other students; behave in a manner consistent with the standards and codes of the profession in which they are practicing; keep official records updated regarding changes in name, address, telephone number, or e-mail address; and meet financial obligations in a timely manner. Students not practicing good academic citizenship may be subject to disciplinary action including suspension, dismissal, or financial holds on records.

All members of the University community are responsible for reviewing the Academic Code of Conduct Policy in the University Catalog and online at www.tesu.edu.

Thomas Edison State University expects all of its students to approach their education with academic integrity—the pursuit of scholarly activity free from fraud and deception. All mentors and administrative staff members at the University insist on strict standards of academic honesty in all courses. Academic dishonesty undermines this objective. Academic dishonesty can take the following forms:

• Cheating
• Submitting credentials that are false or altered in any way
• Plagiarizing (including copying and pasting from the Internet without using quotation marks and without acknowledging sources)
• Forgery, fabricating information or citations, or falsifying documents
• Submitting the work of another person in whole or in part as your own (including work obtained through document sharing sites, tutoring schools, term paper companies, or other sources)
• Submitting your own previously used assignments without prior permission from the mentor
• Facilitating acts of dishonesty by others (including making tests, papers, and other course assignments available to other students, either directly or through document sharing sites, tutoring schools, term paper companies, or other sources)
• Tampering with the academic work of other students

Plagiarism

Thomas Edison State University is committed to helping students understand the seriousness of plagiarism, which is defined as using the work and ideas of others without proper citation. The University takes a strong stance against plagiarism, and students found to be plagiarizing are subject to discipline under the academic code of conduct policy.

If you copy phrases, sentences, paragraphs, or whole documents word-for-word—or if you paraphrase by changing a word here and there—without identifying the author, or without identifying it as a direct quote, then you are plagiarizing. Please keep in mind that this type of identification applies to Internet sources as well as to print-based sources. Copying and pasting from the Internet, without using quotation marks and without acknowledging sources, constitutes plagiarism. (For information about how to cite Internet sources, see Online Student Handbook > Academic Standards > “Citing Sources.”)

Accidentally copying the words and ideas of another writer does not excuse the charge of plagiarism. It is easy to jot down notes and ideas from many sources and then write your own paper without knowing which words are your own and which are someone else’s. It is more difficult to keep track of each and every source. However, the conscientious writer who wishes to avoid plagiarizing never fails to keep careful track of sources.

Always be aware that if you write without acknowledging the sources of your ideas, you run the risk of being charged with plagiarism.

Clearly, plagiarism, no matter the degree of intent to deceive, defeats the purpose of education. If you plagiarize deliberately, you are not educating yourself, and you are wasting your time on courses meant to improve your skills. If you plagiarize through carelessness, you are deceiving yourself.

For examples of unintentional plagiarism, advice on when to quote and when to paraphrase, and information about writing assistance and originality report checking, click the links provided below.

Examples of Unintentional Plagiarism

When to Quote and When to Paraphrase

Writing Assistance at Smarthinking

Originality Report Checking at Turnitin

Disciplinary Process for Plagiarism

Acts of both intentional and unintentional plagiarism violate the Academic Code of Conduct.

If an incident of plagiarism is an isolated minor oversight or an obvious result of ignorance of proper citation requirements, the mentor may handle the matter as a learning exercise. Appropriate consequences may include the completion of tutorials, assignment rewrites, or any other reasonable learning tool in addition to a lower grade for the assignment or course. The mentor will notify the student and appropriate dean of the consequence by e-mail.

If the plagiarism appears intentional and/or is more than an isolated incident, the mentor will refer the matter to the appropriate dean, who will gather information about the violation(s) from the mentor and student, as necessary. The dean will review the matter and notify the student in writing of the specifics of the charge and the sanction to be imposed.

Possible sanctions include:

• Lower or failing grade for an assignment
• Lower or failing grade for the course
• Rescinding credits
• Rescinding certificates or degrees
• Recording academic sanctions on the transcript
• Suspension from the University
• Dismissal from the University