MATH 115 Introduction to Mathematical Modeling
Spring 2004 Assignments

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Assignment #1 - Due on Monday, February 2

Turn in a written response to item (3) below.
1)  Get your computer account activated.  (You should change your initial password.)  Access your Groupwise e-mail account and send an e-mail message to your instructor.  If you have another e-mail account that you prefer to use, go through the steps to have your SU Groupwise e-mail forwarded to that preferred account.
2)  Log in on the campus computer system and do the following:
a. Use Netscape or Internet Explorer to access your instructor's web page. Find the home page for this course.
b. Follow the appropriate links and read the letter "To the Student," "Tentative Course Syllabus," and the "Instructors' Policies."  You will note that some topics, guidelines, and policies have changed and are no longer exactly what you find written in the "Cathcart and Horseman" text "[C&H]."
(3) Write up an analysis of the situation explored in class on Wednesday, January 28.  Include appropriate discussion and express the relevant relationship using (a) a table, (b) a formula, (c) a graph, and (d) a complete English sentence.
Look a a sample student's write-up for this exercise.
4) You will find a scientific calculator very useful.  If you do not have one, you can obtain one good enough for our purposes for about $10.
5)  Read pp. v-viii in the "Preface" to the "Kalman" text "[K]."
6)  Read, and work through, Chapter 1," pp. 1-8 in [K].
7)  For your own benefit, work the following exercises on pp. 8-9 in [K]:
       Reading Comprehension: 1-5 all
       Problems in Context:  1-3 all

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Assignment #2 - Due on Monday, Feburary 9

1.  Visit the www site:  http://www.towson.edu/csme/mctp/Courses/Mathematics/UnitIIIA.html

When you get to that site, do a complete a write-up for exercise 1 in Section 3.1  Patterns of Change. When you arrive at that site, you will be looking at "Unit III: Things Change" in a set of materials developed by Dr. Jim Fey for a modeling course at UMCP.  After completing exercise #1, look under "Conclusions and Connections" and work, just for your own benefit, exercises 1-6 all, but don't submit write-ups for these exercises.

2.   Work through Section 3.2 Linear Models of Dr. Jim Fey's "Unit III: Things Change."  For your own benefit, try to work  the exercises. (You may use a spreadsheet rather than a calculator.) Write up and turn in only exercises 1 and 7.  Exercise 1 relates to leasing a car, and Exercise 7 describes a maket survey of prospective bunge jumpers.

Assignment #3 - Due on Monday, February 16

Write up and submit solutions only for the items in parentheses and italics.

1.  Read and work through Chapter 2 (pp. 11-28) of the blue "Kalman" text "[K]."
2.  Work the following exercises on pp. 28-31 in the "Kalman" text "[K]."
     a.  Reading Comprehension:  4, 5, 6
     b.  Mathematical Skills:  1, 4, 5
3.  Revisit the web site http://www.towson.edu/csme/mctp/Courses/Mathematics/UnitIIIA.html
     Do a complete write-up for exercises 8 and 10 in Section 3.2 Linear Models of Dr. Jim Fey's
     "Unit III: Things Change."  Exercise 8 involves a possible relationship between unemployment
     and crime, and exercises 10 asks for a comparison of two modeling lines.

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Assignment #4 - Due on Monday, Feburary 23

Write up and submit solutions only for the items in parentheses and italics.

1.  Read and work through Chapter 3 (pp. 37-47) of the blue "Kalman" text. [K].
2.  Work the following exercises on pp. 47-50 of the blue text by Kalman.
     a.  Reading Comprehension:  3
     b.  Mathematical Skills:  (1b), (1d), (2b), (2d), (3b), (4b), (7b)
     c.  Problems in Context:  Carefully write up (3) following the steps  on pp. 43-44.  Use a spreadsheet
          to facilitate the creation of an attractive table and graph.  Put an appropriate title on your graph
          and appropriately label your axes.

Assignment #5 - Due on Monday, March 1

Write up and submit solutions only for the items in parentheses or italics.

1.  Read and work through Chapter 4 (pp.  55-72) of the blue "Kalman" text [K].
2.  Work the following exercises on pp. 72-76 of [K].
      a.  Reading Comprehension:  2, 3, 9, 10
      b.  Mathematical Skills:  1, 3
      c.  Problems in Context:  4
      d.  Write up the Group Activity (pp. 75-76).  Start early on this activity and work with another person
           if feasible.  Work through the steps 1-7 on page 76 and respond in writing to each question.  Your
           paper will be evaluated on its neatness, accuracy, completeness, and style.  Rather than using the
           reference desk at the Library, you may use the internet.  In either case, provide the source of your data.

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Assignment #6 - Due on Monday, March 8

Write up and submit solutions only for the items in parentheses.
1.  Read and work through Chapter 5 (pp. 79-108) of the blue "Kalman" text [K].
2.  Work the following exercises on pp. 108-111 of [K].
     a.  Reading Comprehension:  1, 3, 4, 5, 9
     b.  Mathematical Skills:  1, (2), (3), (6), (8), (10), (13)
     c.  Problems in Context:  (5)  Compare Kalman's predictions with yours.

Assignment #7 - Due on Wednesday, March 17

Write up and submit a solution for the following problem:
Problem #6 on pp. 142-144 of Kalman.

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Assignment #8 - Due on Wednesday, April 21

Write up and submit solutions for the following exercises.
Show your very best work
(1)  Exercise #13 on pp. 75-76 of the yellow modeling text.
(2) Exercise #16 on pp. 78-79 of the yellow modeling text.

Assignment #9 - Due on Wednesday, May 5

Write up the following revised version of Exercise 17 on page 80 of the yellow modeling text.

Revised Exercise 17 on page 80 of the yellow [C & H] text.

Use the data below rather than the graph in Figure 1 on p. 80.

U.S. National Censuses Figures 1790-1900

              Years                 Resident
Year     Since 1790         Population
                                      (in thousands)
1790         0                         3929
1800         10                       5308
1810         20                       7240
1820         30                       9638
1830         40                     12866
1840         50                     17069
1850         60                     23192
1860         70                     31443
1870         80                     39818
1880         90                     50156
1890         100                   62948
1900         110                   75995

a.   Construct a graph representing the data in the table.  Place appropriate titles and labels on the graph.

b.   Construct a table similar to the one in Exercise 8 on p. 71 and consider each decade’s average annual rate of change and each decade’s percent change.

c. Develop both a linear model and an exponential model approximately relating the U.S. resident population, P(t), to the number of years since 1790 over the 110-year period.  Comment on how well each of the two models fit the data.

d. Use your models to estimate the size of the U.S. resident population in 1910, 1940, and 2000.  Look up the official census figures for those years to determine the accuracy of the estimates derived from your models.  Comment on factors affecting the accuracy of your estimates.



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