Modeling Our World/Functions Modeling Change

From this page, students may get class "news" updates, various handouts in Microsoft Word 97 format, assignments, and news.

News:

See the syllabus for required texts, etc.

The final synthesis assignment has been released to the wild, and is due on December 18.

Software and Links:

Graphmatica graphing software (Windows)

Curvus Pro graphing software (Mac)

Least Squares Regression Calculator

Animation: Finding the least squares line by really minimizing squares

Non-linear least squares curve fitter (we'll use for polynomial and exponential curve fitting)

Ruben Puentedura's paper on the Prisoner's Dilemma

Handouts:

Course syllabus

Guide to turning in assignments

In-Class Activities:

The Rolling Ball

Cricket Chirp Rates

Cricket Chirp Rates data (in Excel 97 format)

Corvette Speeds

Corvette Speeds data (in Excel 97 format)

Build a box for Bob

Accident rates on Saturdays

Accident rate data (in Excel 97 format)

Paper folding activity

Shroud of Turin activity

Dueling Bank Accounts activity

Ernie and Bert's Eats activity, part I

Ernie and Bert's Eats activity, part II

Prisoner's dilemma activity

Substitution cipher activity

Vigenere cipher activity

Children's puzzle and other Eulers activity

Fleury's algorithm activity (minus the graphs)

Assignments:

Assignments will be handed out weekly. Remember that literary form is important; your goal is not just to solve the problem, but communicate its solution.

Don't forget: I will only be marking some of the questions you turn in. A senior student will mark the rest. I will provide a solution sheet.

Read the assignment tip sheet first!


Assignment 1 (due Thursday, Sept. 26): For some of you this assignment will be easy; for others you will be bewildered to know how to start almost every question. If you're having trouble at first, don't be disheartened. The solution is to find help. TALK about each question with someone who knows (me, the tutors, a mathematically experienced classmate). Don't let that person off the hook until you REALLY UNDERSTAND the conceptual thread through the question!

Remember, the purpose of the assignment is to continue the journey, NOT to judge your value as a human being. The journey may seem quite steep at first, but you'll reach a plateau before long!

 OK, enough with the metaphors...

The rolling ball activity
The cricket chirp rate activity
Section 3.1 # 3, 7, 11(a)-(c), 5
Section 3.2 # 4, 8(a)-(b), 14

For 3.2 # 14, no American data is provided. First do part (b) using the English data, then answer part (a).

Assignment 2 (revised due date Monday, October 7):

The Corvette speeds activity
Build a box for Bob activity
Accident rate on Saturdays activity

Web problem: Selling a college education
(a) At Bennington College, an annual tuition rate of $28,000 attracts 200 freshman students annually. Let x represent the tuition rate, between $0 and $50,000. Draw a graph of y, the number of freshman students attracted, as a function of x. (You don't have an equation; just speculate!)
(b) On your graph, draw a tangent line at the point corresponding to $28,000 tuition. Get an equation for your tangent line and use it to predict the size of the freshman class if we raised tuition to $30,000.
(c) If tuition was raised to $30,000, would the school take in more revenue?

Sec. 3.5 #1(c) (skip the question that refers to (b).) Which of these five graphs seems to you to be the best model, and why?

Sec. 3.5 #17(a), (d); repeat (d) for the Bachelors degree data

Sec. 3.5 #18(a), (d)

Assignment 3 (due Monday, October 14):

The paper folding activity
The Shroud of Turin activity
The dueling bank accounts activity

Web problem: Musical scales and the Pythagorean problem
Remember our experiment with the monochord, which produced an octave (from middle C to high C) when the length of the string was cut in half, from 60 cm to 30 cm.
(a) Construct an exponential function for the length of the string, y, as a fucntion of the number of octaves, x. (We may have done this in class.)
(b) The next two most common chords are the fifth, which goes from middle C up to G; and the fourth, which goes from G up to high C. The ratio of string lengths for the fifth is 3/2. From this information, tell me: (i) the length of the string needed to produce a middle G note; and (ii) the ratio of string lengths for the fourth.
(c) When musical scales were being standardized in the 16th century, the octave ratio was chosen as the standard. There are twelve "semitone" intervals from low C to high C. What, then, is the appropriate ratio for the semitone?
(d) There are seven semitone intervals from middle C up to G. Using your answer to (c), what is the appropriate string length for middle G? How does this compare with what you got in (b)?

Section 4.1 #8a-e, 10a-d, 14a-c.

Assignment 4 (midterm synthesis, due Wednesday, October 23):

Don't forget to do this assignment on your own!

Olympic record 100m race times (Microsoft Excel format)

Assignment 5 (Game Theory): distributed in class, due Tuesday, November 12

Assignment 6 (Cryptography): distributed in class, due Tuesday, November 26

Assignment 7 (Graph Theory): distributed in class, due Tuesday, December 10


Last modified: December 9, 2002 / Glen Van Brummelen

Office: Dickinson 213. Phone numbers: (w) 440-4467; (h) 440-8142.