Mt/CS 410 Mathematical Modeling - Fall 2002

Department of Mathematics & Computer Science
CARDINAL STRITCH UNIVERSITY
Sr. Barbara E. Reynolds, Ph.D.


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Course Description

(as found in the Cardinal Stritch University Catalog for Undergraduate Studies 2000 - 2002)

Mathematical modeling is a mathematical tool for solving real world problems. In this course, students study a problem-solving process. They learn how to identify a problem, construct or select appropriate models, figure out what data needs to be collected, test the validity of a model, calculate solutions and implement the model. Emphasis lies on model construction in order to promote student creativity and demonstrate the link between theoretical mathematics and real world applications.

Mt/CS 410: Mathematical Modeling Weekly Course Assignments.


Table of Contents:

[ Course Description | Texts and Required Materials | Course Objectives (indicating methods of assessment) | Calculators and Computers | Course Content | Prerequisites | Cooperative Learning Groups | Writing and Speaking across the Curriculum | Requirements (including grading criteria) | Administrative Policies | Office Hours ]

Texts and Required Materials

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Course Objectives

Mathematical Modeling is an area of applied mathematics that uses mathematical tools for exploring and studying "real world" problems. The overall objective of this course is to provide an introduction to the process of mathematical modeling while giving students an opportunity to Through work on assigned projects, students increase their fluency in technical reading and writing, and develop skills in mathematical problem solving. Students learn to

Beyond the content of individual courses, the major in mathematics is designed to prepare students for the 21st century by helping students to become problem solvers, effective communicators, users of appropriate technology, and team players. In this course, students will be engaged in a variety of activities which will help them to move toward achieving these goals.

  • As problems solvers, students will be learning to:

  • As effective communicators, students will be learning to:

  • As users of appropriate technology, students will be learning to:

  • As team players, students will be learning to:

    In this course, projects give students an opportunity to apply the principles of mathematical modeling creatively in various problem scenarios. While each project is related to the mathematical strategies that covered in class activities and lecture, students are expected to do some reading beyond the textbook and some library research to gain a solid background understanding of the problem scenario. Students are be expected to use appropriate technology as they study the problem, and to include the results of their investigations in a written report.

    In-class tests give students an opportunity to demonstrate mastery of the various mathematical strategies and calculational techniques that are studied in this course. Students are expected to bring a scientific calculator to use during a test.

    Each year in early February, there is an international Mathematical Modeling Contest. A secondary objective of this course is to assist students in developing skills to participate in this contest. The skills needed to participate in the math modeling contest -- working cooperatively in a group, developing and carrying out a problem-solving plan, using whatever resources are available, collecting appropriate data -- are essential in today's competitive job market.

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    Calculators and Computers

    Calculators and computers are legitimate tools for doing mathematics. One of the goals of the Department of Mathematics & Computer Science is that our students develop a facility with various forms of technology and learn to use these effectively to explore and solve problems. Throughout the semester, students will be given opportunities to use electronic communication tools (such as email and a graphical web browser). Students will be encouraged to use a spreadsheet, statistical software, an electronic scratchpad, graphing tools, and other software when it is appropriate for the problems which are being studied. Students who have access to a graphing calculator will find it helpful throughout the semester.

    Each student will need to have access to computers and/or to work in the computer lab on some of the homework assignments and projects. Computer lab schedules are posted on the doors of the computer lab. Although other classes also meet regularly or occasionally in the labs, there is one lab which is always reserved for student use. You will need to plan to hold some of your outside-of-class group meetings in the computer labs.

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    Course Content

    We will begin by looking at the modeling process -- a multi-step process for studying problem situations. All the mathematical techniques you have studied in previous courses -- algebra, trigonometry, calculus, statistics -- are tools to help in solving the model once you have formulated it mathematically. We will use the technique of proportionality which is useful in situations where we can assume that there is an underlying geometric similarity. We will study a variety of techniques -- both graphical and analytic -- for fitting a curve to a set of data points; we will explore linear, exponential, logarithmic, and polynomial models. We will develop and examine criteria for determining which of several possible models "best fits" the data. Finally, we will set up a simulation model to study a complex situation experimentally.

    See the Weekly Course Assignments for an outline of the sequence of topics and content to be covered in this course.

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    Prerequisites

    To be successful in this course, the student should have completed at least two semesters of calculus. The student is expected to have real fluency with college-level algebra, and a working knowledge of basic trigonometry; students are expected to understand and be able to evaluate first- and second-derivatives, and simple integrals. The first benchmark test will cover these prerequisite skills. Please see the instructor if you have any question about your preparation for this course.

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    Cooperative Learning Groups

    Students will do much of the work of this course in cooperative learning groups. These groups will work together on in-class problems, on some homework problems, and as a team on several projects.

    The objective of group work in this course is primarily to engage the students in thinking more deeply about important mathematical issues. Even though a lot of the work of the course is done in small groups, students are expected to learn to solve problems on their own. Working with colleagues in this class and talking about problems in small groups are strategies for developing an understanding of a problem situations from several points of view. Learning theory research has shown that cooperative learning leads to deeper understanding and longer retention of material that is studied.

    Working well in a group is an important skill. Some students enjoy the group work more than others, and all will benefit from further developing this skill. Most of our graduates are employed in workplace settings where they are expected to function as a member of a project team. Many of our graduates tell us that the skill they developed by working in cooperative learning groups is very beneficial in the workplace.

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    Writing and Speaking across the Curriculum

    The faculty of Cardinal Stritch University are committed to developing writing and speaking skills for all students across all disciplines. Students will have opportunities in every class session to speak with peers informally in small-group and full-class discussions. Students will also have some opportunities to give short presentations to their colleagues on some topic that each one has been investigating. Any written work that is turned in -- graded or ungraded homework assignments, tests, papers, and projects -- is to be written in standard English using complete sentences. Throughout the semester, students will receive feedback from the instructor (and from their peers) which is intended to assist in developing good speaking and writing skills.

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    Requirements

    Regular attendance, participation, lab activities, quizzes: 10%

    Regular attendance is expected. Some material will be presented in class from a different perspective than that give in the text. Getting someone's notes is a poor substitute for being present and involved in class discussion. However, if you must miss a class, it is your responsibility to find out what you missed.

    Problem solving is not a spectator sport. During most class periods there will be time for large and/or small group discussions about selected problems. It is important to learn to ask helpful questions and to listen constructively to each other. Constructive participation sometimes means allowing others time and space to think about the problem.

    Homework assignments will include reading the text, checking the library and other sources for information beyond that given in the text, and doing problems from each chapter. If the discussion is lively, with everyone contributing, I will collect and grade fewer problems and have fewer quizzes; if the discussion lags or is dominated by a few individuals, I may find it necessary to collect homework and/or give (unannounced) quizzes.

    At the end of each class period, I will ask you to fill out a Class Participation / Self-Evaluation form. I will use these forms to check attendance, respond to your self evaluation, and give you a score for class participation. If you must miss a class for any reason (excused or unexcused absence), your participation score for that day will be recorded as 0. However, if you wish to make up for these absences, you may turn in written evidence that you have done some work to make up missed lab/class activities. This make up work must be turned in within two class periods of the missed classes.

    Projects: 40%

    This course will be organized around projects. Eight projects will be assigned throughout the semester. These projects are equivalent to short/medium-length papers, and will often require research (both deep thought about the problem, and library work or reading that goes beyond a superficial reading of the text). Some of the projects are to be done individually, others will require work with your group outside of scheduled class times. In general, projects (after the first two) will be due about two weeks after they are assigned.

    The
    project report format is similar to the format required by the international Mathematical Modeling Contest, held annually in February. The project grading criteria are designed to give students constructive feedback help each student learn to communicate effectively in writing.

    See the class assignment page for the schedule of projects with their due dates. The first two project assignments are now available.

    Tests: 25%
    There will be two tests; the first will contribute 10%, the second 15% to your final course grade. Tests are tentatively scheduled for the following dates:

    The posted test outlines will be up-dated about one week before the scheduled test date to reflect more accurately the material that will be included on the test.

    Ordinarily, I do not give make-up tests; exceptions to this policy will be considered on a case-by-case basis.

    Benchmark Tests: 10%
    Benchmark testing is the department's way of assuring that students have achieved minimum levels of calculational competency. Although students are encouraged to use computers and calculators throughout this course, they are expected to be able to do basic computations by hand. These basic computations are covered in the benchmark tests.

    There will be two benchmark tests in this course. These are offered outside of regular class meetings. Each student should make an appointment with the instructor to take the benchmark test during the scheduled window-of-opportunity.

    • Benchmark 1: available September 3; completed by September 13

      This benchmark will cover concepts and skills which are prerequisite for this course.

    • Benchmark 2: available December 2; completed by December 9

    This benchmark will cover computational strategies that are emphasized throughout the course.

    Procedures for Benchmark Tests:

    • To pass the benchmark test, a student must get nine or ten of ten problems completely correct; there will be no partial credits. If a student passes on the first attempt, the score will be recorded as 100%.

    • If a student does not pass the benchmark test on the first attempt, he/she may demonstrate that that he/she has done some additional practice, and make an appointment with the instructor to try the test up to two more times.

    • If a student passes a benchmark test on the first or second re-test, the score will be recorded as the average of the scores made on each attempt.

    • If a student has not passed a benchmark after two re-tests or by the specified date, the score will be recorded as 0%.

    The Study Guide for Benchmark Test #1 is now available.

    Note: Each student's midterm grade will be based on four or five projects, one test, one benchmark, and half the semester of participation. This represents 40 to 45% of the final course grade. Midterm is October 17, and the last day to withdraw from fall semester courses is November 8. If you have concerns about your progress or ability to keep up with course assignments, please feel free to discuss these with the instructor.

    Final Exam 15%

    The cumulative final exam is scheduled for Thursday, December 12 at 8:00 a.m.

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    Administrative Policies

    Academic Integrity Policy

    Inherent in the mission of Cardinal Stritch College is the strong belief in the principle of academic integrity. Students who cheat violate their own integrity and the integrity of the College by claiming credit for work they have not done and knowledge they do not possess. All students are expected to recognize and to abide by the policy on academic integrity found in the Student Handbook. Because you will be asked to do a lot of work in collaboration with your colleagues (i.e., classmates), whenever I give you a take-home assignment or test on which I expect you to work on your own, I will make this very explicit.

    Compliance with the Rehabilitation Act of 1973 (Rehabilitation Act 504)

    If you have any special needs for alternative instruction and/or evaluation procedures, please feel free to discuss these needs with me so that appropriate arrangements can be made.

    Cell Phones and Pagers

    As a matter of courtesy, students are expected to turn off cell phones and pagers during class. If extraordinary circumstances require an exception to this policy, the student is expected to discuss this with the instructor before class begins.

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    Office Hours

    My office is located in CH 34, just across the hall from the classroom where this course meets. I will be on-campus and regularly available for students most weekdays. If you wish to make an appointment with me, you may sign up on the sheets which are posted on the in the hallway just outside the door of my office. The best way to contact me is via email, which I check regularly (several times a day) both while I am on campus and from home.

    If you need to reach me between classes:

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    Return to Sr. Barbara E. Reynolds Home Page.
    Return to course list for 2002 -- 2003.
    Go to Mt/CS 410: Mathematical Modeling Syllabus.
    Return to Mt/CS 410: Mathematical Modeling Assignments.

    The easiest way to contact me is to send an email message to Sr. Barbara E. Reynolds.
    This page was updated on August 23, 2002.