226 Gray Hall

michaelr at american {dot} edu

Office hours:

- Tuesdays: 10am-noon,
- Wednesdays: 10am-noon, 1-2pm,
- Thursdays: 10am-noon, 4-5pm, or
- by appointment (please contact me 24 hours in advance to make arrangements)

Feel free to contact me with

Homework assignments

Course schedule

Information about exams

Some useful links

Course policies

The course textbook is

The overall objectives of this course are to

- Postulate mathematical models using numerical tables, graphs, and recursive equations
- Understand the solutions to recursive equations through numerical and graphical representations
- Interpret the solutions produced by mathematical models in terms of real-world problems

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!

- Describe linear behaviors through numerical, graphical, and difference equation models
- Explain the solution of linear difference equations using numerical experiments
- Describe the qualitative structure of the graphs of these solutions
- Manipulate the algebraic structure of these solutions
- Interpret these solutions through the context of word problems

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

- Detect when linear models are insufficient to represent data in a tabular or graphical format
- Construct quadratic models and geometric growth models according to data
- Describe the solutions to these models and their implications
- Manipulate the algebraic representations needed to represent these solutions, especially using sigma notation

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

- Develop simple models of mixtures and population growth with limited resources
- Describe and manipulate the solutions that arise from these models
- Identify bifurcations that arise from harvesting and organize them into a bifurcation diagram
- Explain the mathematical idea of chaos

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**

- At the beginning, I will take attendence
- 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!
- 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!
- We'll finish up with a quick summary that I'll present.

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.

- For each exam, you will be permitted to bring one double sided 3" x 5" card with handwritten notes on it.
- Scientific (non-graphing) calculators are permitted, but all models other than TI-30X IIB or TI-30X IIS require pre-approval by me before you may use them on an exam.
- Cell phones, graphing calculators, headphones, tablets, and other computers are not permitted.
- Missing an exam without appropriate (
**prior**in all but a few situations) authorization is cause for a zero on that exam!

20% Homework

20% Exam 1

20% Exam 2

20% Exam 3

20% Final exam

- I will automatically drop your lowest homework score
- 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