Northern Illinois University

**MODEL BUILDING IN APPLIED MATHEMATICS
(3 semester hours)**
An introduction to the formulation, analysis, and interpretation of
mathematical models in the study of selected problems in the natural
sciences, the social sciences, and management science.

Not open for credit to students having credit in MATH or STAT courses numbered 420 or above, except by consent of department.

*ADVISING NOTE:* Majors in mathematical sciences must take this
course. Because of the preceding catalogue language, these students
should take this course *early* in their programs. Consult with
your academic advisor before registering for post-calculus courses.

**PREREQUISITE:**
Math 230

- To engage effectively and efficiently in problem solving, as an individual and in cooperative situations.
- To understand and connect concepts of marthematics with real world problems and other scientific disciplines.
- To communicate mathematics clearly, in writing and orally.
- To develop creative thinking.
Topics in the course will vary by semester and sometimes by section. The emphasis is on the development and application of a variety of mathematical models; the specific choice of application will certainly vary. But the tools developed in the course will include - The modeling process in general.
- Models involving proportion and geometric similarity.
- Graphical and analytical model-fitting; least squares.
- Optimization problems.
- Dimensional analysis.
- Ordinary differential equations.
- Autonomous systems of differential equations.

**WITHDRAWAL:**The last day for undergraduates to withdraw from a full-session course is Friday, October 17, 2015.**GRADING:**Semester grades will be assigned on the basis of 1100 points, earned as follows:- 5 written projects @100 points
- 1 project presentation @50 points
- 2 one hour exams (mid-term) @100 points
- 1 final exam @200 points.
- homework as assigned with total 150 points

- Section 1, MWF 9:00-9:50 p.m., DU 428, James Benson
- Section 2, MWF 12:00-12:50 p.m., DU 428, Ilya Krishtal

**PROJECTS:**Students will individually complete five projects during this course. Each should be considered a major writing assignment, and each counts as much as an hour exam. We will provide prompts and questions but your papers should be understandable to a person who does not have them and is not in the class. (You may someday soon show one of these to a prospective employer and you should write with that kind of audience in mind!) In particular the paper should have insightful introduction and conclusion sections. Each project report is to be printed on good quality paper and appropriately stapled or bound. A portion of the project grade (20 points) will be based on the quality of the writing, including grammar and spelling; neatness counts as well. More details about project preparation will be supplied when the first project is distributed.The class will be divided into groups to prepare the projects. Students are expected to investigate each of their projects in groups, but to prepare their written reports individually. Any information received from other group members should be appropriately cited. Each group will present one of the projects orally, taking one class period. Group presentations are intended to be professional, as if you were presenting to a workplace supervisor. This means, in part, that you will use some form of graphical presentation software. Additionally, because presentations will be made by groups, full group participation during the creation and preparation of the presentation, including contributing and refining plots and figures, creating slides, and taking part in the presentation. Because of this, a portion of your presentation grade will be based on a brief post presentation group survey administered after the presentation.

Please note that these exams are not necessarily comprehensive, and thus there are topics which were not included on these exams which may be tested on your final exam.

Your own instructor will write and grade your midterm exams and will grade your final exam.

**FINAL EXAM:**The final exam will be a comprehensive, departmental examination. All sections of this course will take the same final exam at the same time:*Friday, December 11, 8:00-9:50 AM.*The exam will probably NOT be in your regular classroom. Room assignments are usually made one to two weeks before the final exam week. They will be announced in class later on.**TECHNOLOGY:**Students will be expected to use calculators and computers on a regular basis when preparing project reports and completing other assignments. One class meeting early in the semester will be held in a computer lab to introduce students to some software tools they can use (spreadsheets, mathematical word-processing, etc.)Here is information about the TeX mathematical typesetting system. Students whose career aspirations include anything mathematical (research, teaching, or applications) are encouraged to learn to use TeX, and during Math 360 is a great time to try it.

**TEXT:***"A First Course in Mathematical Modeling"*, Giordano, Fox and Horton, 5th ed., publ. Cengage LearningSome additional references:

**STUDENT HANDOUTS:**Please note that any information provided by*your*instructor supersedes these data.- Sample Project: Locating a Railway Supply Depot
- Example Computations for Discrete Systems Note that this is a computable document, so a) you will need a Plugin for your browser/app on your computer and b) the sliders on three of the figures work: they allow you to change initial conditions/rate parameters to explore the outcomes.
- Computer Orientation Material

**PROJECT HANDOUTS:**Project problems will appear here.- Understanding Mathematics: a study guide, from the University of Utah

**ACADEMIC CONDUCT:**Academic honesty and mutual respect (student with student and instructor with student) are expected in this course. Mutual respect means being on time for class and not leaving early, being prepared to give full attention to class work, not reading newspapers or other material in class, not talking to other students, not using cell phones during class time, and not looking at another student's work during exams. Academic misconduct, as defined by the Student Judicial Code, will not be treated lightly.**DRC STATEMENT:**If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let your instructor know early in the semester so that your learning needs may be appropriately met. You will need to provide documentation of your disability to the DRC Office located in the Health Services Building, 4th floor.**ADVICE:**In Math 360 you will frequently make use of SHORT topics introduced in other courses (Math 240, Math 336, Stat 350, Phys 250, ...). You are NOT expected to know this material in advance; you ARE expected to work with your instructor and your classmates to learn that material. This is deliberate --- we want you to see in advance why the ideas presented in your future courses will be useful and interesting.You may very frequently find that the projects or the classroom discussions assume familiarity with something that you know little about --- scientific phenomena, investments, sociological patterns, etc. Don't be discouraged! Ask questions, and take the opportunity outside of class to do a little outside reading. This is a very common situation when mathematicians are working on applications. Ignorance is not a crime --- only the refusal to do something about it is criminal.

If you have difficulty with the

*writing*of project reports (as opposed to the*mathematical understanding*of them), you should take advantage of the University Writing Center.Since you will work hard on your projects you should keep clean copies of the best versions of your favorites; these projects can make a very good impression on employers who may not understand what you can offer them as a result of taking advanced mathematics courses.

Students who enjoy working on projects like these should consider participating in the Mathematical Competition in Modeling, an international contest for undergraduates held every February. NIU has had several teams do well in this competition and we hope to field one or more teams again this year. Ask your instructor for more information about this opportunity.

Last update: August 21, 2015