MATH 155 (Spring 2014)

Instructor's contact information

Michael Robinson
226 Gray Hall
michaelr at american {dot} edu
Office hours:
My research website
Feel free to contact me with any and all questions (course-related or not)

Quick Links

Course description
Homework assignments
Course schedule
Information about exams
Some useful links
Course policies

Course description

Study of mathematical subjects including linear, quadratic, polynomial, rational, exponential, and logarithmic functions, in the context of difference equations models. Emphasizes concepts and applications using numerical, graphical, and theoretical methods. Also includes an introduction to the mathematical subject of chaos. Usually offered every term. Prerequisite: three years of high school mathematics or equivalent. Note: No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.
The course textbook is Elementary Mathematical Models by Dan Kalman (edition not critical)
The overall objectives of this course are to
  1. Postulate mathematical models using numerical tables, graphs, and recursive equations
  2. Understand the solutions to recursive equations through numerical and graphical representations
  3. Interpret the solutions produced by mathematical models in terms of real-world problems


You must staple your assignments before submission; points will be deducted otherwise! Homeworks are due on the dates listed, to be turned in at the beginning of lecture. If you think that you need more practice, just ask! I'll be happy to give you more problems to work, and will also be happy to answer questions about them.

Homework 1: due January 16 (Math autobiography)
Homework 2: due January 23 (Chapters 1 and 2)
Homework 3: due January 30 (Chapter 3)
Homework 4: due February 6 (Chapter 4)
Homework 5: due February 20 (Chapter 5)
Homework 6: due February 27 (Chapter 6)
Homework 7: due March 6 (Chapter 9)
Homework 8: due March 20 (Chapter 10)
Homework 9: due April 3 (Chapter 12)
Homework 10: due April 10 (Chapter 13)
Homework 11: due April 17 (Chapter 14)
Additional Homework 1: due before the first exam: come visit me during my office hours!
Additional Homework 2: due before the second exam: come visit me during my office hours!

Course schedule

The planned course schedule is below; we will not deviate more than a day in terms of the sections covered. The exams, however, will occur on the days listed below.

Unit 1: Difference equations

After this unit, you should be able to
  1. Describe linear behaviors through numerical, graphical, and difference equation models
  2. Explain the solution of linear difference equations using numerical experiments
  3. Describe the qualitative structure of the graphs of these solutions
  4. Manipulate the algebraic structure of these solutions
  5. Interpret these solutions through the context of word problems
January 14: Chapter 1
January 16: Chapter 2
January 21: Chapter 3
January 23: Chapter 3
January 28: Chapter 4
January 30: Chapter 4
February 4: Review for Exam 1
February 6: Exam 1

Unit 2: Nonlinear equations

After this unit, you should be able to
  1. Detect when linear models are insufficient to represent data in a tabular or graphical format
  2. Construct quadratic models and geometric growth models according to data
  3. Describe the solutions to these models and their implications
  4. Manipulate the algebraic representations needed to represent these solutions, especially using sigma notation
February 11: Chapter 5
February 13: Chapter 5
February 18: Chapter 6 (Bring a graphing calculator, if you have one!)
February 20: Chapter 6 (Bring a graphing calculator, if you have one!)
February 25: Chapter 9
February 27: Chapter 9
March 4: Chapter 10
March 6: Chapter 10
March 18: Review for Exam 2
March 20: Exam 2

Unit 3: Geometric and logistic growth

After this unit, you should be able to
  1. Develop simple models of mixtures and population growth with limited resources
  2. Describe and manipulate the solutions that arise from these models
  3. Identify bifurcations that arise from harvesting and organize them into a bifurcation diagram
  4. Explain the mathematical idea of chaos
March 25: Chapter 12
March 27: Chapter 12
April 1: Chapter 13
April 3: Chapter 13
April 8: Chapter 14
April 10: Chapter 14
April 15: Review for Exam 3
April 17: Exam 3

April 22: Make up exam day
April 24: Final exam review

Final exam: May 6, 5:30-8:00pm

Course policies

A typical course meeting

On most non-exam days, there is a usual cadence to the classes, which goes something like this...
  1. At the beginning, I will take attendence
  2. I will either give you a quick quiz or select students to present specific problems (which I choose) from the homework that pertain to the section covered in the previous class. (Come prepared to at least attempt all the problems!) If you have trouble articulating your solution (or you get stuck), that's OK! The rest of the class and I will help you!
  3. We'll work though an in-class activity, which is usually a worksheet. You'll work on portions alone or in pairs. I'll incorporate new material as we go!
  4. We'll finish up with a quick summary that I'll present.


You are expected to attend all the class meetings. I will take attendence, usually as roll call at the beginning of class. There may be unexpected quizzes, and you may not take these at a different time! Please contact me in advance if you cannot attend (this includes both religious observances as well as sporting obligations), especially in the case of an exam. Missing an exam without appropriate (prior in all but a few situations) authorization is cause for a zero on that exam!

Late homeworks are not accepted without a University-approved excuse. You have the schedule in front of you now; turn assignments in early if you plan to be absent.



The course grade will be determined from the following components. You'll accumulate points for each of these over the course of the semester.
20% Homework
20% Exam 1
20% Exam 2
20% Exam 3
20% Final exam

  1. I will automatically drop your lowest homework score
  2. You will have the opportunity to retake an exam of your choosing (it will have slightly different problems) on the make-up exam day. The highest score you can get on the make-up exam is 90%. You get to keep the higher of the make-up exam score and your original exam score. If you miss an exam due to a University-approved reason, please see me as soon as possible.

Here's how to associate letter grade equivalents to the percentage of points you've gotten (weighted as above):
A = 93 or above
A- = 88 to 92.9
B+ = 85 to 87.9
B = 82 to 84.9
B- = 78 to 81.9
C+ = 75 to 77.9
C = 72 to 74.9
C- = 68 to 71.9
D = 60 to 67.9
F = below 60

Academic dishonesty

Academic dishonesty is a serious offense. Read our University policies. As applied to this course, you may work together on homeworks, but the work you turn in must be your own. I'm happy to answer any questions you have about these policies.