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

  1. Ordinary Differential Equations
  2. Optimization
  3. Sensitivity analysis
  4. Probability
  5. Simulation

COURSE OBJECTIVES

After completing this course, you should be able to:

  1. CO1 Develop and construct appropriate models for various problems and situations.
  2. CO2 Analyze existing models to identify underlying assumptions and limitations.
  3. CO3 Apply the modelling process to translate problem situations to mathematical expressions.
  4. CO4 Use difference equations to model change and dynamical systems.
  5. CO5 Use graphical and analytic methods to fit a model to a given data set.
  6. CO6 Construct empirical higher-order models to fit a given data set.
  7. CO7 Simulate deterministic and probabilistic problems using Monte Carlo simulation.
  8. CO8 Develop a probabilistic model for a Markov process.
  9. CO9 Apply linear programming methods for constrained discrete optimization problems.
  10. CO10 Use graph models to solve real-world problems.
  11. CO11 Apply dimensional analysis in the model-building process.
  12. CO12 Develop and solve continuous models using differential equations.
  13. 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 College’s textbook supplier, MBS Direct.

Required Textbook

  1. Giordano, Frank R., Fox, William P., Horton, Steven B., & Weir, Maurice D. (2009). A First Course in Mathematical Modeling 4th ed. Belmont, CA: Brooks/Cole, Cengage Learning.

ISBN-13: 978-0-495-01159-0

COURSE STRUCTURE

Mathematical Modeling is a three-credit online course, consisting of six (6) modules. Modules include an overview, topics, learning objectives, study materials, and activities. Module titles are listed below.

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

  1. Module 5: Graphs of Functions as Models and Modelling with Differential Equations
  2. 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 (6) 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 (6) 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 web site 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 web site for further details.

GRADING AND EVALUATION

Your grade in the course will be determined as follows:

  1. Online discussions (6)18 percent
  2. Written assignments (6)36 percent
  3. Midterm project16 percent
  4. Final project30 percent

All activities will receive a numerical grade of 0–100. You will receive a score of 0 for any work not submitted. Your final grade in the course will be a letter grade. Letter grade equivalents for numerical grades are as follows:

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 nonarea of study course), 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:

  1. 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.
  2. Take time to red 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 College.
  3. Arrange to take your examination(s) by following the instructions in this Syllabus and the Online Student Handbook.
  4. 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.
  5. 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:

  1. 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.
  2. Check Announcements regularly for new course information.

ACADEMIC INTEGRITY

Students at Thomas Edison State College 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 outlines 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.

Academic Dishonesty

Thomas Edison State College 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 College insist on strict standards of academic honesty in all courses. Academic dishonesty undermines this objective. Academic dishonesty takes the following forms:

  1. Cheating
  2. Plagiarizing (including copying and pasting from the Internet without using quotation marks and without acknowledging sources)
  3. Fabricating information or citations
  4. Facilitating acts of dishonesty by others
  5. Unauthorized access to examinations or the use of unauthorized materials during exam administration
  6. Submitting the work of another person or work previously used without informing the mentor
  7. Tampering with the academic work of other students

Academic dishonesty will result in disciplinary action and possible dismissal from the College. Students who submit papers that are found to be plagiarized will receive an F on the plagiarized assignment, may receive a grade of F for the course, and may face dismissal from the College.

A student who is charged with academic dishonesty will be given oral or written notice of the charge. If a mentor or the College official believes the infraction is serious enough to warrant referral of the case to the academic dean, or if the mentor awards a final grade of F in the course because of the infraction, the student and the mentor will be afforded formal due process.

If a student is found cheating or using unauthorized materials on an examination, he or she will automatically receive a grade of F on that examination. Students who believe they have been falsely accused of academic dishonesty should seek redress through informal discussions with the mentor, through the office of the dean, or through an executive officer of Thomas Edison State College.

Plagiarism

Using someone else’s work as your own is plagiarism. Although it may seem like simple dishonesty, plagiarism is against the law. Thomas Edison State College takes a strong stance against plagiarism, and students found to be plagiarizing will be severely penalized. 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, 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 the 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.

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