Syllabus Math 155 Spring 2016

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Elementary Mathematical Models (Math 155)

Materials: [New Lectures for Spring 2016][Problems/Homework/Exercises][Links and Other Materials]

Instructor: Sean Carver, Ph.D., Professorial Lecturer, American University.


  • 107 Gray Hall
  • office phone: 202-885-6629

Learning Outcomes: [Credit Prof. Mitchell, 2013]: (May be adjusted within the first few weeks of semester):

My goal is that the students will (1) develop a general understanding of how mathematical models are developed and used, (2) learn specific methods for one modeling methodology (difference equations), (3) experience the progression from simpler to more complex models, (4) observe how traditional mathematical operations and functions arise out of the models we study, (5) learn the organizational strategy of grouping functions into families defined in terms of parameters, and (6) learn the core concepts of chaos as a significant limitation on the discrete mathematical modeling methodology.

What I expect that students will take away from the course of most value to them is greater confidence vis-a-vis mathematics.

Confidence with Mathematics: Increased confidence in mathematics will help you in other areas, no matter what you choose to do. Developing confidence requires challenging yourself, and working hard to meet your challenges. I will help you do that.

Text: "Elementary Mathematical Models: Order Aplenty and a Glimpse of Chaos," by Dan Kalman, The Mathematical Association of America, 1997.

Office Hours: Students are strongly encouraged to come to office hours if they need or want help.

My office is Gray Hall, Room 107. Office hours are TENTATIVELY scheduled as follows: (may be adjusted throughout the semester)

  • Monday, Wednesday, Thursday: 4:30 PM TO 6:30 PM.

NOTE: If you would like to come to office hours on a regular or irregular basis and you have a compelling reason why you cannot make it during the hours listed above, please send me an email. I cannot guarantee that I can find a time that works, but I will try.

Tutoring through AU's Academic Support and Access Center. By appointment. See

Tutoring through MATH/STAT tutoring center: Gray Hall, Room 110, Hours:

  • Walk-ins welcome
  • The tutoring center has not posted its hours for the Spring semester.

Tutoring Lab Hours during Fall Semester:

  • Monday - Thursday: 11:00 AM - 8:00 PM
  • Friday: 11:00 AM - 3:00 PM
  • Sunday: 3:00 PM - 8:00 PM
  • Saturday: Closed

Class times and locations:

  • Monday & Thursday: 11:45 AM - 1:00 PM, MARY GRAYDON CENTER, Room 331

Important Dates:

  • January 11 (Monday): First day of class
  • January 18 (Monday): Martin Luther King Day, no class
  • February 4 (Thursday): Midterm Exam 1 (tentative date pending availability of computer lab for another class)
  • March 7 & 10 (Monday, Thursday) Spring Break, no class.
  • March 31 (Thursday): Midterm Exam 2 (tentative date pending availability of computer lab for another class)
  • May 2 (Monday): Final Exam (11:45AM - 2:15PM, in our classroom MGC 331)

Tentative grading scheme:

Homework 15%
Exam 1 25%
Exam 2 25%
Final 25%
Attendance and Participation 10%

Class Etiquette: Please give the class your full attention and refrain from talking during lectures, texting, surfing the web, and similar distractions. Please participate in class by asking questions when you do not understand something. Invariably other students benefit from these questions.

Academic Integrity: Cheating is not acceptable and will not be tolerated. Consider this: in subtle ways, cheating to get a better grade on an exam can result in lowering the grades of some of your classmates. Certainly this is true when a specific curve is used to assign grades. Even when I don't use curves explicitly, they can be implicit in decisions about writing and grading exams. As required by the policy of American University, I will report all suspected cases of cheating to the Dean's office who will proceed to investigate and adjudicate the issues. Cheating is giving or receiving unauthorized assistance on exams, from other students or other people, from notes, from books, or from the web. When inappropriate copying between students is caught, both parties may be culpable.

Homework, Attendance and Participation Policy: Usually I award a maximum of 10 points for each homework set, due one week after it is assigned. Additionally I award 5 points per day for class attendance. I sometimes give the solutions to homework problems at the same time I assign the problems. Conscientious students, who wrestle with problems before looking at the answers, benefit from having instant feedback about their solutions, right, wrong, or incomplete. Less conscientious students who use the answers to easily complete the assignments often do poorly on exams. The responsibility for your education rests in your own hands. Don't be one of the outliers who use shortcuts to avoid preparing for the exams. Concerning homework, you are encouraged to work with your classmates, if you find that helpful. In fact, you are encouraged to do whatever you find most helpful with the homework, but by turning in a solution to a problem, you pledge that you understand the solution, or that you talked to me in office hours or during or after class and made a good faith effort to understand how to do the problem. If it looks like you got the full benefit from the assignment, I will award you a perfect 10 points. I may mark you down if it seems that you have copied the answers without including any of the required calculations. You must include your work. One more thing about homework: you can turn in your homework by showing me your solutions during office hours or during active-learning periods of class, or after class. If you do this, please DO turn in a mostly blank page of paper with your name on it and the numbers of the homework set(s) you have completed. After I check your work, I will put my initials on your mostly blank page, then keep the page for my records. Some students prefer to turn in their work this way because they prefer not to tear pages with work from their notebooks. Absences will be excused if you have a compelling reason why you can't make it to class. Please email me ahead of time if possible. Also, this semester, I may experiment with computer graded homework or other methods.

Public Service Announcement: A representative of AU's Students Against Sexual Violence (SASV) approached me and asked me to include on my syllabi a list of resources available for survivors of sexual assault and their friends. While sexual violence is by no means the only challenge faced by students, I agree that this issue merits particular attention, so I am honoring her request by attaching the list she gave me:

Sexual Assault Resources

  • It’s never the survivor’s fault. There are many people you can talk to if you or someone you care about has been sexually assaulted:
  • AU's Sexual Assault Prevention Coordinator Daniel Rappaport (
  • AU's Coordinator for Victim Advocacy Sara Yzaguirre (
  • DC SANE Program (Sexual Assault Nurse Examiner) 1-800-641-4028
  • The only hospital in DC area that gives Physical Evidence Recover Kits (rape kits) is Medstar Washington Hospital
  • DC Rape Crisis Center: 202-333-7273
  • Students found responsible for sexual misconduct can be sanctioned with penalties that include suspension or expulsion from American University, and they may be subject to criminal charges
  • If you want to submit a formal complaint against someone who has sexually assaulted you, harassed you, or discriminated against you based on your gender identity or sexual orientation, you can do so online at, or contact the Dean of Students at or 202-885-3300. These are Title IX violations, and universities are legally required to prohibit these actions.
  • Resources on campus that are required to keep what you tell them confidential are Daniel Rappaport, Sara Yzaguirre, ordained chaplains in Kay, and counselors at the counseling center. (OASIS may also belong here but it didn't exist when this list was created.)